ECONPress of Northeastern University

ECONPress is a publication for undergraduate compositions in economics. We publish twice a year during each fall and spring semester. ECONPress invites the highest quality submissions from undergraduate students in various economics related disciplines. It provides a forum for the undergraduate economics community to engage in active discussion and debate about the topics, theories, and applications they’ve learned in the classroom. Editorial Board Alec Loudenback Editor-in-Chief , President

Robert Dent Director of Finance, Editor

Victor Martinelli Director of Content, Editor

Tala Borno Director of Logistics, Editor

Pooja Trivedi Director of Public Relations and Marketing, Editor

Michael Onore Director of Programming, Editor

Selection Committee Advisory Board Eric Johnston Dr. Peter J. Simon Anna Mandell Dr. Daniel Greenfield Jason Fertig Li Pan Special Thanks Yi Liu Xinyi Zhu Edward J. Meehan Sam Kasuli Marcel Landesmann Prof. Steven Morrison ECONPress of Northeastern University

Spring 2012 Volume II, Number II

Letter from the Editors...... 5 Voting with Bidirectional Elimination ...... 6 Matthew Stephen Cook An Econometric Inquiry into the Effect of Religious Profiles on National Wealth...... 23 Edited and published at Northeastern University Brian Joel Feldman Editorial Offices: Equity Volatility across Industries from IPO Day...... 35 ECONPress Andrew Nielsen Lewis 360 Huntington Avenue 301 Lake Hall Should Punitive Damages be Scaled to Wealth?...... 51 Boston, MA 02115-5000 Harrison A Seitz ISSN: International Collective Action on Climate Change....58 2158-8864 (Print) Evan Richards Sankey 2158-8872 (Online) Submissions Process and Guidelines...... 66 Electronic Mail: [email protected]

Web Site: www.ECONPress.org R -4- ECONPress Letter from the Editors -5-

Letter from the Editors

The greatest insights into our world are often not revolutionary, but evolutionary. Progress is not made in leaps and bounds but by small, determined steps. The authors that we present you in this edition of ECONPress have all taken well-founded topics, ap- proached them with new questions and set into motion a process of researching answers that have not been given before. We at ECONPress have not developed the research within, but instead provide an outlet for such work to be distributed and recognized. Non-published research is akin to a tree fall not heard. We seek to make the work heard. Submitting to ECONPress is perhaps the easiest part of the entire research process and the labor of “rethinking our world” the most difficult. Yet all of the authors who submit- ted to ECONPress should be commended in their confidence and determination because as undergraduates we have not traditionally had such a way to share our work before. Each submission requires a modest confidence that one’s work is quality research - quality that each one of us undergraduates possess. The authors and research here are distinguished for hard work, unique insights, economic understanding, and adept prose - qualities that all other undergraduates like you possess and that are waiting to be shared. Let the research presented within inspire and instigate a debate in your own mind. Put that question to the test and build upon the work of those that have come before us. R “Rethink your world” and share it with all of us. Such is a process to continue throughout your lifetime, and we at ECONPress hope to be but a small part. Thank you for reading,

Alec Loudenback Victor Martinelli Robert Dent Pooja Trivedi Michael Onore Tala Borno

The Editorial Board of ECONPress -6- ECONPress Voting with Bidirectional Elimination -7-

of Bidirectional Elimination was born. Jon “This scheme, [known as] instant-runoff mechanism. The purpose of this paper is Voting with Bidirectional also independently created his own proof of voting, doesn’t necessarily get you the to define important criteria, explain their Elimination Condorcet efficiency for the [3 candidates, M movie (or the candidate) with the most importance, and evaluate a new voting voters] case. Tyler Mullen showed me the first committed supporters, but it does get mechanism using these criteria. The mech- Matthew Stephen Cook set of conditions under which my algorithm you a winner that a majority can at anism I will analyze is called Bidirectional would not elect the Condorcet winner. This least countenance. It favors consensus. Elimination and is conducted in a manner Stanford University led me to design the specifications for the pro- Now here’s why it may also favor The similar to IRV. The criteria I will use are the gram Jaehyun coded. Thanks to the four of you Hurt Locker. A lot of people like Avatar, Condorcet criterion and strategy proofness. R for your support of this stimulating project. obviously, but a lot don’t—too cold, too I will primarily analyze the mechanism Abstract formulaic, too computerized, too de- based on the Condorcet criterion, using rivative. . . . Avatar is polarizing. So is mathematical proofs and experimental data Two important criteria for judging the James Cameron. He may have fattened from computer simulations. I will discuss quality of a voting algorithm are strategy- 1. Introduction the bank accounts of a sizable bloc of strategy proofness briefly, and recommend proofness and Condorcet efficiency. While, Academy members—some three thou- an experimental methodology one could according to the Gibbard-Satterthwaite For decades, the Academy of Motion sand people drew Avatar paychecks— use for a rigorous analysis. theorem, we can expect no voting mecha- Picture Arts and Sciences used a plurality but that doesn’t mean that they all long nism to be fully strategy proof, many Con- vote to determine Best Picture: Over five to recrown him king of the world. . . . The paper is organized as follows. Sec- dorcet methods are highly susceptible to thousand voters would submit a single vote These factors could push Avatar toward tion 2 reviews criteria, background, ter- compromising, burying, and bullet voting. among just a few nominees, and the movie the bottom of many a ranked-choice bal- minology, and theorems related to social In this paper I propose a new algorithm with the most votes would win. In 2010, lot. choice theory that are necessary for analyz- which I call “Bidirectional Elimination,” a the Academy replaced plurality voting with ing a voting mechanism. Section 3 dissects composite of Instant Runoff Voting and the a new system called Instant Runoff Voting On the other hand, few people who have Instant Runoff Voting, the Coombs Meth- Coombs Method, which offers the benefit (IRV). Instead of submitting a single choice, seen The Hurt Locker—a real Iraq War od, and Condorcet Methods. Section 4 of greater resistance to tactical voting while voters were asked to submit a preferential story, not a sci-fi allegory—actively dis- introduces Bidirectional Elimination, runs nearly always electing the Condorcet win- ranking of ten nominees. After all ballots like it, and many profoundly admire it. the algorithm step by step on a given set of ner when one exists. A sophisticated pro- were cast, the mechanism would systemati- Its underlying ethos is that war is hell, preferences, and analyzes based on certain gram was tailor-made and used to test IRV, cally eliminate candidates with the fewest but it does not demonize the soldiers it criteria presented in section 2. Section 5 the Coombs Method, and Bidirectional first-place votes until one winner remained. portrays, whose job is to defuse bombs, offers logic proofs related to Condorcet ef- Elimination on tens of billions of social not drop them. Even Republicans (and ficiency. Section 6 presents and analyzes ex- preference profiles in combinations of up to IRV offered several advantages over a there are a few in Hollywood) think it’s perimental results from a computer simula- ten voters and ten candidates. I offer math- simple plurality vote. The plurality mecha- good. It will likely be the second or third tion. Section 7 offers concluding remarks. ematical proofs showing the new algorithm nism could have easily elected candidates preference of voters whose first choice is meets the Condorcet criterion for up to 4 many voters strongly disliked, and it also one of the other ‘small’ films that have Results from the computer simulation voters and N candidates, or M voters and allowed for the spoiler effect—the negative been nominated.” show that Bidirectional Elimination comes up to 3 candidates; beyond this, program effect a weaker candidate has over a stron- very close to meeting Condorcet efficiency. results show Bidirectional Elimination of- ger candidate by stealing away votes. To As a process, voting requires design. Given the susceptibility of most Condorcet fers a significant advantage over both IRV compensate for the spoiler effect, voters in According to Allan Gibbard and Mark Sat- methods to tactical voting, and given that and Coombs in approaching Condorcet ef- the plurality elections were able to strate- terthwaite, no voting mechanism is fully failure to elect the Condorcet winner oc- ficiency. gize by failing to report actual first choices; strategy proof, and according to Kenneth curs less than .6% of the time for up to 10 voters could compromise by voting for the Arrow, no voting mechanism meets all rea- voters and 10 candidates using Bidirection- Acknowledgments candidate they thought realistically had the sonable criteria of fairness. A theoretical al Elimination, I find this new algorithm best chance of winning. IRV eliminated framework must be constructed to evaluate may offer a significant advantage over I am grateful to Jonathan Levin for his the spoiler effect and reduced the chance methods of aggregating individual interests Condorcet methods, and certainly a strict instructive insights, engaging discussions, and of electing candidates whom a majority into a collective decision. This theoretical advantage over Instant Runoff Voting and thoughtful guidance. A special thanks to Jae- disliked. framework, dating back to the work of over the similar Coombs Method. The im- hyun Park for lending his world class coding French philosopher and mathematician portance: Bidirectional Elimination has the talents in creating the program used on tens In his February 15, 2010 article for The Condorcet, is called social choice theory. potential to improve justice in democratic of billions of samples. Discussions with Jona- New Yorker, Hendrik Hertzberg explains systems. than Zhang were enlightening: It was dur- the effects of IRV in the context of that Within this framework, criteria ex- ing conversation with him that the concept year’s Academy Awards: ist for evaluating the justness of a voting -8- ECONPress Voting with Bidirectional Elimination -9-

2. Background and Terminology loser criterion but fails monotonicity, inde- Failure to meet certain criteria creates pendence of irrelevant alternatives, and the until one is eliminated; then continue with The first key term is Condorcet win- susceptibility to strategic voting. Among Condorcet criterion. The Coombs Method regular IRV. If potential losers ever tie in ner. The Condorcet winner is the candi- these criteria is the monotonicity criterion, is susceptible to compromising and bury- the rightmost column containing potential date who, when paired against any other which states that a candidate X must not ing. losers, all potential losers are eliminated individual candidate, will always capture a be harmed—that is, changed from being a then. Under certain tiebreaker conditions, majority vote. A voting method that always winner to a loser—if X is raised on some Condorcet Methods no winner will be elected; all candidates are elects the Condorcet winner when one ex- ballots without changing the orders of the eliminated. ists is called Condorcet efficient,or is said to other candidates. Conversely, the later-no- Condorcet methods, methods that will meet the Condorcet criterion. TheCondorcet harm criterion states that giving a more always elect the Condorcet winner, include Stage 2: Use the Coombs Method to loser is one who always loses such pairwise positive ranking, or simple an additional Copeland’s method, the Kemeny-Young elect a potential winner Y. If in any round runoffs. A system that never elects the Con- ranking, to a less preferred candidate must Method, Minimax, Nanson’s method, of elimination two or more candidates share dorcet loser is said to meet the Condorcet not cause a more preferred candidate to ranked pairs, and the Schulze method. the highest number of last choice votes, a loser criterion. A Condorcet method is a lose. No Condorcet method satisfies the later- special tiebreaker is performed. To perform mechanism that will always elect the Con- no-harm criterion or independence of ir- the tiebreaker, create a set of “potential los- dorcet winner. A Condorcet winner does relevant alternatives. The methods vary in ers” consisting of all the candidates sharing not always exist. Sometimes there will be monotonicity. the highest number of last choice votes in a tie, or a cycle; the latter is an example of 3. Relevant Voting Methods the rightmost column. Then move to the Condorcet’s paradox. For example, three vot- Condorcet methods are generally quite next column to the left and reiterate this ers with preferences (A>B>C), (B>C>A), Instant Runoff Voting susceptible to tactical voting—in particular, form of the Coombs Method among po- and (C>A>B) cause a cycle; in this case, the compromising, burying, and bullet voting. tential losers only, possibly narrowing the group chooses A over B, B over C, and C Instant Runoff Voting is a system using set of potential losers, until one is eliminat- over A, so there is no clear winner. ranked preferences to elect a single winner. ed; then continue with the regular Coombs The procedure works as follows. Voters sub- Method. If potential losers are ever tied in A second criterion for evaluating voting mit ranked preferences, and the candidate 4. Bidirectional Elimination the leftmost column containing any poten- systems is strategy proofness. A voting system with the fewest first choice votes is system- tial losers, all potential losers are eliminated is said to be strategy proof if, given full in- atically eliminated until only the winner I now propose a new voting mechanism at once. Under certain tiebreaker condi- formation over everyone else’s preferences, remains. In some cases, candidates will be using ranked preferences. I call this new tions, no winner will be elected; all candi- no individual can improve his outcome tied for the position of “fewest first choice mechanism “Bidirectional Elimination,” as dates are eliminated. by misreporting his own preferences. Such votes.” If this happens, special tiebreaker it is a hybrid of both Instant Runoff Voting misreporting is called tactical voting. Ac- rules must be constructed. IRV satisfies the and the Coombs Method. The algorithm Stage 3: If X and Y are the same can- cording to the Gibbard-Satterthwaite theo- later-no-harm criterion and the Condorcet works as follows. (Note: The tiebreaker pro- didate, X = Y= winner; if X and Y are dif- rem, no preferential voting system is fully loser criterion but fails monotonicity, inde- cedure described in stages 1 and 2 is impor- ferent candidates, a simple pairwise runoff strategy proof. pendence of irrelevant alternatives, and the tant in preventing premature elimination between X and Y determines the winner; if Condorcet criterion. IRV is susceptible to of the Condorcet winner.) only one of the stages elects a potential win- Various types of tactical voting can push-over voting. ner, the potential winner is the final win- occur. The first is called push-over voting, The Bidirectional Elimination Algorithm ner; if neither former stage elects a potential in which a voter ranks a weak alternative Coombs Method winner, there is no final winner. higher, but not in the hopes of getting that Stage 1: Use regular IRV to elect po- alternative elected. The second is called The Coombs Method is a system simi- tential winner X. If in any round of elimi- Non-Monotonic compromising, which occurs when voters lar to IRV using ranked preferences to elect nation two or more candidates share the dishonestly rank an alternative higher than a single winner. Instead of systematically least number of first choice votes, a special Bidirectional Elimination fails the their true alternative in hopes of getting it eliminating the candidate with the fewest tiebreaker is performed. To perform the monotonicity criterion and is therefore elected. The third strategy, called burying, first choice votes, Coombs systematically tiebreaker, create a set of “potential los- not strategy-proof. The social preference occurs when a voter dishonestly ranks a eliminates the candidate with the most last ers” consisting of all candidates sharing the profiles below are examples susceptible to candidate lower in hopes of seeing it de- choice votes until one remains. Similarly, a least number of first choice votes in the tactical voting. feated. The last form is called bullet voting, special tiebreaker must be devised to deal leftmost column. Then move to the next which means voting for only one candidate with cases in which candidates are tied for column to the right and reiterate this form in a preferential system when submitting a the position of “most last choice votes.” The of IRV among potential losers only, pos- list of ranked preferences is an option. Coombs Method satisfies the Condorcet sibly narrowing the set of potential losers, -10- ECONPress Voting with Bidirectional Elimination -11-

pending on the nature of the collective de- Bidirectional Elimination may not # Voters True Preferences cision, either no winner should be elected, eliminate cycles, but the mechanism does or an alternative method should be used to satisfy other pleasant, though informal, cri- 4 A > B > C arbitrarily select a winner. teria. The IRV stage of the mechanism will rarely eliminate a candidate whom voters 3 B > C > A Electoral cycles can be similar to ties in find appealing, while the Coombs stage will that no mathematically just winner exists. rarely elect a candidate whom voters find 2 C > A > B The classic example of Condorcet’s para- unappealing, and between the two stages, dox—three voters with profiles (A>B>C), the better candidate is chosen. IRV and Coombs would each elect A in (B>C>A), and (C>A>B) has no clear win- this case, so Bidirectional Elimination also ner (this is an example of a circular tie). But elects A. However, a voter with preferences what if votes are not as symmetrical? What (B>C>A) could simply state falsely that if we add a fourth voter with preferences 5. Logic Proofs for IRV, Coombs his preferences were (C>A>B). Preferences (A>B>C)? Now, A is strictly preferred over Method, and Bidirectional Elimination would then look like this: B, which is strictly preferred over C; but A and C are tied in a pairwise runoff. This is IRV, Coombs Method, and Bidirec- # Voters Reported Preferences A: Instant Runoff Voting elects can- no longer a circular tie. While there may tional Elimination meet the Condorcet cri- didate A, but Coombs Method does not. still be no clear winner, electing an arbitrary terion in certain specific combinations of N 4 A > B > C candidate seems less than ideal: One could candidates and M voters. In this section I B: Both Instant Runoff Voting and argue that B should be eliminated since it is examine for which sets of [N candidates, M 2 B > C > A Coombs Method elect candidate A. strictly dominated by A; and one could de- voters] each voting system meets the crite- bate whether C should be eliminated, since rion. 3 C > A > B C: Coombs Method elects candidate while tied with A, C is still strictly domi- A, but Instant Runoff Voting does not. nated by B. Establishing criteria for justice For consistency and ease of notation, Now, IRV elects C; Coombs elects A; is more difficult given an asymmetric cycle candidate “A” refers to the Condorcet win- and C wins with Bidirectional Elimination D: Bidirectional Elimination fails to like this one. ner. when compared pairwise with A. By misre- elect candidate A. porting preferences, a voter was able to im- A Condorcet completion method is re- We will ignore two trivial cases, [1 can- prove his outcome, now getting his second When No Condorcet Winner Exists quired to elect a winner when ambigui- didate, M voters] and [N candidates, 1 vot- choice instead of his third choice. ties like these arise. One such completion er], in which voters have no choice between While Bidirectional Elimination fails to method uses the “minimax rule” developed candidates, or one voter has the ultimate Visualization meet the Condorcet criterion, it comes very by Simpson and Kramer. This rule gives a choice (a situation similar to dictatorship). close, as shown in section 6. However, as score to each candidate as follows. Can- Tie and cyclical cases are not discussed here.

The circle below, not to scale, repre- the number of N candidates or M voters in- didate A1 is paired against A2-N. For each I am primarily concerned with electing the sents an arbitrary space for N>3 candi- creases, the number of Condorcet winners pairwise comparison, a score is given to A1 Condorcet winner when one exists. dates and M>4 voters containing permu- generally decreases. equal to the number of votes his opponent tations of voter preferences. has, minus the number of his own votes. Logic Proofs: Instant Runoff Voting When no Condorcet winner exists, The maximum of these scores is recorded

A + B + C + D: Permutations of pref- there must be new criteria for evaluating as W1 (there are various ways of calculating Instant Runoff Voting, the weakest of erences such that candidate A is a Con- the justness of a voting algorithm. No Con- a W score; this one, called using margins, the three voting mechanisms studied here, dorcet winner. dorcet winner exists in the presence of a tie is the simplest). The minimum of (W1…N) meets the Condorcet criterion for up to 2 or a cycle. corresponds to the winner. voters and N candidates, or M voters and A + B + C: Bidirectional Elimination up to 2 candidates. elects candidate A. When votes are tied—such as in the Andrew Caplin and Barry Nalebuff simplest case, when two voters disagree over proposed a system based on Simpson and N candidates, 2 voters A + B: Instant Runoff Voting elects which of two candidates to elect—there is Kramer’s minimax using a “64%-majority candidate A. no mathematically “just” way of choosing rule” that can in fact eliminate all electoral When only two voters are present, a between candidates. Bidirectional Elimina- cycles given a restriction on individual pref- Condorcet winner can exist only when a tie B + C: Coombs Method elects can- tion does not choose a winner in cases of erences, and on the distribution of prefer- does not exist; that is, when the voters agree didate A. ultimate ties. This is not a bad thing; de- ences. on the candidate to be chosen. Both candi- -12- ECONPress Voting with Bidirectional Elimination -13- dates have therefore ranked this candidate follows that A can appear in the rightmost If A does appear in the rightmost col- Additionally, Bidirectional Elimination (candidate A) as their first choice. All other column at most once. If A were to appear umn once, either (1) a non-A is eliminated meets the Condorcet criterion for 3 can- N-1 candidates will be eliminated at once, in the rightmost column more than once, right away, or (2) all different candidates didates and M voters, which is more than leaving A as the winner from IRV. at least one non-A would be preferred in appear in the last column, in which case either IRV or the Coombs Method can ac- majority over A. This is impossible, as A is A cannot be eliminated in the tiebreaker, complish alone. 2 candidates, M voters the Condorcet winner. because one of the other three potential los- ers must be eliminated first. This is because 3 candidates, M voters When only two candidates are present, If A does appear in the rightmost col- as we move leftward through columns, A a Condorcet winner exists when either M umn once, either (1) the same non-A is cannot appear before another candidate: At Here we use an example with a total is odd, or M is even but the two candidates now ranked in last-place by two voters, in least three voters rank every other candidate number of voters equal to X1+X2 . . . +X6 are not tied in their votes received. In both which case this non-A is eliminated, or (2) below A. choosing between candidates A, B, and C­. cases, candidate A captures more than 50% three different candidates appear in the last A is given as the stable Condorcet winner. of the voters. If this is the case, the non-A column, in which case A cannot be elimi- If A appears in the rightmost column We wish to prove that Bidirectional Elimi- candidate will be eliminated in the first and nated in the tiebreaker, because one of the zero times, it will not be eliminated in this nation will always elect candidate A given only iteration of IRV. other two potential losers will be eliminat- round of the Coombs Method. the [3 candidates, M voters] condition. ed first. This is because as we move leftward Proving that Bidirectional Elimination will Logic Proofs: Coombs Method through columns, A cannot appear before Candidate A can never be eliminated never eliminate A is the same as proving another candidate: At least three voters as the algorithm iterates. Under [N candi- that Bidirectional Elimination will always The Coombs method, which meets the rank every other candidate below A. dates, 4 voters], Candidate A can never be elect A if and only if a candidate is elimi- Condorcet criterion in a larger set of can- eliminated using the Coombs method. A nated each round. Since one candidate is didate/voter combinations, works consis- If A appears in the rightmost column will always win. eliminated each round, I will prove Bidi- tently for up to 4 voters and N candidates, zero times, it will not be eliminated in this rectional Elimination will never eliminate or M voters and up to 2 candidates. round of the Coombs Method. Logic Proofs: Bidirectional Elimination A—in order to show that Bidirectional Elimination will always elect A. N candidates, 2 voters Candidate A can never be eliminated Bidirectional Elimination meets the as the algorithm iterates. Under [N can- Condorcet criterion for up to 4 voters and The table below represents all possible When only two voters are present, a didates, 3 voters] conditions, Candidate A N candidates, or M voters and up to 3 can- permutations of voter preferences. Condorcet winner can exist only when a tie can never be eliminated using the Coombs didates. does not exist; that is, when the voters agree method. A will always win. Since we are given that A is the stable on the candidate to be chosen. Both candi- Since Bidirectional Elimination utilizes Condorcet winner, to satisfy the stable dates have therefore ranked this candidate N candidates, 4 voters IRV and the Coombs Method in electing Condorcet condition, A must have more (candidate A) as their first choice, and the two potential winners who eventually face votes than either B or C in pairwise counts. losing candidates (candidate non-A) as This proof is directly parallel to the [N off in a pairwise election, when IRV or the The following two statements must be true: their second and last choice. All other N-1 candidates, 3 voters] proof. To preserve Coombs Method elects a Condorcet win- candidates will be eliminated systematically the existence of a Condorcet winner un- ner, so will Bidirectional Elimination. Thus X3 + X4 + X6 < X1 + X2 + X5 until only A remains from the Coombs der these conditions, only one of the four from the proofs above, we have already Method. voters may rank a given non-A candidate established that Bidirectional Elimination (1, implies A > B) above A; otherwise, a tie could exist, or a meets the Condorcet criterion for up to 4 N candidates, 3 voters majority of the voters could prefer a non-A voters and N candidates, or M voters and candidate over A. up to 2 candidates. To preserve the existence of a Con- dorcet winner under these conditions, only When columns of preferences are Number of Ballots First Choice Second Choice Third Choice one of the three voters may rank a given drawn, while N>1 (a winner as not yet been X1 A B C non-A candidate above A; otherwise, at found, as multiple candidates remain), it X A C B least two-thirds of the voters would prefer follows that A can appear in the rightmost 2 X B A C a non-A candidate over A. column at most once. If A were to appear 3

in the rightmost column more than once, X4 B C A When columns of preferences are at least one non-A would be preferred in X C A B drawn, while N>1 (a winner as not yet been majority over A. This is impossible, as A is 5 X C B A found, as multiple candidates remain), it the Condorcet winner. 6 -14- ECONPress Voting with Bidirectional Elimination -15-

X + X + X < X + X + X nates B; the second round eliminates A. 4 5 6 1 2 3 Candidate A, the Condorcet winner, is (2, implies A > C) Coombs Case 2: The first round elimi- eliminated in the IRV nates C; the second round eliminates A. stage in one of three If the Condorcet condition is to be ways: satisfied by Bidirectional Elimination, then Coombs Case 3: The first round elimi- we must show that A cannot be eliminated nates A. by both IRV and the Coombs Method. For this to be true, if the stable Condorcet IRV Case 1 is impossible: If B is elimi- Candidate B is eliminated Candidate C is eliminated winner A is eliminated in one of these two nated in the first round, only A and C re- in the first round. in the first round. Candidate A is eliminated Candidate A is eliminated Candidate A is eliminated in the first round. mechanisms, the other mechanism must main in the final pairwise runoff. By (2), in the second round. in the second round. not eliminate it. A would win this runoff and C would be eliminated, not A. Impossible Impossible Possible Candidate A could be eliminated in the IRV stage in one of three ways: IRV Case 2 is impossible: If C is elimi- nated in the first round, only A and B re- IRV Case 1: The first round eliminates main in the final pairwise runoff. By (1), Candidate A is also eliminated in the B; the second round eliminates A. A would win this runoff and B would be Coombs stage one of eliminated, not A. three ways: IRV Case 2: The first round eliminates C; the second round eliminates A. This leaves us with only Coombs Case 3—the first round eliminates A—which IRV Case 3: The first round eliminates would require the following to hold: A. Candidate B is eliminated Candidate C is eliminated in the first round. in the first round. Candidate A is eliminated X1 + X3 < X4 + X6 (5) Candidate A is eliminated Candidate A is eliminated in the first round. IRV Case 1 is impossible: If B is elimi- in the second round. in the second round. nated in the first round, only A and C re- X2 + X5 < X4 + X6 (6) main in the final pairwise runoff. By (2), Impossible Impossible Impossible A would win this runoff and C would be From (1) and (3), we can show algebra- eliminated, not A. ically, 6. Experimentation via Computer Simulation

X1 < X6 (11) always elects the Condorcet winner given IRV Case 2 is impossible: If C is elimi- X6 < X5 (7) A Program to Simulatethe [3 Votingcandidates, M voters] condition. nated in the first round, only A and B re- From (5) and (2), we can show algebra- main in the final pairwise runoff. By (1), From (7) and (6), we can show algebra- ically, Jaehyun Park generously wrote a program accordingThe toproof my specifications can be visualized to test the in a tree A would win this runoff and B would be ically, results of IRV, the Coombs Method, and Bidirectiona(above).l Elimination for various social preference profiles. The simulation takes in three inputs: N candidates, M voters, and X cases. Here we eliminated, not A. X5 < X2 (12) define “social preference profile” as the set of ranked preferences for all voters V . When a X2 < X4 (8) 0…M Let us continue unraveling IRV Case userThe enters following X=0, the program chain willcan test be all derived possible permutations of social preference profiles 3. If first-round IRV eliminates A, then we From (6) and (1), we can show algebra- fromexactly numbers once and (7) output through results. (12) (For above: example, for 2 voters6. Experimentation and 3 candidates, V via1 has Computer 6 possible know: ically, rankings, and V2 has 6 possible rankings, for a total of 36 possible socialSimulation preference profiles. Entering X=0 tests each one of these.) When a user enters X>0, the program will create X X5 < X 2 < X4 < X3 < X1 < X6 < X5 random social preference profiles and perform the algorithms on each one. Since these profiles X1 + X2 < X3 + X4 (3) X3 < X1 A Program to Simulate Voting are random when X>0, it is possible, though rare as M and N increase, for duplicate profiles to Since X5 cannot appear on both sides be tested. This duplication is generally expected of Monte Carlo experiments, and in this X1 + X2 < X5 + X6 (4) From (4) and (2), we can show algebra- of the inequality, Coombs Case 3 must also Jaehyun Park generously wrote a pro- ically, beexperiment impossible. does We not have significantly just shown affect that results. it is gram according to my specifications to test Given these conditions, can candidate impossibleOutputs for candidateof the simulation A to be include: eliminated the results of IRV, the Coombs Method, and

A now also lose in a Coombs election? A X4 < X3 (10) by IRV, and also by the Coombs Method. Bidirectional Elimination for various social loss could happen in one of three ways: It is therefore impossible for A to be elimi-17 preference profiles. The simulation takes in From (5) and (10), we can show alge- nated by Bidirectional Elimination under three inputs: N candidates, M voters, and Coombs Case 1: The first round elimi- braically, these conditions. Bidirectional Elimination X cases. Here we define “social preference -16- ECONPress Voting with Bidirectional Elimination -17-

profile” as the set of ranked preferences for winner. By symmetry, we can multiply R by Table 1: Number of Cases Tested (Q) all voters V1…M. When a user enters X=0, the number of candidates to determine for the program will test all possible permuta- how many permutations a Condorcet win- Candidates Voters 1 2 3 4 5 6 7 8 9 10 tions of social preference profiles exactly ner exists. 1 1 2 6 24 120 720 5040 40320 362880 3628800 once and output results. (For example, for 2 1 4 36 576 14400 518400 25401600 1000000000 1000000000 1000000000 3 1 8 216 13824 1728000 373248000 1000000000 1000000000 1000000000 1000000000 2 voters and 3 candidates, V1 has 6 possible (N*R)/Q, percentage of cases with a Con- 4 1 16 1296 331776 207360000 1000000000 1000000000 1000000000 1000000000 1000000000 rankings, and V2 has 6 possible rankings, dorcet winner. Dividing N*R by the total for a total of 36 possible social preference number of cases tells us the percentage of 5 1 32 7776 7962624 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 6 1 64 46656 191102976 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 profiles. Entering X=0 tests each one of cases for which a Condorcet winner exists. 7 1 128 279936 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 these.) When a user enters X>0, the pro- 8 1 256 1679616 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 gram will create X random social preference S, the IRV success figure. This is equal 9 1 512 10077696 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 profiles and perform the algorithms on to the number of times that A is the Con- 10 1 1024 60466176 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 each one. Since these profiles are random dorcet winner, and Instant Runoff Voting Number of cases to test equals = ((number of candidates)!)^(number of voters) when X>0, it is possible, though rare as M elects A. Cases tested capped at 1 billion. and N increase, for duplicate profiles to Table 2: Percentage of Cases where A is a Condorcet Winner (R/Q) be tested. This duplication is generally ex- S/R, the IRV success ratio. Dividing S by pected of Monte Carlo experiments, and in the number of cases where A is the Con- Candidates this experiment does not significantly affect dorcet winner returns a valuable percent- Voters 1 2 3 4 5 6 7 8 9 10 results (only by thousandths of a percent). age. 1 100.000% 50.000% 33.333% 25.000% 20.000% 16.667% 14.286% 12.500% 11.111% 10.000% 2 100.000% 25.000% 11.111% 6.250% 4.000% 2.778% 2.041% 1.559% 1.221% 0.998% 3 100.000% 50.000% 31.481% 22.222% 16.800% 13.296% 10.866% 9.111% 7.786% 6.759% Outputs of the simulation include: T, the Coombs Method success figure.This 4 100.000% 31.250% 14.815% 8.550% 5.535% 3.862% 2.839% 2.176% 1.712% 1.389% is equal to the number of times that A is 5 100.000% 50.000% 31.019% 21.528% 16.001% 12.474% 10.054% 8.318% 7.024% 6.030% Q, number of total cases, or social prefer- the Condorcet winner, and the Coombs 6 100.000% 34.375% 16.958% 10.002% 6.571% 4.623% 3.425% 2.633% 2.091% 1.695% ence profiles, tested.Q is equal to X when Method elects A. 7 100.000% 50.000% 30.833% 21.248% 15.694% 12.148% 9.736% 8.006% 6.727% 5.745% X>0, or (N!)M when X=0. Individual pref- 8 100.000% 36.328% 18.397% 11.034% 7.295% 5.180% 3.857% 2.985% 2.377% 1.935% 9 100.000% 50.000% 30.734% 21.099% 15.526% 11.977% 9.562% 7.841% 6.570% 5.595% erences were restricted to include only sets T/R, the Coombs Method success ratio. 10 100.000% 37.695% 19.447% 11.781% 7.876% 5.620% 4.208% 3.262% 2.604% 2.125% in which each voter gave a ranking to every Dividing R by the number of cases where A candidate. That is, if options A through E is the Condorcet winner returns a valuable Table 3: Percentage of Cases where a Condorcet Winner Exists (N*R/Q) were available, each voter included options percentage. A through E in his individual preference Candidates Voters 1 2 3 4 5 6 7 8 9 10 profile, omitting no option from his or- U, the Bidirectional Elimination success 1 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% dering. Removing this domain restriction figure. This is equal to the number of times 2 100.000% 50.000% 33.333% 25.000% 20.000% 16.667% 14.286% 12.473% 10.988% 9.983% would expand the total number of possible that A is the Condorcet winner, and Bidi- 3 100.000% 100.000% 94.444% 88.889% 84.000% 79.778% 76.060% 72.884% 70.071% 67.587% social preference profiles to (N! + N!/2! + rectional Elimination elects A. 4 100.000% 62.500% 44.444% 34.201% 27.675% 23.172% 19.875% 17.410% 15.406% 13.889% N!/3! . . . + 1)M, making the program un- 5 100.000% 100.000% 93.056% 86.111% 80.005% 74.845% 70.375% 66.543% 63.217% 60.304% U/R, the Bidirectional Elimination suc- 6 100.000% 68.750% 50.874% 40.008% 32.857% 27.738% 23.974% 21.066% 18.821% 16.955% feasible. 7 100.000% 100.000% 92.498% 84.992% 78.469% 72.888% 68.153% 64.051% 60.540% 57.452% cess ratio. Dividing U by the number of cas- 8 100.000% 72.656% 55.190% 44.136% 36.474% 31.083% 27.001% 23.881% 21.396% 19.346% R, number of cases with A as Condorcet es where A is the Condorcet winner returns 9 100.000% 100.000% 92.202% 84.395% 77.632% 71.863% 66.935% 62.729% 59.132% 55.949% winner. The program labels one of the can- a valuable percentage. 10 100.000% 75.391% 58.340% 47.122% 39.382% 33.723% 29.459% 26.098% 23.435% 21.252% didates as A and tests preference permuta- tions to determine if A is a Condorcet win- The program reports the most accurate and set X=0; when (N!)M > 1 billion, we set with repeat simulations. ner. results when X=0, and all cases are tested X=1,000,000,000. This way, the program exactly once. However, since Q grows as- will never test more than a billion samples. Tables from Sample Runs R/Q, percentage of cases with A as Con- tronomically as N or M increase, the pro- dorcet winner. This calculation performs gram can take years to run beyond a [N=5 Although for a [N=10 candidates, The tables of results from Park’s voting R/Q, the number of times that A is a Con- candidates, M=5 voters] simulation. We M=10 voters] simulation one billion tri- simulator appear below. dorcet winner divided by the number of approximate by setting X equal to a large als represent an extremely small fraction cases tested. number—in this case, one billion—when of the total possible permutations, (exactly Table 1 reports the number of social necessary to shorten the simulation. When 2.53x10-52), the results are still closely ac- preference profiles tested. When the num- N*R, number of cases with a Condorcet (N!)M < 1 billion, we test all possible samples curate and change in the thousandths place ber is less than a billion, all possible social -18- ECONPress Voting with Bidirectional Elimination -19-

Table 4: IRV Success Ratio (S/R) Graph 1: Probability of Existence of Condorcet Winner Graph 2: Probability of Existence of Condorcet Winner Percentage of Cases where a Condorcet Winner Exists, and IRV Elects the Condorcet Winner Given Odd Number of Voters Given N Candidates and Odd M Voters N Candidates Candidates 120.000% 1 120.000% Voters 1 2 3 4 5 6 7 8 9 10 100.000% 2 100.000% M Voters 1 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 80.000% 3 80.000% 1 2 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 60.000% 4 60.000% 3 100.000% 100.000% 100.000% 98.438% 96.429% 94.359% 92.349% 90.466% 88.720% 87.070% 3 40.000% 5 40.000% 4 100.000% 100.000% 100.000% 100.000% 99.729% 99.241% 98.560% 97.839% 97.019% 96.168% 5 20.000% 6 20.000% 5 100.000% 100.000% 97.512% 95.758% 93.947% 92.078% 90.172% 88.326% 86.560% 84.800% 7 0.000% 7 0.000% 6 100.000% 100.000% 100.000% 99.970% 99.768% 99.313% 98.668% 97.883% 96.989% 96.030% 9 1 3 5 7 9 8 1 2 3 4 5 6 7 8 9 10 7 100.000% 100.000% 99.676% 98.360% 96.815% 95.143% 93.403% 91.644% 89.938% 88.212% M Voters 9 N Candidates 8 100.000% 100.000% 99.275% 98.377% 97.563% 96.748% 95.890% 94.986% 94.099% 93.001% 9 100.000% 100.000% 98.332% 96.598% 94.941% 93.309% 91.677% 90.066% 88.497% 86.938% 10 100.000% 100.000% 99.893% 99.613% 99.031% 98.309% 97.493% 96.594% 95.621% 94.627% Graph 3: Probability of Existence of Condorcet Winner Graph 4: Probability of Existence of Condorcet Winner Given Even Number of Voters Given N Candidates and Even M Voters N Candidates Table 5: Coombs Method Success Ratio (T/R) 120.000% 1 120.000% Percentage of Cases where a Condorcet Winner Exists, and the Coombs Method elects the Condorcet Winner 100.000% 2 100.000% M Voters Candidates 80.000% 3 80.000% 2 Voters 1 2 3 4 5 6 7 8 9 10 60.000% 4 60.000% 4 1 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 40.000% 5 40.000% 6 2 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 20.000% 6 20.000% 8 3 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 0.000% 7 0.000% 4 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 10 2 4 6 8 10 8 1 2 3 4 5 6 7 8 9 10 5 100.000% 100.000% 100.000% 95.758% 97.755% 96.672% 95.820% 95.161% 94.637% 94.183% M Voters 9 N Candidates 6 100.000% 100.000% 100.000% 100.000% 99.862% 99.630% 99.374% 99.143% 98.944% 98.779% 7 100.000% 100.000% 98.054% 96.663% 95.709% 94.863% 93.999% 93.130% 92.286% 91.516% 8 100.000% 100.000% 100.000% 99.716% 99.450% 99.255% 99.060% 98.847% 98.593% 98.305% Existence of a Condorcet Winner voters: 9 100.000% 100.000% 98.698% 97.232% 95.775% 94.569% 93.613% 92.827% 92.118% 91.431% 10 100.000% 100.000% 99.429% 99.034% 98.565% 98.082% 97.661% 97.320% 97.039% 96.765% Table 3 reveals interesting trends relat- Observe the major difference between Table 6: Bidirectional Elimination Success Ratio (U/R) ing to the existence of Condorcet winners Tables 3A and 3B, or Graphs 1 and 3. For Percentage of Cases where a Condorcet Winner Exists, and Bidirectional Elimination Elects the Condorcet Winner for various combinations of N candidates an odd number of voters, the probability of Candidates and M voters. the existence of a Condorcet winner starts Voters 1 2 3 4 5 6 7 8 9 10 high and decreases with the addition of vot- 1 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 2 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% In the row with 2 voters, we observe ers. For an even number of voters, the same 3 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% that the result (percentage of cases where a probability starts low and increases with the 4 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% Condorcet winner exists) is equal to 1/N. addition of voters. This interesting result 5 100.000% 100.000% 100.000% 100.000% 99.979% 99.947% 99.905% 99.855% 99.798% 99.731% Probabilistically this makes sense: With two leaves room for further study; probabilistic 6 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 99.999% 99.998% voters, a Condorcet winner can exist only analysis could lead to a theorem that would 7 100.000% 100.000% 100.000% 99.994% 99.968% 99.925% 99.865% 99.787% 99.689% 99.577% when both voters rank the same candidate answer these questions: 8 100.000% 100.000% 100.000% 100.000% 99.999% 99.998% 99.995% 99.993% 99.990% 99.983% 9 100.000% 100.000% 100.000% 99.983% 99.942% 99.881% 99.804% 99.713% 99.609% 99.485% in first place; that is, when the second voter 10 100.000% 100.000% 100.000% 100.000% 99.999% 99.995% 99.990% 99.981% 99.971% 99.956% chooses the same candidate as the first voter, Why does p, the probability of the ex- which happens with a probability of 1/N. istence of a Condorcet winner given a spe- preference profiles were tried. Table 4 tells us how often an existing cific even number of voters and arbitrary N Condorcet winner will be elected by IRV. For two candidates and an odd number candidates, increase with more voters? Why Table 2 divides the number of social of voters, a Condorcet winner will always does q, the probability of the existence of preference profiles for which A is the Con- Table 5 tells us how often an existing exist because even splits or ties are not pos- a Condorcet winner given a specific odd dorcet winner by the total number of social Condorcet winner will be elected by the sible. number of voters and arbitrary N candi- preference profiles tested. The result is the Coombs Method. dates, decrease with more voters? percentage of cases for which candidate A is Except for the dictatorship case when the Condorcet winner. Table 6 tells us how often an existing M=1, the addition of candidates lowers the Why does p follow a linear pattern as N Condorcet winner will be elected by Bid. probability of the existence of a Condorcet increases, while q bows steeply? Multiplying Table 2 by number of can- Elim. winner. didates tells us how often a Condorcet win- As M approaches infinity, what do p ner exists. Analysis of Results The results become quite interesting and q approach? when we split Table 3 into odd and even -20- ECONPress Voting with Bidirectional Elimination -21-

Table 3A: Percentage of Cases where a Condorcet Winner Exists (N*R/Q); Odd Voters Only This study could be facilitated with a operations required to conduct this simu- program similar to Jaehyun Park’s, that lation, testing all cases could require vast Candidates would work as follows. Given inputs for amounts of time. A Monte Carlo method Voters 1 2 3 4 5 6 7 8 9 10 1 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% N candidates and M voters, the program will be necessary. M 3 100.000% 100.000% 94.444% 88.889% 84.000% 79.778% 76.060% 72.884% 70.071% 67.587% would generate (N!) permutations of true 5 100.000% 100.000% 93.056% 86.111% 80.005% 74.845% 70.375% 66.543% 63.217% 60.304% preferences for voters V1 through VM. A Bidirectional Elimination’s robustness 7 100.000% 100.000% 92.498% 84.992% 78.469% 72.888% 68.153% 64.051% 60.540% 57.452% “case counter” would start at zero. For each should come as promising news to econo- 9 100.000% 100.000% 92.202% 84.395% 77.632% 71.863% 66.935% 62.729% 59.132% 55.949% possible permutation of true preferences, mists. The algorithm holds potential to Table 3B: Percentage of Cases where a Condorcet Winner Exists (N*R/Q); Even Voters Only the following would happen (a nested for significantly improve democratic processes. loop): (1) The voting algorithm in ques- Moreover, this new simulation method for Candidates tion would be performed on true prefer- testing criteria can be applied to other vot- Voters 1 2 3 4 5 6 7 8 9 10 ences, and a winner W would be elected. ing methods, enabling further experimen- 2 100.000% 50.000% 33.333% 25.000% 20.000% 16.667% 14.286% 12.473% 10.988% 9.983% (2) Holding all other voters’ preferences tation and eventual comprehensive, data- 4 100.000% 62.500% 44.444% 34.201% 27.675% 23.172% 19.875% 17.410% 15.406% 13.889% 6 100.000% 68.750% 50.874% 40.008% 32.857% 27.738% 23.974% 21.066% 18.821% 16.955% constant, the program would then gener- driven comparisons of voting methods. 8 100.000% 72.656% 55.190% 44.136% 36.474% 31.083% 27.001% 23.881% 21.396% 19.346% ate all remaining (N!-1) false permutations 10 100.000% 75.391% 58.340% 47.122% 39.382% 33.723% 29.459% 26.098% 23.435% 21.252% of voter V1’s preferences, and perform the algorithm on each of these. If at least one R

Approaching Condorcet Efficiency very close to meeting the Condorcet crite- set of false preferences existed for V1 such rion and may in fact be a more just alter- that reporting these false preferences would

Tables 4, 5, and 6 show success ratios native to Condorcet methods—depending elect a candidate whom V1 preferred over for IRV, Coombs, and Bidirectional Elimi- on the designer’s emphasis on Condorcet W, one would be added to a “case coun- nation. efficiency versus strategy proofness. While ter,” and the program would move onto the there are some possible arrangements of next set of true preferences, skipping steps 3 The success ratio is rather poor for voter preferences such that the mechanism and 4. (3) If nothing had been added to the Instant Runoff Voting. The column with will fail to elect the Condorcet winner, case counter after trying all permutations of eight candidates already drops below 90% these cases comprise less than .6% of the false preferences for V1, the program would (when M=5). total in a 10x10 matrix of candidates and repeat step 2 for V2…M. If at least one set voters. of false preferences existed for any Vi such The success ratio is much improved that reporting these false preferences would with the Coombs Method, never once Bidirectional Elimination is probably elect a candidate whom Vi preferred over dropping below 90% throughout the entire less susceptible to strategic voting, but this W, one would be added to a “case counter,” 10x10 matrix. It is more difficult to arrange should be proven rigorously. I say “proba- and the program would move onto the next preferences in such a way that A remains bly” because IRV and the Coombs Method permutation of true preferences. (4) If after the Condorcet winner, but is eliminated us- are each individually less susceptible than step 3 no set of false preferences were found ing the Coombs Method. most Condorcet methods; it seems logi- for any voter Vi that could improve his out- cal Bidirectional Elimination would be as come, the “case counter” would remain at The success ratio for Bidirectional Elim- well. This question leaves room for future its current value, and the next permutation ination is even stronger than the former, study and experimentation: Given most of true preferences would be tested similar- not once dropping below 99.4%. Through- Condorcet methods’ vulnerability to tacti- ly, until all permutation of true preferences out the 10x10 matrix, Bidirectional Elimi- cal voting, Bidirectional Elimination may had been tested. (5) Dividing the final “case nation comes extremely close to Condorcet ironically be more successful at electing counter” value by (N!)M would output the efficiency. the Condorcet winner. I encourage future percentage of cases, given N and M as in- economists to rigorously examine the sus- puts, for which the voting algorithm in ceptibility of Bidirectional Elimination to question is susceptible to tactical voting. strategic voting, and compare with that of 7. Conclusion Condorcet methods, as well as IRV and the The program would need to be de- Coombs Method individually. signed, as Park designed his, to be capable The system of Bidirectional Elimi- of random sampling in addition to testing nation, an algorithm using IRV and the Experimentation for Strategy-Proofness all cases. As N and M grow, (N!)M grows Coombs Method in various stages, comes astronomically—and given the number of -22- ECONPress An Econometric Inquiry into the Effect of Religious Profiles on National Wealth -23-

Works Cited An Econometric Cleary’s “Religion and Economic Develop- ment: The advantage of moderation”2, and Arrow, Kenneth (1963). Social Choice Inquiry into the Effect Marcus Noland’s “Religion, Culture, And and Individual Values. New York: John Economic Performance”3. It was these ar- Wiley & Sons Inc., Second Edition. of Religious Profiles ticles that laid the framework for this study by setting forth a precedent on which to Caplin, Andrew and Nalebuff, Barry on National Wealth build. (1988). “On 64% Majority Rule.” Econometrica, Vol. 56, No. 4. 787-814. Brian Joel Feldman In her study on “a pooled sample of 63 ex-colonial states” Grier contributed signif- Dennis, Gregory (2008). “Why I Prefer Northeastern University icantly to the argument of religion as a sig- IRV to Condorcet.” Fairvote: The nificant factor in real GDP growth. In her Center for Voting and Democracy. Introduction argument, Grier opposes the hypotheses of Weber, most notably the ‘Protestant Ethic’ Gehrlein, William (2006). Condorcet’s With the ever expanding debate over (which states that the industrial revolution Paradox. Theory and Decision economic wealth raging on around the boom and subsequent rise of capitalism Library. Series C: Game Theory, world, many countries (especially devel- in Europe can be attributed to the strong Mathematical Programming, and oping ones) have gone under-microscope Protestant roots of the area) , by saying “my Operations Research. Springer. to see what stimulates growth and what results show that religion is not the sole de- hinders it, but are social scientists and terminant of differential development and Gibbard, Allan (1973). “Manipulation economists looking at the right things? So growth.” Although Grier aims to refute the of Voting Schemes: A General Result.” much of their time is spent talking about points of Weber’s ‘Protestant Ethic,’ she Econometrica, Vol. 41, 587-601. the technologies, workforces, and govern- clearly suggests the effect of religion on na- ments of these countries that often the tional wealth to be a significant one4. This R religious profiles and cultures of develop- is later reflected in her econometric analysis ing countries get shoved aside, tossed into of her collected data. “The results support footnotes, or are all together omitted from my hypothesis that the growth rate of Prot- the conversation. With this in mind, the emerging field of economics of religion is Economic Development: A Cross National Study under immense pressure to come forward of 63 Former Colonies” Kyklos: International and possibly answer the question on many Review for Social Sciences, 50, (1997). Accessed peoples’ minds, “Why are these developing Oct 2011. http://faculty-staff.ou.edu/G/ countries not growing?” Robin.M.Grier-1/religion.pdf 2 Rachel M. McCleary, “Religion and Economic Development: The advantage of moderation”, Hoover Institution, Stanford University, 147 (March 28, 2008) Accessed Oct. Review of the Literature 2011 http://www.hoover.org/publications/policy- review/article/5729 Numerous studies have been produced 3 Marcus Noland, “RELIGION, during the brief history of economics of re- CULTURE, AND ECONOMIC ligion, all of which have asked important PERFORMANCE” (Working Paper), The questions about the impact of religion on Peterson Institute for International Economics the surrounding world. The most notable Accessed Oct. 2011 http://www.iie.com/ topics and papers that arose in my research publications/wp/03-8.pdf for this original study include: Robin Gri- 4 Robin Grier, “The Effect of Religion on Economic Development: A Cross National Study er’s “The Effect of Religion on Economic Kyklos: International Development: A Cross National Study of 63 Former Colonies” 1 Review for Social Sciences, 50, (1997). Accessed of 63 Former Colonies” , Rachel M. Mc- Oct 2011. http://faculty-staff.ou.edu/G/ Robin.M.Grier-1/religion.pdf 1 Robin Grier, “The Effect of Religion on -24- ECONPress An Econometric Inquiry into the Effect of Religious Profiles on National Wealth -25- estantism is significantly correlated with Another important point that Mc- rates.”6 This allusion to his results suggests have been included in the model because real GDP growth, and that Protestantism Cleary makes is on religious terrorism, that religion’s impact is insignificant on his economic theory suggests a strong correla- is one of many determinants of develop- where she says “Religious terrorists feel a dependent variables (total factor produc- tion between these variables and per capita ment.”4 As she has implied with her argu- sense of alienation from the larger society... tivity)6, and ultimately this suggests that GDP or because their omission may have ments, and stated explicitly with her analy- [Krueger] found that the deterioration in religious variables might not be significant led to a bias in the coefficients of other in- sis, religion clearly has a significant impact economic conditions over time is associ- in studies of religious variables impact on dependent variables. on national economies. The information ated with the likelihood of educated men national wealth. This of course is not reason in Grier’s study has been adapted into this becoming terrorist attackers.”5 This spurs enough to halt since there are a few major Since there are various major religions study in the form of the inclusion of spe- an intriguing argument into the effects of distinctions to be made between this study’s in the world, an observed country’s religious cific religions, which Grier had proved rel- religious diversity and tolerance. Although model and Noland’s, most notably the dif- identity has been captured with variables in evant in her conversation specifically about the two are not perfectly correlated, it is ference in dependent variables. a few different forms. Protestantism. presumed that the more diverse religious bodies are the less likely they are to breed It is clear that although economics of The first form that the observed coun- The second study to be analyzed is Mc- religious extremism because of the increases religion is still emerging, a great amount of try’s religious makeup, or religious profile, Cleary’s study on religious moderation. in tolerance and decrease of the sense of research has been brought forth, but even was included as, was a direct measure of One of the stronger topics the article dis- ‘alienation’. This, according to McCleary’s more clear is the room for expansion and what religions made up the population cusses is the ‘two-way causation’5 of religion article and Krueger’s quoted research would improvement on previously existing mod- of the observed country. Since there was and development in which McCleary states mean that less religiously diverse popula- els. This is made obvious in the contradic- little to no unbiased literature on the spe- “The more educated a person is, the more tions would hinder economic stability and tory points of many articles in the field, cific economic effect of one religion over likely he is to turn to science for explana- growth. Ultimately, McCleary’s findings on such as McCleary’s and Roland’s articles another, numerous specific religions have tions of natural phenomena… [a]ccording religious diversity within populations sug- that have been analyzed here. been included in the model independently to this view, the higher the levels of educa- gest that my four religion ratio should have of one another as to test their specific ef- tional attainment, the less religious people both a large and statistically significant im- fects on per capita GDP. These specified will be… On the other hand, an increase pact on per capita GDP, as well as fitting religions include: Christianity, Buddhism, in education will also spur participation in into a larger context of religious variables Explanation of the Model Islam, Hinduism, Sikhism, Judaism, and religious activities, because educated people that have significance. Irreligion. tend to appreciate social networks and other For this model pertaining to per capita forms of social capital.”5 This two-way cau- Finally, in the article most similar and gross domestic product (GDP) numerous The second form chosen to incorporate sation, from the viewpoint of the study at relevant to this one, Noland states that independent variables were chosen for sev- a country’s religious profile was a four reli- hand, suggests that variable literacy would there is “[a]bundant evidence affirm[ing] eral reasons. The variables nominated have gion ratio within an observed country. This share in the effect of religion on per capita that religious belief affects a wide range of been consider either because of research measurement, adapted from the ‘four firm GDP possibly creating a bias. But more behavioral outcomes (Iannaccone 1998), done by prominent economists in the field concentration ratio’ measurement common importantly what McCleary suggests is and religious activity can affect economic of economics of religion, or because they in industrial organization, serves as a quan- the possibility that the full effect of religion performance at the level of the individual, have been suggested as relevant through tification of the religious diversity within very well may not be felt until the popu- group, or nation.” 6 As Noland goes through economic theory. These bases exclude the an observed country. Since it was observed lation is educated, and although questions the observations of Weber, Greif, and explanatory variables on religion, which are that more oppressive governments often re- of causality arise, this increasing returns in Solow though, he goes into extensive detail the focus of this study, because the correla- duce religious tolerance, as well as the same wealth presents a situation of exponential about historical examples only to conclude tions of these variables are currently only corrupted regimes also hindering wealth, it returns to religion, possibly observing a sort by saying “What does this have to do with speculative; meaning these were not chosen was expected that as this measure of reli- of economies of scale in which wealth in- economic performance? … [T]hese cultural from either previous studies or from theo- gious diversity will be negatively correlated creases faster as more people capture their measures [can’t] directly explain economic ry since they are believed to be novel and with GDP per capita. human capital potentials. performance, and indeed, they do not ap- therefore have not been explored directly pear to be correlated with economic growth through any previously existing works. Finally, the last form that was chosen to incorporate religious profiles in to the The variables chosen to explain the model was the measurement of years of in- 5 Rachel M. McCleary, “Religion and 6 Marcus Noland, “RELIGION, variation in per capita GDP included the dependence that the observed country had Economic Development: The advantage of CULTURE, AND ECONOMIC moderation”, Hoover Institution, Stanford PERFORMANCE” (Working Paper), The real GDP growth rate, the inflation rate, experienced. This measurement was include University, 147 (March 28, 2008) Accessed Oct. Peterson Institute for International Economics the unemployment rate, urbanization, because it was theorized that a country that 2011 http://www.hoover.org/publications/policy- Accessed Oct. 2011 http://www.iie.com/ the literacy rate, and finally the industrial has been occupied by a foreign power most review/article/5729 publications/wp/03-8.pdf makeup of the country. These variables likely would have had its religious identity

Industrial Makeup (e.g. Service) An Econometric Inquiry into the Effect of Religious Profiles on National Wealth -26- ECONPress -27- Industrial Makeup (e.g. ܩܦܲௌ௘௥௩௜௖௘ ݑ݌ ൌ݁݇ܽܯ ݈ܽ݅ݎݐݏݑ݀݊ܫ .IndustrialService) Makeup (e.g IndustrialUrbanization Makeup (e.g. ܩܦܲ௧௢௧௔௟ IndustrialService) Makeup (e.g. ௌ௘௥௩௜௖௘ IndustrialService) Makeup (e.g. ܩܦܲ GDP/capita ($) Unemployment (%) Inflation rate (%) ݑ݌ ൌ݁݇ܽܯ ݈ܽ݅ݎݐݏݑ݀݊ܫ Service)Industrial Makeup Service)Urbanization ܩܦܲௌ௘௥௩௜௖௘௧௢௧௔௟ Mean 15431.15 Mean 14.00 Mean 4.88 ܩܦܲௌ௘௥௩௜௖௘ ݏܽ݁ݎܣܾ݊ܽݎܷ ݊݅ ௌ௘௥௩௜௖௘ܲܦܩ ݑ݌ܲ݋݌ݑ݈ܽݐ݅݋݊ ൌ݁݇ܽܯ ݈ܽ݅ݎݐݏݑ݀݊ܫ (e.g. Service) ௌ௘௥௩௜௖௘௧௢௧௔௟ Standard Error 1572.54 Standard Error 1.20 Standard Error 0.34ܲܦܩܲܦܩݑ݌ ൌ݁݇ܽܯ ݈ܽ݅ݎݐݏݑ݀݊ܫ Urbanization ௧௢௧௔௟ ܲܦܩݑ݌ ൌ ൌ݁݇ܽܯ ݐܴ݁ܽ ݈ܽ݅ݎݐݏݑ݀݊ܫݖܽݐ݅݋ܾ݊݅݊ܽݎܷ Urbanization ௧௢௧௔௟ ܲ݋݌ݑ݈ܽݐ݅݋݊ Median 8400.00 Median 8.50 Median 3.70ܲܦܩܲܦܩݑ݌ ൌ ܶ݋ݐ݈ܽ݁݇ܽܯ ݈ܽ݅ݎݐݏݑ݀݊ܫ Urbanization ݏܽ݁ݎܣܾ݊ܽݎܷ ݊݅ ௧௢௧௔௟ܲܦܩUrbanizationLiteracyUrbanization Rates ܲ݋݌ݑ݈ܽݐ݅݋݊ ݖܽݐ݅݋݊ ܴܽݐ݁ ൌ Mode 2500.00 Mode 6.70 Mode 2.30ܾ݅݊ܽݎܷ ݋ݐ݈ܽ ܲ݋݌ݑ݈ܽݐ݅݋݊ܶ Standard Deviation 21272.98 Standard Deviation 15.21 Standard Deviation 4.55 ݏܽ݁ݎܣܾ݊ܽݎܷ ݊݅ Literacy Rates ܲ݋݌ݑ݈ܽݐ݅݋݊ ݏܽ݁ݎݏܽ݁ݎܣܣܾ݊ܽݎܷ ܾ݊ܽݎܷ ݊݅ ݊݅ ݖܽݐ݅݋݊ ܴܽݐ݁ ൌ ܲ݋݌ݑ݈ܽݐ݅݋݊ܲ݋݌ݑ݈ܽݐ݅݋ܾ݊݅݊ܽݎܷ Minimum 300.00 Minimum 0.50 Minimum -2.40 ݏܽ݁ݎܣܾ݊ܽݎܷ ݖܽݐ݅݋݊ ܴܽݐ݁ ൌܲ݋݌ݑ݈ܽݐ݅݋݊ܲ݋݌ݑ݈ܽݐ݅݋݊ܶ݋ݐ݈ܽ ݅݊௢௟ௗ௘௥௧௛௔௡ଵହǡ௖௔௡௥௘௔ௗ ܲ݋݌ݑ݈ܽݐ݅݋ܾ݊݅݊ܽݎܷ ݖܽݐ݅݋݊ ܴܽݐ݁ ൌ ܶ݋ݐ݈ܽ ܲ݋݌ݑ݈ܽݐ݅݋ܾ݊݅݊ܽݎܷ Literacy Rates ݕ ܴܽݐ݁ ܴܽݐ݁ ൌ ൌ ܶ݋ݐ݈ܽ ܲ݋݌ݑ݈ܽݐ݅݋݊௧௢௧௔௟ Maximum 179000.00 Maximum 95.00 Maximum 28.20ܿܽݎݐ݁݅ܮݖܽݐ݅݋ܾ݊݅݊ܽݎܷ Literacy Rates LiteracyLiteracy Rates Rates ܶ݋ݐ݈ܽܲ݋݌ݑ݈ܽݐ݅݋݊௢௟ௗ௘௥௧௛௔௡ଵହǡ௖௔௡௥௘௔ௗ ܲ݋݌ݑ݈ܽݐ݅݋݊ Literacy Rates ܲ݋݌ݑ݈ܽݐ݅݋݊ % of GDP Services % of GDP Industry % of GDP Agriculture ݕ ܴܽݐ݁ ൌ ௧௢௧௔௟ܿܽݎݐ݁݅ܮ Percent of Population ݋݌ݑ݈ܽݐ݅݋݊௢௟ௗ௘௥௧௛௔௡ଵହǡ௖௔௡௥௘௔ௗ Mean 56.43 Mean 29.63 Mean 13.85ܲ by religion)(e.g. Islam) ܲ݋݌ݑ݈ܽݐ݅݋݊ ௢௟ௗ௘௥௧௛௔௡ଵହǡ௖௔௡௥௘௔ௗ) ݕ ܴܽݐ݁ ൌ ܲ݋݌ݑ݈ܽݐ݅݋݊௢௟ௗ௘௥௧௛௔௡ଵହǡ௖௔௡௥௘௔ௗܿܽݎݐ݁݅ܮ Percent of Population ݋݌ݑ݈ܽݐ݅݋݊௢௟ௗ௘௥௧௛௔௡ଵହǡ௖௔௡௥௘௔ௗ௧௢௧௔௟ Standard Error 1.13 Standard Error 1.04 Standard Error 1.03ܲ ݕ ܴܽݐ݁ ൌܲ݋݌ݑ݈ܽݐ݅݋݊ܲ݋݌ݑ݈ܽݐ݅݋݊ ௧௢௧௔௟ܿܽݎݐ݁݅ܮ ݕ ܴܽݐ݁ ൌ ܲ݋݌ݑ݈ܽݐ݅݋݊௧௢௧௔௟ ூ௦௟௔௠௜௖ Median 57.90 Median 26.60 Median 9.50ܿܽݎݐ݁݅ܮ (by religion)(e.g. Islam) ݕ ܴܽݐ݁ ൌ ܲ݋݌ݑ݈ܽݐ݅݋݊ூ௦௟௔௠ ܲ݋݌ݑ݈ܽݐ݅݋݊௧௢௧௔௟ܿܽݎݐ݁݅ܮ Percent of Population ݐ ݋݂ ܲ݋݌ݑ݈ܽݐ݅݋݊ܲ݋݌ݑ݈ܽݐ݅݋݊ൌ ௧௢௧௔௟ Mode 58.20 Mode 24.40 Mode 2.40݊݁ܿݎ݁ܲ PercentPercent of of Population Population Percent(by religion)(e.g. ofof PopulationPopulation Islam) ܲ݋݌ݑ݈ܽݐ݅݋݊ܲ݋݌ݑ݈ܽݐ݅݋݊ூ௦௟௔௠௜௖ (by religion)(e.g.(by religion) Islam) ூ௦௟௔௠ Standard Deviation 15.46 Standard Deviation 14.25 Standard Deviation 13.99 ݐ ݋݂ ܲ݋݌ݑ݈ܽݐ݅݋݊ ൌ ௧௢௧௔௟݊݁ܿݎ݁ܲ (by religion)(e.g. Islam) byFour religion)(e.g. religion ratio Islam) (FRR) ܲ݋݌ݑ݈ܽݐ݅݋݊ூ௦௟௔௠௜௖) e.g. Islam) ூ௦௟௔௠ ܲ݋݌ݑ݈ܽݐ݅݋݊ ூ௦௟௔௠௜௖ Minimum 3.80 Minimum 5.40 Minimum 0.00) ݐ ݋݂ ܲ݋݌ݑ݈ܽݐ݅݋݊ ൌ ܲ݋݌ݑ݈ܽݐ݅݋݊ூ௦௟௔௠௜௖݊݁ܿݎ݁ܲ Four religion ratio (FRR) ூ௦௟௔௠ ூ௦௟௔௠௜௖௧௢௧௔௟ ݐ ݋݂ ܲ݋݌ݑ݈ܽݐ݅݋݊ூ௦௟௔௠ ൌܲ݋݌ݑ݈ܽݐ݅݋݊ܲ݋݌ݑ݈ܽݐ݅݋݊ܲ݋݌ݑ݈ܽݐ݅݋݊ Maximum 92.50 Maximum 93.90 Maximum 76.90݊݁ܿݎ݁ܲ Four religion ratio ݐ ݋݂ ܲ݋݌ݑ݈ܽݐ݅݋݊ூ௦௟௔௠ ൌ ܲ݋݌ݑ݈ܽݐ݅݋݊௧௢௧௔௟݊݁ܿݎ݁ܲ (%) ݐ ݋݂ ܲ݋݌ݑ݈ܽݐ݅݋݊ ൌ ௧௢௧௔௟ Literacy Urbanization (% in cities) GDP real growth rate݊݁ܿݎ݁ܲ ݋݊ ܴܽݐ݅݋ ܲ݋݌ݑ݈ܽݐ݅݋݊ܲ݋݌ݑ݈ܽݐ݅݋݊௧௢௧௔௟݈ܴ݅݃݅݁ ݎ݋ݑܨ (Four religion(FRR) ratio (FRR Four religion ratio (FRR) Mean 82.28 Mean 56.52 Mean 3.80 ݋݊ ܴܽݐ݅݋݈ܴ݅݃݅݁ ݎ݋ݑܨ (FourFour religionreligion ratioratio (FRR)(FRR ሻ Standard Error 1.49 Standard Error 1.72 Standard Error 0.27ݏݐܽ݃݁݊݁ܿݎሺ݌݁ݏݐ ܴ݈݁݅݃݅݋݊ݏ݁݃ݎܽܮ ǡ Ͷݐ݄݀ݎ͵ ݐǡ ʹ݊݀ǡݏൌ  ෍ ͳ

ሻ Median 91.80 Median 58.00 Median 3.85ݏݐܽ݃݁݊݁ܿݎሺ݌݁ݏݐ ܴ݈݁݅݃݅݋݊ݏ݁݃ݎܽܮ ǡ Ͷݐ݄݀ݎ͵ ݐǡ ʹ݊݀ǡ ܴܽݐ݅݋ݏൌ  ෍ ܴ݈݁݅݃݅݋݊ ͳݎ݋ݑܨ Years Independent ݋݊ ܴܽݐ݅݋݈ܴ݅݃݅݁ ݎ݋ݑܨ YearsYears Independent Independent ሻ Mode 99.00 Mode 52.00 Mode 4.20ݏݐܽ݃݁݊݁ܿݎሺ݌݁ݏݐ ܴ݈݁݅݃݅݋݊ݏ݁݃ݎܽܮ ǡ Ͷݐ݄݀ݎ͵ ݐǡ ʹ݊݀ǡ ܴܽݐ݅݋ݏൌ  ෍ ܴ݈݁݅݃݅݋݊ ͳݎ݋ݑܨ ݋݊ ܴܽݐ݅݋݈ܴ݅݃݅݁ ݎ݋ݑܨ ሻ Standard Deviation 20.08 Standard Deviation 23.17 Standard Deviation 3.70ݏݐܽ݃݁݊݁ܿݎሺ݌݁ݏݐ ܴ݈݁݅݃݅݋݊ݏ݁݃ݎܽܮ ǡ Ͷݐ݄݀ݎ͵ ݐǡ ʹ݊݀ǡݏYears Independent ൌ  ෍ ͳ ݌݁݊݀݁݊ܿ݁݁݀݊ܫ݀݁ݎ݈ܽܿ݁ܦ ݋݂ ݎܻܽ݁ ሻݏݐܽ݃݁݊݁ܿݎሺ݌݁ݏሻ ܴ݈݁݅݃݅݋݊ݏݐܽ݃݁݊݁ܿݎሺ݌݁ݏݐ ʹͲͳʹ െܴ݈݁݅݃݅݋݊ݏ݁݃ݎܽܮ ݐൌݏ݁݃ݎܽܮ ǡ Ͷݐ݄ Ͷݐ݄݀ݎ͵ ǡ݀ݎ͵ ݌݁݊݀݁݊ܿ݁ ʹ݊݀ǡ ʹ݊݀ǡ݁݀݊ܫ ݐǡݏݐǡ ͳݏ݋݂ൌൌ  ෍ ෍ ͳݏݎܻܽ݁ Years Independent Minimum 21.80 Minimum 11.00 Minimum -13.00 Years IndependentIndependent ܻ݁ܽݎݏ݋݂ ܫ݊݀݁݌݁݊݀݁݊ܿ݁ ൌ ʹͲͳʹ െ ܻ݁ܽݎ ݋݂ ܦ݈݁ܿܽݎ݁݀ܫ݊݀݁݌݁݊݀݁݊ܿ݁ Table 1. Formulae of calculated variables. Maximum 100.00 Maximum 100.00 Maximum 16.30

ܻ݁ܽݎݏ݋݂ ܫ݊݀݁݌݁݊݀݁݊ܿ݁ ൌ ʹͲͳʹ െ ܻ݁ܽݎ ݋݂ ܦ݈݁ܿܽݎ݁݀ܫ݊݀݁݌݁݊݀݁݊ܿ݁ Buddhism% Muslim % Christian % ܻ݁ܽݎݏ݋݂ ܫ݊݀݁݌݁݊݀݁݊ܿ݁ ൌ ʹͲͳʹ െ ܻ݁ܽݎ ݋݂ ܦ݈݁ܿܽݎ݁݀ܫ݊݀݁݌݁݊݀݁݊ܿ݁ Since much of the dataܻ݁ܽݎݏ݋݂ collected ܫ݊݀݁݌݁݊݀݁݊ܿ݁ is directly related ൌ ʹͲͳʹ to െthe ܻ݁ܽݎ definition ݋݂ ܦ݈݁ܿܽݎ݁݀ܫ݊݀݁݌݁݊݀݁݊ܿ݁ of the collector, an Mean 3.25 Mean 24.12 Mean 56.16 Since much of the ܻ݁ܽݎݏ݋݂data collected ܫ݊݀݁݌݁݊݀݁݊ܿ݁ is directly related ൌ ʹͲͳʹ to െthe ܻ݁ܽݎ definition ݋݂ ܦ݈݁ܿܽݎ݁݀ܫ݊݀݁݌݁݊݀݁݊ܿ݁ of the collector, an stripped or suppressed in that time of oc- and estimates when available. Standard Error 0.95 Standard Error 2.60 Standard Error 2.81 cupation, importantSince suchnote much isas the ofthe thesources 15 data countries collectedof the data. formerly is directly The industrial related tomakeup, the definition GDP real of thegrowth collector, rate, aninflation rate, Median 0.02 Median 3.47 Median 70.14 importantSince note much is theof the sources data collectedof the data. is directlyThe industrial related makeup, to the definition GDP real ofgrowth the collector, rate, inflation an rate, part ofSinceSince the much muchSoviet ofof the Unionthe data data collected incollected which is is directlyreligion directly related related to toAs the the noted definition definition above, of of the the some collector, collector, of thean an variables Mode 0.00 Mode 0.00 Mode None important note is the sources of the data. The industrial makeup, GDP real growth rate, inflation rate, wasunemploymentunemployment objectively rate, abolishedrate, urbanization, urbanization, and replaced literacy,literacy, and withand years years specified of of independence independence in my were weremodel all allcalculated required calculated using calculation. using data data Standard Deviation 12.89 Standard Deviation 35.14 Standard Deviation 38.07 important7 note is the sources of the data. The industrial makeup, GDP real growth rate, inflation rate, importantimportantatheism. notenote isis thethe sources sources of of the the data. data. The The industrial industrialBelow makeup, makeup, is GDPa GDP table real real ofgrowth growth formulas rate, rate, inflation explaining inflation rate, rate, each Minimum 0.00 Minimum 0.00 Minimum 0.10 unemploymentcollected from rate,the CIA urbanization, World Factbook. literacy, The and remainder years of independence of the data (religiouswere all calculated profiles and using FRR) data has been Maximum 85.27 Maximum 99.09 Maximum 98.07 unemploymentcollected from rate, the CIAurbanization, World Factbook. literacy, The and remainder years ofvariable’s independence of the data calculation (religious were all profiles(see calculated table). and usingFRR) has data been unemployment rate,rate, urbanization, urbanization, literacy, literacy, and and years years of of independence independence were were all all calculated calculated using using data data Judaism % Sikhism % Hinduism % collected from the CIA World Factbook. The remainder of the data8 (religious profiles and FRR) has been basedbased of of data data collected collected byby thethe World ChristianChristian Encyclopedia EncyclopediaSince8. This. Thismuch data data wasof was thedeemed deemed data “best” collected “best” since since itis was itdi was - Mean 0.50 Mean 0.04 Mean 2.26 collected from the CIA World Factbook. The remainder of the data (religious profiles and FRR) has been Standard Error 0.39 Standard Error 0.01 Standard Error 0.68 collectedcollected fromfromDescription thethe CIACIA World World of Factbook. Factbook.the Data TheThe remainder remainder rectlyof of the the8 data relateddata (religious (religious to the profiles profiles definition and and FRR) FRR) hasof has beenthe been col - based of data collected by the World Christian Encyclopedia . This data was deemed “best” since it was Median 0.01 Median 0.00 Median 0.01 thethe most most thorough thorough and and largelarge‐‐scale of anyany datadata source sourcelector, in in the the8 fieldan field importantsince since it hadit had estimatesnote estimates is thefor forevery sources every of based of data collected by the World Christian Encyclopedia . This data was deemed “best” since it was Mode 0.00 Mode 0.00 Mode 0.00 based ofof datadata collectedcollected by by the the World World Christian Christian Encyclopedia Encyclopedia8.8 This. This data data was was deemed deemed “best” “best” since since it itwas was the Themost thoroughdata collected and large for‐scale this of any study data consource- thein the data. field Thesince itindustrial had estimates makeup, for every GDP real sistscountrycountry of ina in the cross-sectionalthe world, world, which, which, evencollection if estimated, from makes makes growth for for an an even rate,even playing playinginflation field field on rate, on which which unemployment to compareto compare all all Standard Deviation 5.28 Standard Deviation 0.20 Standard Deviation 9.26 the most thorough and large‐scale of any data source in the field since it had estimates for every Minimum 0.00 Minimum 0.00 Minimum 0.00 thethe188 mostmost of thoroughthethorough 196 andcountriesand large large‐‐scalescale in theof of any any world. data data source sourceThe in inrate, the the field fieldurbanization, since since it it had had estimates literacy,estimates for andfor every every years of in- country in the world, which, even if estimated, makes for an even playing field on which to compare all Maximum 71.39 Maximum 2.19 Maximum 72.82 omittedcountryreligions,religions, in eight eventhe even world, in inwere countries countries which, left even withoutout ifdue estimated, proper to either census census makes data. data. dependencefor Thisan This even was was playingalso alsowere important important field all oncalculated becausewhich because to the compare using the definition definition dataall country in the world, which, even if estimated, makes for an even playing field on which to compare all Years of independence Four-firm concentration (of religions) Irreligion % countryunreliablereligions, in the even gross world, in countries domestic which, evenwithout product if estimated, proper (GDP) census makes data. forcollected This an even was alsoplayingfrom important thefield CIAon because which World to the compare definitionFactbook. all of irreligion differed from source to source particularly since different sources defined irreligion Mean 127.82 Mean 92.00 Mean 5.88 figures,religions,of irreligion evenmissing differed in countries religious from withoutsource profile to proper source estimates, census particularly data. The This since remainder was different also important ofsources the becausedata defined (religious the irreligion definition profiles religions, even in countries without proper census data. This was also important because the definition Standard Error 18.81 Standard Error 0.995 Standard Error 0.66 religions,orof becauseirreligion even differedof in countriesother from anomalies sourcewithout to proper sourcein the census particularly data. data. and sinceThis FRR) wasdifferent also has important sources been baseddefined because of irreligion datathe definition collected differently, so using data from multiple sources would have been out of the question. Median 52.00 Median 97.96 Median 1.99 Allofdifferently, irreligionof the data, differedso using religious from data source from or multiple economic,to source sources particularly was would by since havethe different beenWorld out sources ofChristian the defined question. irreligionEncyclopedia8. of irreligion differed from source to source particularly since different sources defined irreligion Mode 21.00 Mode 100.00 Mode None ofderiveddifferently, irreligion from differed so using the from data most source from recent multiple to source publishing sources particularly would This sincehave beendifferentdata outwas ofsources deemedthe question. defined “best” irreligion since it was the 8 Standard Deviation 253.75 Standard Deviation 13.464 Standard Deviation 8.94 differently,8 David B. Barrett,so using et.al, data “World from Christianmultiple Encyclopedia”.sources would Oxfordmost have University beenthorough out Press. of theand 2001. question. large-scale Web Accessed of 2011. any data differently, David B. soBarrett, using et.al, data “Worldfrom multiple Christian sources Encyclopedia”. would have Oxford been University out of the Press. question. 2001. Web Accessed 2011. Minimum 0.00 Minimum 32.01 Minimum 0.00 differently,8 so using data from multiple sources would sourcehave been in outthe of field the question. since it had estimates for David7 B. ”RevelationsBarrett, et.al, “Worldfrom the Christian Russian Encyclopedia”. Archives: Oxford University Press. 2001. Web Accessed 2011. Maximum 2000.00 Maximum 100.00 Maximum 49.76 8 David B. Barrett, et.al, “World Christian Encyclopedia”. Oxford University Press. 2001. Web Accessed 2011. 8 ANTI-RELIGIOUS CAMPAIGNS”. Library of 8 David B. Barrett, et.al, “World Christian Encyclopedia”. Oxford University Press. 2001. Web Accessed 2011. Congress David B. Barrett,. July 22, et.al, 2010. “World Web Christian accessed Encyclopedia”. October Oxford University8 David Press. B. 2001.Barrett, Web et.al, Accessed “World 2011. Christian Table 2. Summary Statistics of the Data.

2011. http://www.loc.gov/exhibits/archives/anti. Encyclopedia”. Oxford University Press. 2001. html Web Accessed 2011. -28- ECONPress An Econometric Inquiry into the Effect of Religious Profiles on National Wealth -29- every country in the world, which, even if not a per country average like suggested in that economic theory considers to be strong be accounted for by the other independent estimated, makes for an even playing field this study’s data. Similar observations can factors that account for GDP. The remain- variables then we assume multicollinearity on which to compare all religions, even in be made about the 56.16% Christian that ing nine variables have been included to ac- exists. This creates issues with the VIFs as- countries without proper census data. This was mentioned before. count for the suspected impact that religion sociated with the industrial makeup vari- was also important because the definition would have on the model. With all seven- ables (the measurement of GDP from the of irreligion differed from source to source Some numbers from the above table teen variables included, initial estimates of agricultural, service, and industrial sectors particularly since different sources defined have some very interesting implications. the model did not live up to expectations of an observed countries economy), and irreligion differently, so using data from The variation in the dependent variable and immediately raised major questions the variables representing the Christian multiple sources would have been out of (GDP per capita) was expectedly great from about possible error. percentage of the population of a country the question. prior knowledge of poor wealth distribu- and a Muslim percentage of the population tion of society and was reflected as such in With all seventeen variables incorporat- of a country. The VIFs for these problem Table 2 contains a summary of the data the standard deviation of $21,272, which ed, the model was only able to account for variables were calculated as 105.9, 150.73, that has been collected and entered for all of compared to the mean of $15,431 was very 26.62% of the variation found in GDP per 123.79, 20.1, and 15.97 respectively; all of the independent variables from this model large. The median of $8,400 per capita capita. This relatively low adjusted R2 did which are substantially over the accepted testing the effect of religious profiles on per GDP has the most interesting implications not meet expectations since variables were rule of thumb amount. capita GDP. though. The median suggests that the ma- included that were expected to be strong jority of countries around the world are indicators of GDP per capita. This hinted To correct for multicollinearity in the There are a few major clarifications that struggling (portrayed by a median well less towards the possible existence of a specifi- model, the culprit variables were examined need to be made about the data specifically. than the mean, suggesting that more that cation error and more specifically that the to determine the root causes of the multi- The first difference is described by the dis- 50% of countries in the world live below wrong form function may have been cho- collinearity and to establish which variables crepancy in average populations by religion the world average) and the mean statistic sen. This was supported by a graphical pre- should be removed to correct the model. from their counterparts that reflect the was so high likely because of some outliers sentation of the data collected for GDP per Since the VIFs on the industrial makeup of world’s population. According to adhear- skewing the data upwardly, suggesting that capita, which portrays the dependent vari- the observed country were so high, and the ents.com, 33% of the world’s population is a few countries have abnormally high levels able as exponentially growing from obser- three make up an identity in which the three Christian9, whereas the data for this model of wealth. vation to observation, suggesting that the must equal 100% since the entirety of GDP shows the average country at 56.16%. This log-level form should be used. is generated through either agriculture, ser- difference arises because the data collected Another set of data worth discussing is vice, or industry and therefore represent a was based on each country producing an the data retaining to the variable describ- Once the model was specified in the textbook example of multicollinearity. To unweighted percent of the population that ing Sikhism in a population. This variable’s log-level form, suggested to be the correct solve for this, the variables representing the does not take into account the relative size data has relatively low variation and there- form from the graphical depiction of GDP percent of GDP from service and percent of the country, so for the purposes of this fore is expected to have little to no explana- per capita, some of the expectations that of GDP from industry were removed. This study, the Cook Islands have the same tory power over GDP per capita. This is were previously unmet became fulfilled. left just the variable measuring the percent weight as United States or India. important to keep in mind since it will like The new model accounted for 77.07% of of GDP from agriculture which, with the lead to the variables omission. The same the variation of the dependent variable other two variables excluded, had a VIF of The second clarification that needs to be can be said for Judaism since the mean is (now the natural log of GDP per capita just 2.24; a great improvement from 105.9. made refers to the interpretation of means only 0.5, meaning a sum of Jewish percent- and therefore not comparable to the origi- from the above data. Since smaller coun- ages is only 94 (since there are 188 observa- nal model in which GDP per capita was the The correction for multicollinearity as- tries have larger impacts on this data set, tions) and 71.39 of that comes from one dependent variable) but still showed signs sociated with the religious variables (specifi- a variable with a mean above what is sepa- country hinting at relatively low variance, of some major econometric issues includ- cally the variables measuring the percentage rately published should be interpreted dif- particularly if you were to exclude the out- ing multicollinearity (as suggested through of the population that is Christian in the ferently. This means that the $15,431 GDP lying observation. variance inflation factors), irrelevant vari- observed country and the percentage of the per capita mean should not be compared to ables, and heteroskedasticity (as suggested population that is Muslim in the observed the $9,216 published by the World Bank. through White’s test). country) was achieved in a slightly different This is because the World Bank’s publica- method than that of the industrial makeup tions are based on a per person average and Estimation of the Model The first of the issues addressed, multi- solution since the multicollinearity was not collinearity, was identified by creating vari- as obvious as the identity observed in the 9 “Major Religions of the World Ranked When initially estimating the model for ance inflation factors (VIFs) which can be industrial makeup variables. by Number of Adherents”.Adherents.com. August religion’s impact on Gross Domestic Prod- compared against the rule of thumb of 5. 9, 2007. Web. Accessed Oct. 2011. http://www. uct (GDP) per capita, seventeen variables This means that if more than 80% of the To investigate which variables might adherents.com/Religions_By_Adherents.html were incorporated including eight variables variance of one independent variable can be causing the high VIFs for the Christian -30- ECONPress An Econometric Inquiry into the Effect of Religious Profiles on National Wealth -31- and Muslim variables, separate regressions the White test to test for heteroskedasticity, Ultimately, the remaining variables literacy (hypothesized to have a positive im- were run in which the Christian and Mus- to test for the problem, and indeed the re- (percent of GDP from agriculture, infla- pact on GDP per capita) and GDP from lim variables were set as the dependent sults suggested that heteroskedasticity did tion rate, unemployment rate, and literacy agriculture (hypothesized to have a negative variables. The variables that most likely exist. rate) were all tested in multiple functional impact on GDP per capita) were both sig- caused the multicollinearity, which would forms to determine the positive or nega- nificant, while other key variables such as be represented by high t-statistics in both To fix this issue, the model was esti- tive impact that the change in form would inflation rate and unemployment were not models, included the other specific reli- mated again with robust standard errors. have on the model. After testing each vari- significantly different from zero. gions measured (Sikhism, Judaism, Hin- This new model using robust standard er- able in their level form as well as the natu- duism, Buddhism, and Irreligion) and the rors saw all of the standard errors increase, ral log form the model’s R2, RESET test To focus on the main point of the re- variable measuring the number of years except for the standard errors of the four f-statistic, VIF, and White test results were search though, it was necessary to test the independence the observed country had religion ratio variable and the Hinduism compared to determine the best form func- significance of the religious variables as a experienced. These variables, particularly variable. Although the Hinduism variable tion on a variable by variable basis. The whole. This entailed running an F-test on Judaism, Sikhism, and Irreligion, were not remained at a level of insignificant impact results of these comparisons suggested that the five variables describing religious sta- statistically significant in measuring GDP on the dependent variable, the four reli- the variables associated with inflation rate, tistics. This produced an F-statistic of only per capita and did not contain a great gion ratio variable went from insignificant unemployment rate and percent of GDP .7639 which at the degrees of freedom pro- amount of variation in the data collected, to significant with the inclusion of robust from agriculture would all be better served vided by the data produced a P-value of leading me to believe they were weak indi- standard errors. Oppositely, the variable ac- in the log-log form instead of the semi-log 0.42 on the f-statistic10. This is interpreted cators of the observed GDPs and could be counting for urbanization became insignifi- form. It is important to note here though as meaning that the inclusion religious in- readily dropped from the model. Similarly, cant with the increase in its standard error. that when minimizing the F-statistic of the dicators in a model explaining GDP per the t-statistic associated with the years of This ultimately led me to the realization RESET test, versions of the model exist capita has an insignificant impact on the independence, like the t-statistics of Juda- that urbanization was the variable creating that were able to get the F-statistic as low model’s statistical significance. ism and Sikhism, were relatively low mean- heteroskedasticity in the model, and led me as 1.50 (compared to the 4.11 produced ing that we (as researchers) could not ac- to omit the variable. Omitting the variable by the final model) but this required drop- cept the variable to be statistically different resulted in a correction of the results from ping the R2 down as low as .66 compared from zero, leading me to believe that the the White test, as well as the same desired to the .82 that the final model produced, Model Results best course of action would be to drop the result that the robust standard errors gener- and accepted heteroskedasticity, which can variable. ated with regard to four religion ratio. be corrected by using Robust standard er- See Table 3. rors. The results for this alternative model With the above corrections made, the Now down to nine independent vari- which reduces the RESET f-statistic are in VIFs for the variables Christian and Mus- ables, the model accounting for variation in appendix 1. lim both dropped below 10, but were un- the natural log of GDP per capita was sig- Conclusions able to drop below 5 without omitting nificantly stronger as it was cleared of mul- With the model finally correctly speci- the other variable. In the best interest of ticollinearity and heteroskedasticity follow- fied, the correlation coefficients, robust This study and subsequent regression the investigatory power of the model both ing the above fixes. The last specification standard errors, and t-statistics were calcu- analysis shone a light on a real world is- variables were left in since the effect of spe- test that was run was the Ramsey’s RESET lated for the remaining variables as well as sue that haunts all political systems, not cific religions would be best observed in the test to test for omitted variables. The results the F-statistic for the model as a whole. This just that of developing nations. Although two largest religions in the world. This of of the RESET test suggested that there was final model accounted for a large amount of the regression proved that the religious course doesn’t completely rule out the pos- in fact an omitted variable, which is be- variation in the dependent variable as rep- profile of a country does not have a sig- sibility of multicollinearity, but because the lieved to be the omitted measure of religi- resented by the R2 of 0.82; a very high R2 nificant impact on the country’s observed VIFs were low enough, suggested that the osity for each country. This variable would for cross sectional data. This coupled with Gross Domestic Product, the statistical effect that the multicollinearity has on the affect each variable in the model differently, the F-statistic of 99.37 (significant even at significance of the four religion ratio and variable’s standard errors is low enough to by giving weight to the religions on a coun- the 0.0001 level) gave good indication to Christian population of an observed coun- proceed with the regression analysis and try by country basis instead suggesting that the strong explanatory power of the model. try could be interpreted as evidence for the more specifically hypothesis testing. all members of a religion practice with the same devotedness from country to country. Some other highlights of the regres- The next issue that arose in the model Unfortunately this data is not available, and sion results include the statistically signifi- 10 Calculated by using the “p-Value Calculator for an F-Test” on Dr. Daniel Soper’s accounting for variations in the natural log admittedly leaves something to be desired cant effect that the four religion ratio has website. of GDP per capita is in reference to hetero- for future expansion of the model as more in a negative direction, which verifies the -Dr. Daniel Soper “Statistics Calculators” skedasticity. The model, which now incor- countries conduct extensive censuses. assumptions that diversity would have a Statistics Calculators Index, Web. 2006. http:// porated eleven variables, was put through positive effect of GDP per capita. Similarly, www.danielsoper.com/statcalc3/calc.aspx?id=7 -32- ECONPress An Econometric Inquiry into the Effect of Religious Profiles on National Wealth -33-

Semi-Log Model Semi-Log Model w/ (Robust Std Err) Percent of GDP from Agriculture -.7113~ (.0469)* -.7113~ (.0584)* Unemployment Rate -.0475~ (.0504) -.0475~ (.0716) Inflation Rate -.0017~ (.0573) -.0017~ (.0593) Literacy .0183 (.0035)* .0183 (.0037)* Percent of Population Christian .0074 (.0029)* .0074 (.0030)* Percent of Population Muslim .0049 (.003) .0049 (.0031) Percent of Population Buddhist .0081 (.0046)* .0081 (.0049) Percent of Population Hindi .0038 (.0056) .0038 (.0049) Four Religion Ratio -.0738 (.0494) -.0738 (.0342)*

R Square 0.8231 0.8231 Adjusted R Square 0.8120 -- F-statisticistic ( 9, 143) 73.94* 99.37* *-Significant at Alpha of .05 ~ - Log-Log Est.

Table 3. Regression results. argument supporting government policy to control religious profiles in its country. It is observed that some other coefficients, specifically the percent of GDP from the agricultural sector, have much stronger impacts on the model and would make for more productive policy topics with respect R to many of the developing nations around the world. This study is admittedly limited due to the lack of data for so many countries around the world and in the future, studies within economics of religion could be bet- ter served by a model similar to this one if panel data could be collected. This would prove substantially stronger since it would be implied (since it is one observation over Appendix 1 (opposite top). Linear Regres- time) that similar methodologies of data sion. collection would be used in panel data, whereas the consistency of religious data Appendix 2 (opposite bottom). Final available today, like that used in this model, Regression. is not nearly as accurate as it could be. -34- ECONPress Equity Volatility across Industries from IPO Day -35-

Works Cited Equity Volatility across IPOs than they are after years of active trading. In addition, industries that are Industries from IPO Day characterized by increased uncertainty typi- Brown, Timothy T. “A Monetary Valu- McCleary, Rachel M. , “Religion and cally include companies with more volatile ation of Individual Religious Behav- Economic Development: The advantage stock prices. This study examines the trends ior: The Case of Prayer” (Working of moderation”, Hoover Institution, of intraday stock volatility by industry over Paper), The Association of Religion Stanford University, 147 (March 28, Andrew Nielsen Lewis time from IPO date and determines which Data Archives, Accessed Nov. 2011 2008) Accessed Oct. 2011 http:// Princeton University industries have the most volatile IPOs, http://www.thearda.com/work- www.hoover.org/publications/ which industries’ stocks take the longest ingpapers/download/Valuing%20 policy-review/article/5729 amount of time to stabilize after IPO day, Religious%20Behavior.pdf Abstract and which industries’ stocks stabilize the Noland, Marcus , “RELIGION, CUL- most over time. Central Intelligence Agency, “The World TURE, AND ECONOMIC PER- While the volatility of any given stock Factbook”, cia.gov, Accessed Oct. FORMANCE” (Working Paper), The changes over time, certain identifiable fac- Although many studies have investi- 2011 https://www.cia.gov/library/ Peterson Institute for International Eco- tors consistently contribute to increased gated returns following IPO date or general publications/the-world-factbook/ nomics Accessed Oct. 2011 http://www. stock price volatility. For example, stocks trends in equity volatility, they have not iie.com/publications/wp/03-8.pdf are typically more volatile immediately fol- focused on modeling trends in volatility Fitzgerald, Michael , “Satan, the great lowing their IPOs than they are after years relative to IPO dates. The study of de facto motivator” Boston.com (Boston, World Christian Database Vol.2 , of active trading. In addition, industries IPO returns is more appealing in that it has MA) Nov.15.2009 http://www. “Excel Datafile” worldmapper.org, that are characterized by increased uncer- quick and obvious applications – after dis- boston.com/bostonglobe/ideas/ http://www.worldmapper.org/ tainty typically include companies with covering a way to predict abnormal stock articles/2009/11/15/the_curious_eco- data/nomap/religion_data.xls more volatile stock prices. This study exam- returns around an IPO, traders or hedge nomic_effects_of_religion/?page=full ines the trends of intraday stock volatility fund managers can quickly apply their new by industry over time from IPO date and knowledge to realize excess gains. The find- Franck, Raphaël and Iannaccone Laurence determines which industries have the most ings of this study regarding volatility trends R., “Why did religiosity decrease in the volatile IPOs, which industries’ stocks take from IPO, however, can also be used by Western World during the twentieth the longest amount of time to stabilize after investors to profit. The ability to predict century?” From the April 1, 2010 IPO day, and which industries’ stocks stabi- volatility can lend insight into forecasting Seminar, Bar-Ilan University, April lize the most over time. It uses a nonlinear option prices by using the Black-Scholes 1, 2010. Accessed Oct 2010 http:// model to estimate the trends of stock price options pricing model; being able to pre- www.biu.ac.il/soc/ec/seminar/ volatility in various industries as well as the dict with some certainty the change in a data/4_01_2010/franck%20iannac- overall market.1 stock’s volatility from its IPO day will also cone%20religiosity%20biu.pdf allow a trader to predict with more accuracy the motion of related option prices. With Grier, Robin , “The Effect of Religion information about volatility trends in an on Economic Development: A Cross Section I: Introduction industry, an investor can more accurately National Study of 63 Former Colonies” value a stock’s options. Kyklos: International Review for Social While the volatility of any given stock Sciences, 50, (1997). Accessed Oct changes over time, certain identifiable fac- Additionally, the findings of this study 2011. http://faculty-staff.ou.edu/G/ tors consistently contribute to increased can help companies to make better choices Robin.M.Grier-1/religion.pdf volatility. For example, stocks are typically regarding their own IPOs – having an un- more volatile immediately following their derstanding of typical industry volatility Iannaccone, Laurence R. , “Introduc- will help to guide decisions on whether tion to the Economics of Religion” to go public and how to price IPOs. This Journal of Economic Literature, 1 Acknowledgements: I greatly appreciate will not only benefit the few who stand to XXXVI (September 1998). Accessed the guidance provided to me by Professor Yuliy make extraordinary profits from such busi- Oct 2011. http://www.scribd.com/ Sannikov (Princeton University Department of Economics), Wei Cui (Princeton University ness deals but the entire stock market and doc/62863336/Iannaccone-Introduc- Department of Economics), and Oscar Torres- economy as the IPO market becomes more tion-to-the-Economics-of-Religion Reyna (Princeton University Data and Statistical efficient. The findings can also be used for Services) during this study. risk management purposes, in behavioral Equity Volatility across Industries from IPO Day Equity Volatility across Industries from IPO Day

was meant to reflect the real effects of dividend payments on shareholder value. For example,Microsoft was meant to reflect the real effects of dividend payments on shareholder value. For example,Microsoft issued a one-­‐time special dividend of $3.00 on November 15, 2004; because the price drops associated issued a one-­‐time special dividend of $3.00 on November 15, 2004; because the price drops associated with dividend payouts do not affect shareholder value, 3 was added to the closing prices, low prices, and with dividend payouts do not affect shareholder value, 3 was added to the closing prices, low prices, and high prices for allMicrosoft observations on or after the day the dividend was issued. This does not lead high prices for allMicrosoft observations on or after the day the dividend was issued. This does not lead to a perfectadjustment fordividend payouts. S ince no stocks paid out dividends within their first thirty to a perfectadjustment fordividend payouts. S ince no stocks paid out dividends within their first thirty days of trading, however,no observations used in regression were affected; as a result, this inaccuracy days of trading, however,no observations used in regression were affected; as a result, this inaccuracy did not affect results. did not affect results.

The data is subject to some level of selection bias. All of the companies chosen were still trading as of The data is subject to some level of selection bias. All of the companies chosen were still trading as of December 31, 2009; as a result, companies taken private for reasons including bankruptcy and December 31, 2009; as a result, companies taken private for reasons including bankruptcy and acquisition may be underrepresented. Furthermore, the accuracy of the S&P 500 as a true market acquisition may be underrepresented. Furthermore, the accuracy of the S&P 500 as a true market benchmark is not perfect because the S&P 500 includes only large companies that have maintained benchmark is not perfect because the S&P 500 includes only large companies that have maintained consistent profitability. If stock resilienceor company sizes are correlated withIPO period volatility consistent profitability. If stock resilienceor company sizes are correlated withIPO period volatility trends, the results of this study may be skewed as a result. trends, the results of this study may be skewed as a result. Section IV: Methodology Section IV: Methodology

The methodology followed throughout this study consists oftwo processes. First is the calculation of The methodology followed throughout this study consists oftwo processes. First is the calculation of values that represent average intraday price volatility foreach industry. Second is the nonlinear 
Equity Volatilityvalues that across represent Industries average from intraday IPO price Day volatility foreach industry. Second is the nonlinear 
regression of values against time from IPO in order to estimate volatility trends following IPO day in regression of values against time from IPO in order to estimate volatility trends following IPO day in Equity Volatility acrosswas meant Industries to reflect from the IPO real Day effects of dividend
payments on shareholder value. For example,Microsoft Equity Volatility across Industries from IPO Dayeach industry. -36- ECONPress each industry.
-37- issued a one-­‐time special dividend of $3.00 on November 15, 2004; because the price drops associated was meant to reflect the realEquity effects Volatility of dividend across Industries payments from on shareholder IPO Day value. For example,Microsoft Methodology Subsection I: Calculating with dividendMethodology payouts Subsection do not affect I: Calculating shareholder value, 3 was added to the closing prices, low prices, and finance studies, and other industry-based equity returns in “Stock Returns and Vola- issuedreplaced a one with-­‐time their special absolute dividend values of before $3.00 on NovemberCalculating 15, 2004 ; because the price drops associated stock studies. tility” (1990, p. 211). This study differs in continuing. Since CRSPfrom cannot IPO. O automatin 
 
- IPO day, the variableequals 1 . On the day immediately  following IPO, the variable that it only analyzes and models trends in cally adjust priceshigh to pricesreflect for the all Microsoft impact of observations TheThe calculation calculation on or after process the process day thewas was dividendrun runindividually in- was using issued. This data does setsthat not include lead the trading history forthe S&P with dividend payouts do not affect shareholder value, 3 was added to the closing prices, low prices, and price volatility instead of returns. dividend payments, a cumulativeEquityequalsThe Equity calculation Volatility 2. For dividend Volatility each across process additional acrossdividually Industries was Industries day run individuallyusing from data from IPO IPO, the sets using Day variable IPO that Day data includeis sets incremented that the include by the one. trading The creation history of this forthe S&P payment variableto was a perfectgeneratedadjustment and added for dividend trading500 payouts. history and
each S forince of the no the S&P ten stocks selected 500 paid and industry outeach dividends groups provided within their by first MarketWatch thirty . For allexamined data sets, Section II: Literature Review Section III: Data highto all prices price for variables; allMicrosoft this500 observations adjustment and
each of was on the ten orof afterselected the the ten day industry selected the dividend industry groups provided wasgroups issued . by provid This MarketWatch does- not . leadFor allexamined data sets, EquityEquity Volatility Volatilityvariable across across makes Industries comparison Industries from from ofthe IPO IPO chronologically Day Day scattered IPO periods for differentstocks in each meant to reflectdays the real offrom trading effects IPO.from, however, O of IPO.n 
 
dividend O n no 
 
observationsIPOed by dayaIPO MarketWatch.day , the day counter variable , usedthe variable in variableequals For regression equals all 1 . examined On was 1 the . generatedOn were day the data affected;immediately forday each immediately as observation following a result, this following inaccuracy to IPO, mark the IPO, the variable the number variable of days that had passed Existing literature has not focused on Data for all stocks used in this study topayments a perfect adjustment on shareholder fora day dividend value. counter payouts.For variable ex- S incesets, was no a stocksday generated counter for paid each variable out observation dividends was generatedto within mark their the first number thirty of days that had passed trends in volatility from IPO date or indus- were retrieved from the Center for Research ample, Microsoft issuedindustry a one-time possible. special for each observation to mark the number fromfromdid IPO. IPO. not O equals nO affect n
 

 
equals 2 . results.For IPO 2 eachIPO. For day day each, additional the , the variable additional variable dayequals equals from day 1 . from1 On IPO,. the On the variable the IPO, the day day variable immediately is immediately incremented is incremented following following by one. by IPO, IPO,The one. the thecreation The variable variable creation of this of this try-specific volatility trends. in Security Prices (CRSP) daily stock data- daysdividend of trading of $3.00, however, on Novemberno observations 15, 2004; used of in days regression that had were passed affected; from IPO. as a On result, this inaccuracy a 6 base via Wharton Research Data Services. because the price drops associated with stock’s IPO day, the variable equals 1. On 6 equals 2. For each additional day from IPO, the variableis incremented by one. The creation of this Differences between volatility levels For each stock, all available trading data dividend payoutsequals do 2not. variableActualFor affect eachvariable volatility makes shareholder additional makescomparison ( ) was comparison daythe calculated from ofdaythe immediately of IPO, chronologically thefor the every variable chronologically observation is following incremented scattered scatteredusing IPO, IPO by 
 
periodthe one. IPO period The s for intraday creation differents for different trading of stocks this stocks rangein each in each and IPO behavior across industries are was retrieved during the period ranging didvalue, not 3 affect was added results.The to data the closing is subject prices, to low some variable level of equals selection bias2. .For All each of the additional companies day chosen were still trading as of variable makescomparison industry possible. ofthe chronologically scattered IPO periods for differentstocks in each recognized phenomena. In “Stock volatil- from January 1, 1925 through December prices, and highvariable prices makesforindustrysquared all Microsoftcomparison possible. relative ob to of- closingthe from chronologically IPO, price. 
  
the variable scattered is IPOincrementedhigh period prices ( for P Hby) , different low pricestocks (PL), and in each closing price (PC) ity in the new millennium: how wacky is 31, 2009; data after December 31, 2009 servations on or Decemberafter the day 31, the 2009 dividend; as a result one., companies The creation taken privateof this forvariable reasons makes including bankruptcy and Nasdaq?,” G. William Schwert notes that was not comprehensive or fully accurate Thewas data issued. is subject This does to not some lead level to ofa perfect selection bias comparison. All of the of the companies chronologically chosen were scattered still trading as of industryindustry possible. possible.were used to calculate volatility for each trading day: technology stocks and recent IPO stocks in the CRSP database. The decision to use adjustment for dividendacquisitionActual payouts. mayActual volatility be Since volatility underrepresented ( no) was ( IPO )calculated was periods calculated . Furthermore, for for every for different every observationthe accuracy stocks observationusing in of each the using 
 
in S&P- 
 
500intraday asintraday a trading true trading market range range December 31, 2009; as a result, companies taken private for reasons including bankruptcy and exhibit much higher trading volatility than trading data from before 2010 should not stocks paid out dividends within their first dustry possible. other stocks (2002, p. 3-4). A model con- have a significant impact on results. thirty days ofActual trading, volatility however, squared ( ) nowas observa calculated relative - to for closing every observation price. 
  
using 
 
high priceintraday( PH ) trading, low price range ( PL) , and closing price (PC) Actualbenchmark volatilitysquared is not ( relative) was perfect calculated to closing because for every price. the 
  
S&P observation 500 includesusing onlyhigh 
 
large price companies ( PintradayH), low that price trading have ( PL), and range maint ained closing (1) price (PC) structed by Michelle Lowry, Micah Officer, acquisitiontions used may in regression be underrepresented were affected;. Furthermore, as a Actualthe accuracy volatility of the ( ) S&Pwas calculated 500 as a for true market and Schwert shows that technology stocks First, the stocks that were components result, this inaccuracy did not affect results. every observation using the' stock’s!
"( intraday squared relativewere to closing used to price. calculate 
  
volatility for high each price trading( PH), low day: price (PL), and closing price (PC) squaredconsistent relativewere profitability. used to to closing calculate If stock price. volatility 
  
resilience for or company each high trading sizes $ price are day( :P Hcorrelated ), low price with (PL),IPO and period closing volatility price (PC ) see returns that are different from other of the S&P 500 on December 31, 2009 benchmarkEquity Volatility is not perfect across Industries because the from S&P IPO 500trading Day includes onlyrange large squared companies relative that haveto closing maint ained stocks on a statistically significant level were studied in aggregate to create a broad The dataEquity is subject VolatilityMicrosoft to some across level Corporation Industries of se- price. had from its Each IPO initial Day observation’s public offering high on price March (P 13,H), 1986. O n its first day of trading, its weretrends, used the to calculate results volatility of this studyfor each may trading be skewed day: as a result. both including and excluding the technolo- market benchmark. Then a series of Dow lection bias. Allwere of usedthe companies to calculate chosenvolatility low for price each (P tradingL), and closing day: price (PC) were consistent profitability. If stock resilience or company sizes are correlated withIPO period volatility (1) gy bubble of the late 1990s and early 2000s Jones sector indexes (which were not lim- werefrom still IPO. trading O n 
 
as of December IPO day, the 31, variable 2009; equals used to1 . On calculate the day volatility immediately for following each trad IPO,- the variable (1) adjusted low price was $25.50, its adjusted high price! was" $29.25, and its adjusted closing price was (2010, p. 438). ited to S&P 500 stocks) were used to repre- as a result, companiesfrom IPO. O takenn 
 
privateIPO for day rea, -the ing variable day: equals 1 . On the day '! immediately
'"( 
 ( following IPO, the variable sent the ten sectors examined in this study. trends,sons including the results bankruptcy of this studyand acquisition may be skewed as a result. $  (1) equals 2. For each Section additional IV: day Methodology from IPO, the variable is incremented $ by one. The creation of this (1) Existing literature is more concerned The components of these indexes were may be underrepresented.$28.00. Furthermore, the '!
"( (1) equals 2. For Microsoft eachMicrosoft additional Corporation Corporation day had from its had IPO, the initial its variable initial public' offering! publicis
incremented " ( offering on March on by one. March 13, The 1986. 13, O creationn its 1986. O firstn its of this first day of day trading, of trading, its its  with IPO returns or IPO return volatility – provided by MarketWatch.2 An inaccurate accuracy of the S&P 500 as a true market $ which can help to predict immediate returns intraday trading range assigned to one ob- benchmarkvariable makes is notcomparison perfect because ofthe thechronologically S&P Microsoft scattered IPO$Corporation period s for had different its initialstocks in each Section IV:variableMicrosoft Methodology makes Corporationcomparison adjusted had low of its pricethe initial chronologically was public$25.50, offering its scattered adjusted on March IPO high period 13, price s 1986. O for n was its different first $29.25, stocks day and of in its trading, each adjusted its closing price was from IPO investments – than with absolute servation (IdeaRC on December 31, 2009) 500 includes MicrosoftonlyThe mlargeethodadjusted Corporation companiesology low followed price hadthat its throughout was public$25.50, initial publicoffering its this offering adjusted study on consists on March high March price of13,two 13,1986. processes. was 1986. O Onn $29.25, itsits first First and day is its the of adjusted calculation trading,(2 ) its closing of price was stock price volatility near IPO. Investiga- was removed from the Consumer Services haveindustry maintained possible. consistent profitability. If first day of trading, 'its adjusted
 ( low price adjusted low price$28.00. was$25.50, its adjusted high price was $29.25, and its adjusted closing price was tions of volatility trends focus more on pe- industry data set prior to regression. stock resilienceindustryadjusted orvalue company possible.s $28.00.that low price represent sizes wasare$25.50, average cor- its wasintraday adjusted $25.50, price  high volatilityits  adjusted price$ for was each high $29.25, industry price$   and.was Second its adjusted is the closing nonlinear price was 
The methodology followed throughout this study consists oftwo processes. First is the calculation of riod-specific trends or other general trends. related with IPO periodAs avolatility result,  
trends, $29.25,volatility andrating its adjusted for IPO dayclosingwas 0 price.5022321. was A higher calculated represents Actual volatility$28.00. ( ) was calculated for every observationusing 
 
intraday trading range For example, the Schwert 2002 study fo- For each stock, the data retrieved from the results of this$28.00.regression study may of be values skewed agai asnst time$28.00. from IPO in order to estimate volatility trends following IPO day in cuses on volatility trends in the NASDAQ CRSP to complete the study included com- a result. Actual volatility ( ) was calculated for every observationusing 
 
intraday trading
range values that represent average intraday price volatility foreach industry . Second is the nonlinear ( 2) (2) during the dot-com period. In another ex- pany name, CRSP-assigned PERMNO, increased volatility. (2) squared relative to closing price.

  
high price( PH), ' low price'
 (P(L
), and ( closing price (PC) ample, Schwert’s “Why Does Stock Market trading date, dividend amount, daily low each industry.  regression of squared values agai relativenst time to closing from IPO price. in 
  
order to estimate high $ volatility price$( P trendsH), following low $ price $ IPO (PL) , day and in closing (2) price (PC) Volatility Change Over Time?” deals only price, daily high price, and daily closing (2) were used to calculate volatility As a result, for each  
tradingvolatility day: ' rating 
 ( for IPO daywas 0 .5022321. A higher calculated represents with trends in overall market volatility price. All price values were automatically Section IV: MethodologyAsThis a calculation result,  
is based volatility on

   

  

  


  

 rating '   for 
 IPO ( daywas 0 .5022321. A higher calculated represents Volatility were used to calculate volatility for  each $ trading  day: $  throughout modern market history (1989, adjusted by CRSP to reflect the impact of each industry.
Methodology Subsection I: Calculating $  $  p. 1120). David Simon investigates market stock splits on real changes to equity value. The methodologyAsAs a a result, result, followedincreasTrading  
  
increased ( 2008,throughout volatility. volatilityedvolatility p. volatility. 16) . rating  
    rating As for a for result, IPO IPO day Microsoft’s day, was wherewas 0 .5022321.0 .5022321. N volatility defines A A higher higherrating the calculated calculated number of represents periods represents sampled, is:  (1) volatility trends around the dot-com bub- A database error caused some daily closing this study consists of two processes. First for IPO day was 0.5022321. A higher Methodology Subsection increasTheed calculation volatility. I: Calculating process was runindividually ' !
"( using data setsthat include the trading(1) history forthe S&P ble period in “The Nasdaq Volatility Index prices to be returned as negative numbers; is the calculationincreas of ed values volatility. that represent calculated represents increased volatility. During and After the Bubble.” Just as with as a result, all negative closing prices were average intraday price volatilityThis calculationThis for calculation each is inbased - is based on$ 

   

  

  


  

on 

   

  

  


  

'!
"( VolatilityVolatility (3) IPO inquiries and industry-based investiga- dustry.Microsoft Second Corporation is500 the and
nonlinear each had its of initial theregression ten public selected offering industryThis on calculation March groups$  13,provided is 1986. basedO n by its on first MarketWatch “the day stan of- . For trading, allexamined its data sets, tions, much volatility trend research relates Theof calculation values againstThis process calculation time from was is Trading runIPObased individually in on( 2008,order

   

  

  


  

p. using 16)dard. data   
    definition setsthat include of volatility”,  where the  trading as N defined defines history by the forthe number S&P ofVolatility periods sampled, is: 2 Components used for each index can MicrosoftThis calculation CorporationTrading is ( 2008,based had p. on its 16)

   

  

  


  

. initial   
    public offering , on where March N 13, defines 1986. O n the its first number day of of periods trading,Volatility its sampled, is: to predicting security returns. For example, to estimate volatility trends following IPO Euan Sinclair in Volatility $
& Trading' #(2008,
( p. be found at http://bigcharts.marketwatch.com/ adjusted low pricea day was counter$25.50, variable its adjusted was high generated price for each was observation $29.25, andto its mark adjusted the number closing of days price was that had passed Baillie and DeGennaro search for (but do 500day and
in each industry. of the ten selected industry groups16). provided Sinclair’s by MarketWatchdefinition,. For where all examined N defines data sets, industry/bigcharts-com/default.asp (originally adjustedTradingTrading ( low 2008, ( 2008,For price the p. p. 16) purposes 16) was.   
    .$25.50,   
    of its this adjusted study,, N where, is where high equal price N N defines to 1 defines because was the $29.25, the volatility number number and is its of of measured periods adjusted periods on a sampled, closing is: day sampled, is: -­‐ by-­‐ price was day basis : not find) correlation between volatility and accessed March 22, 2011) the number of periods sampled, is: $28.00. (3) a day counter variable was generated for each observationto mark the number of days that had passed (3) 6 $28.00.       $
& '  #
( $
& ' #
( (3()3 ) (4)   6 For the purposes of this study, N is  equal to 1 because   volatility(2) is  measured on a day-­‐by-­‐day basis : For the purposes of this study, N is equal  to 1 because    volatility is measured on a day-­‐by-­‐day basis : $
&  '  #
( '
  $( $
&
& ' ' ##

( ( $ % ' #
( (2)  For the purposes of this study, N$ is equal to 1' because $
 volatility( is measured on a day-­‐by-­‐day basis : For the purposes of this study,  N is  equal to 1 because volatility is measured on a day-­‐by-­‐day basis : 7 As a result,  
volatility rating for IPO daywas $ 0 .5022321. A $ higher  calculated represents (4) As a result,   
volatility rating for IPO daywas 0 .5022321. A higher calculated represents (4 )       increased volatility.      $
&  ' #
( $ %' #
( (4) increas ed volatility. $
& ' #
( $ %' #
( (4)           7 $
& ' #
( $ %' #
( 7 $
& ' #
( $ %' #
( This calculation is based on

   

  

  


  

Volatility This calculation is based on

   

  

  


  

Volatility 7 7 Trading ( 2008, p. 16).   
    , where N defines the number of periods sampled, is: Trading ( 2008, p. 16).   
    , where N defines the number of periods sampled, is:

(3)    (3)   $
& ' #
(  $
& '  #
( For the purposes of this study, N is equal to 1 because volatility is measured on a day-­‐by-­‐day basis : For the purposes of this study, N is equal to 1 because volatility is measured on a day-­‐by-­‐day basis :

(4)     (4)    $
& ' #
( $ %' #
(  $
& '  #
( $ %'  #
( 7 7

Equity Volatility across Industries from IPO Day

Equitywas Volatility meant across to reflect Industries the real from effects IPO of Day dividend payments on shareholder value. For example,Microsoft Equity Volatility across Industries from IPO Day Equity Volatility across Industries from IPO Day Equity Volatility across Industries from IPO Day issued a one-­‐time special dividend of $3.00 on November 15, 2004; because the price drops associated was meant to reflect the real effects of dividend payments on shareholder value. For example,Microsoft was meant to reflect the real effects of dividend payments on shareholder value. For example,Microsoft from IPO. O n 
 
IPO day, the variableequals 1 . On the day immediately following IPO, the with variable dividend payouts do not affect shareholder value, 3 was added to the closing prices, low prices, and from IPO. O n 
 
IPO day, the variableequals 1 . On the day immediately following IPO,issued the a variable one-­‐time special dividend of $3.00 on November 15, 2004; because the price drops associated issued a one-­‐time special dividend of $3.00 on November 15, 2004; because the price drops associated equals 2. For each additional day from IPO, the variableis incremented by one. The creation of thishigh prices for allMicrosoft observations on or after the day the dividend was issued. This does not lead equals 2. For each additional day from IPO, the variableis incremented by one. The creationwith of dividend this payouts do not affect shareholder value, 3 was added to the closing prices, low prices, and with dividend payouts do not affect shareholder value, 3 was added to the closing prices, low prices, and variable makescomparison ofthe chronologically scattered IPO periods for differentstocks in eachto a perfectadjustment fordividend payouts. S ince no stocks paid out dividends within their first thirty variable makescomparison ofthe chronologically scattered IPO periods for differentstocks high in prices each for allMicrosoft observations on or after the day the dividend was issued. This does not lead high prices for allMicrosoft observations on or after the day the dividend was issued. This does not lead industry possible. days of trading, however,no observations used in regression were affected; as a result, this inaccuracy industry possible. to a perfectadjustment fordividend payouts. S ince no stocks paid out dividends within their first thirty to a perfectadjustment fordividend payouts. S ince no stocks paid out dividends within their first thirty did not affect results.Equity Volatility across Industries from IPO Day ActualActual volatility volatility ( ) ( was ) was calculated calculated for for every every observation observationusing using 
 

 
intradayintraday trading tradingdays range range of trading , however,no observations used in regression were affected; as a result, this inaccuracy days of trading, however,no observations used in regression were affected; as a result, this inaccuracy was meant to reflect the real effects of dividend payments on shareholder value. For example,Microsoft squaredsquared relative relative to to closing closing price. price. 
  

  
highhigh price price( P( HP), low), low price price ( P ( LP), and), and closing closingdid not priceThe price affect ( Pdata (CP) ) is results. subject to some level of selection bias. All of the companies chosen were still trading as of H L didC not affect results. issued a one-­‐time special dividend of $3.00 on November 15, 2004; because the price drops associated were used to calculate volatility for each trading day: Equity VolatilityDecember across 31, 2009 Industries; as a result from, companies IPO Day taken private for reasons including bankruptcy and were used to calculate volatility for each trading day: The data is subject to some level of selection bias. All of the companies chosen were still trading as of The data iswith subject dividend to payouts some level do not of affect selection bias shareholder. All of the value, companies 3 was added chosen were to the still closing trading prices, as of low prices, and acquisition may be underrepresented. Furthermore, the accuracy of the S&P 500 as a true market (1)wasDecember meant 31, to reflect 2009; the as a real result effects, companies of dividend taken private payments for on shareholder reasons value. including For example, bankruptcyMicrosoft and (1) '!
"( Decemberhigh 31, prices 2009; as for a result allMicrosoft , companies observations taken private on or for after the reasons day the including dividend bankruptcy was issued. and This does not lead '!
"( benchmark is not perfect because the S&P 500 includes only large companies that have maintained  acquisition may be underrepresented. Furthermore, the accuracy of the S&P 500 as a true market $ issued a one-­‐time special dividend of $3.00 on November 15, 2004; because the price drops associated $  acquisitionto may a perfect be underrepresentedadjustment for.dividend Furthermore, payouts. the S accuracy ince no of stocks the S&P paid 500 out as dividends a true within market their first thirty consistent profitability. If stock resilienceor company sizes are correlated withIPO period volatility MicrosoftMicrosoft Corporation Corporation had had its its initial initial public public offering offering on on March March 13, 13, 1986. O 1986. nO itsn its first first day day of of trading, trading, its its withbenchmark dividend is not payouts perfect do not because affect shareholder the S&P 500 value, includes 3 was only large added companies to the closing that have prices, maintained low prices, and benchmarkdays is not of trading perfect, however, becauseno theEquity observations S&P Volatility 500 includes used only across in large regression Industries companies from were that IPO affected; have Day main astained a result, this inaccuracy trends, the results of this study may be skewed as a result. adjustedadjusted low low price price was was$25.50, $25.50, its its adjusted adjusted high high price price was was $29.25, $29.25, and and its its adjusted adjusted closing closing price was price was highconsistent prices profitability. for allMicrosoft If stock observations resilienceEquity Volatility onor company or after across the sizes day Industries are the correlated dividend from with IPO wasIPO Day issued period. This does volatility not lead consistentdid profitability. not affect If stock results. resilience or company sizes are correlated withIPO period volatility $28.00. was meant to reflect the real effects of dividend payments on shareholder value. For example,Microsoft $28.00. Equity Volatility across Industries from IPO Day Equity Volatility across Industries from IPO Day totrends, a perfect theadjustment results of for thisdividend study payouts. may be S ince skewed no stocks as a result. paid out dividends within their first thirty Section IV: Methodologyimpact of significant non-­‐IPO eventson the regression results; the 30-­‐day period was chosen to capture trends, the results ofEquity thisEquityEquity Equity Volatility study Volatility Volatility Volatility may across be across across across skewed Industries Industries Industries Industries as a result. from from from from IPO IPO Day IPO IPO Day Day Day The data is subject to someissued level a of one -­‐ selectiontime bias special. All of dividend the companies of $3.00 on November chosen were still 15, trading 2004; because as of the price drops associated (days2) of tradingimpact, however, of significantno observations non-­‐IPO events usedon in the regression regression were results ; affected; the 30-­‐day as period a result, this inaccuracy was chosen to capture was meant to reflect the real effects of dividend (2 payments) on shareholder value. For the example, full effectMicrosoft of the IPO event while minimizing the effects of non-­‐IPO events on the data. The '
 ( Section IV: Methodology '
 ( December 31, 2009All; as calculations a resultwith, companies dividend and regres payouts takensions were do private not run affect for using reasons Stata shareholder version including 11.1 value, 3 . F was bankruptcyor a discussion added and to of theStata closing-­‐specific prices, low prices, and  The methodSectionology followed IV: Methodology throughoutAll Allcalculations All calculations calculations this and study and consists and regres regres regressions ofsionssions two were were processes. were run run run using using Stata First usingStata Stata version is version the version 11.1 calculation 11.1 . 11.1 F or. F . aor F of discussion or a discussion a discussion of Stata of ofStata Stata -­‐specific-­‐specific-­‐specific $  $  did not affectthe full results. effect of the IPO event while minimizing the effects of non-­‐IPO events on the data. The issued a$ one-­‐time special$  dividend of $3.00 on November 15, 2004; because the priceregressions drops associated run to estimate all three values for each indexused the following model given known As a result,  
volatility rating for IPO daywas 0 .5022321. A higher calculated represents high prices for allMicrosoft observations on or after the day the dividend was issued. This does not lead As a result,  
volatility rating for IPO daywas 0 .5022321. A higher calculated represents values that representacquisition average maymethodology, intraday methodology, bemethodology,methodology, underrepresentedprice see volatility see Appendix see seeAppendix Appendix forAppendix . Furthermore, each I . I . industry I. I . the . Second accuracy is of the the nonlinear S&P 500 as
a true market The methodregressionsology followed run to throughoutestimate values all for three this and study values consists for : of eachtwo processes. indexused the First following is the calculation model given of known with dividend payouts do not affect shareholder The value, 3 data was is added subjectThe m to ethod to the someology closing levelfollowed prices, of selection throughout low bias prices,. All and this of the study consists companies oftwo chosen were processes. still trading First is as the of calculation of increasincreaseded volatility. volatility. regression of values benchmark against is time not from perfect IPO in becauseto order a perfect to the adjustment estimate S&P 500 volatility for includes onlydividend large trends following payouts. companies IPO S ince that day no havein stocks main paidtained out dividends within their first thirty values that values represent for and average intraday : Section price SectionSection  volatility     V: V: for V: Results each Results Results industry . Second is the nonlinear 
high prices for allMicrosoft observations on or afterDecember the day the 31,value dividend 2009;s as that a represent result was issued, companies. This average Section does takenintraday not V: lead private price Results volatility for reasons foreach including industry . bankruptcy Second is and the nonlinear 
each industry.
consistent profitability. If stock days resilience of tradingor , company however, sizesno observations areEquity correlated Volatility used with in IPO across regression period Industries volatility were ( from8 ) affected; IPO Day as a result, this inaccuracy This calculation is based on

   

  

  


  

Volatility This calculation is based on

   

  

  


  

regressionVolatility of values  agai   nst time from IPO in order to estimate volatility trends following IPO day in to a perfectadjustment forEquitydividend Volatility payouts. across S ince Industries acquisition no stocks from may paid IPO be out Day underrepresented dividends within. Furthermore, their first thirty the accuracy of the S&P 500 as a true market  regressiontrends, of values the agai resultsnst time of this fromdid study not IPO in order affect may be to results.  skewed estimate
  as   a result.
volatility ! trends

following" (8
) IPO day in Trading ( 2008, p. 16).   
    -38- , where N defines the number of periods sampled, is: ECONPress TheTheThe results results resultsEquity of of the of the theVolatility regressions regressions regressions acrossfor for eachfor each Industries eachindustry industry industry and from and and the theIPO the market Day market market benchmark benchmark benchmark are are are as as follows as follows follows with with with -39- Trading ( 2008, p. 16).   
    , where N defines the number of periodseach sampled, is: industry. Methodology 
Subsection I:The CalculatingThe regression results of estimates the regressions average for industry eachindustry volatility and (impact) theas a o function marketf significant benchmark of the non-­‐ IPOare number as events follows ofon days thewith regression from IPO results; the 30-­‐day period was chosen to capture days of trading, however,no observations used inbenchmark regression is not were perfect affected;  because
as a result, this the inaccuracy S&P  500
  includes only
 large ! companies

" 
that have maintained impact of significant non-­‐IPO eventson theeach regression industry. results; the 30-­‐day period was chosen to capture correspondingcorrespondingcorrespondingThe sample sample data sample is sizes sizes subject sizes and and t and -­‐ statistics tot -­‐ t statistics-­‐ statistics some in level in in parentheses parentheses parentheses of selection: bias: : . All of the companies chosen were still trading as of Equity Volatility across Industries from IPO Day The regressionSection estimates( average IV:corresponding ) . Methodology industry On  IPO sample day, volatility the sizes ( ) as and a t -­‐ functionstatistics term in of is parentheses the equal the full number to : effect 0; of this days of means the from IPO that average event IPO while day minimizing volatility the effects of non-­‐IPO events on the data. The did not affect results. After calculatingconsistentMethodologyThe profitability. calculation values Subsection for If every process stock I: Calculatingday resilience was run or individually company using sizes are data correlated setsthat include withIPO the period trading volatility history forthe S&P the full effect of the IPO(3()3 event) while minimizing the effects of non-­‐IPO events on the data. The  (3) from IPO in each industryMethodology (represented Subsection us- I: CalculatingDecember 31, 2009; as a result, companiesregressions taken run to privateestimate for all three reasons values including for each bankruptcy indexused and the following model given known    ( ). On IPO day, is the   estimated by term since Sector is ! equal   the to denominator
0;
 this" means of the that average second IPO term day volatility becomes equal toone . For each day 2 2 2 2    trends, the results of this study may be skewedSectorSectorSector Sector as a result. R R RR from IPO. O n 
 
$IPO
& day , the ' variable#
( equals 1 . On theing day a immediately variable), a500 nonlinearfollowing and
each IPO,regression of the the variable ten was selected industry groups provided by MarketWatch. For allexamined data sets, The data $ is
&  subject ' to#
regressions some ( level run of to selectionestimate bias. All all of three the values companies for each chosen were index stillused trading the following as of model given known For the purposes of this study, N is used to modelThe calculation as a function process of Theday m wasfromethod run individually ology followed using throughoutacquisition data  setsthat may this include study be consists underrepresented(Baselinethe trading of Volatility)two history processes.. Furthermore, forthe (IPO-Driven FirstS&P the is accuracy the calculation of(Stabilization the of S&P 500 as a true market is   estimated by following since !   the IPO, denominator
volatility 
"
 decays of theas the second  term   becomesvalues equalterm g for torowsone and and . For the  each second: day regression   term ForForEquity the the purposes Volatility purposes of across of this this Industries study study, Nequal, N is is equal to equal from 1 because to 1 IPO tobecause 1 because Day volatility volatility volatility is measured is is measured measured on on onIPO. a day a day No-­‐by-­‐by -­‐valuesday-­‐day basis basis besides: : oneThe valuecalculation for each process was runindividually using data(Baseline ( setsBaseline(Baseline(Baselinethat
Volatility
include Volatility
Volatility
Volatility) the ) ) trading ) (IPO (IPO-­‐
(IPODriven (IPO history-­‐
Driven-­‐
Driven-­‐
Driven for the (Stabilization S&P (Stabilization(Stabilization (Stabilization


Rate)
Rate) Rate) Rate) equals 2. For each additional day from IPO, the variableis incremented by one.a day The counter creation variable of this was generated for each observationto mark the number of days thatVolatility) had passed Rate) a day-by-dayDecember basis: 31, 2009; as avalues result, for companies and Equity taken Volatility: value private were
across for required reasons Industries to including run from the re IPO- bankruptcy Day and 
EquityEquity Volatility Volatility across across Industries Industries from from IPO IPO Day Day Section500 and each IV: of the Methodology tenvalue selected  s that
 industry represent groups average provided benchmark intraday by price is MarketWatch not volatility perfect. For for because each allexamined industry the . data S&P Second  500 sets,   is includes the only large nonlinear companies that have maintained Equity Volatility across Industriesgression. from To IPO investigate Day following 500the andIPO
IPO, each period volatility of thein approaches decays ten selected as the 0. industry The Basic model Materials groups effectively provided term (548) g rows !   represents by 0.0303853and MarketWatch the
the
second  significant(47.53)" . For regression all impact0.0632364examined Volatility)Volatility)Volatility) term of (27.65) an data IPO sets, event 1.496436 on stock (7.88) volatility..9675 variable makescomparison Equity Volatility ofthe across chronologically Industries scattered from IPO IPO Day periods for differentstocks in each Volatility) (8) Since the term merely representsacquisitiondeviation Equity may Volatility be with underrepresented Equity respect across Volatility to an Industries . average, Furthermore, isolation,   across fromintraday Industries observations the IPO trading accuracy Day from range for of IPO theany Day S&Pday past 500 30 as a true market Consumer Goods (653) 0.0390784 (31.01) 0.1378587 (30.74)6 1.463953 (8.81) .9929 Equity Volatility across Industries from IPO Day (4a) day counter variableregression was generated of forvalues each agai!    observationnstconsistent time
fromto
 " mark profitability. IPO the in order number If tostock estimate of days resilience that volatilityor had company passed trends following sizes are IPO correlated day in withIPO period volatility from IPO. O n 
 
IPO day, the variableequals 1 . On the day immediately (4) following wereimpact dropped o IPO,f significant(4 the) from variable approachesthe non regression-­‐IPO events 0. The inon order model the Equity regression effectively Volatility results representsConsumer ; across the 30 the-­‐ Industries dayServices ( significant8 ) period (798) from was impact0.0598604 IPO chosen Day of an (24.60) IPO to capture event 0.4793099 on stock (47.82) volatility. 3.806189 (8.87) .9884  Since the  term merely represents  deviation  with respect  to an average, intraday trading rangea day counter variableBasic Basic wasBasic MaterialsBasic generated Materials Materials Materials for (548) each(548) (548) (548) observation 0.03038530.03038530.0303853to 0.0303853 mark (47.53) (47.53) the (47.53) (47.53) number 0.0632364 0.06323640.0632364 of days0.0632364 (27.65) that (27.65) (27.65) (27.65) had 1.496436 passed 1.4964361.496436 1.496436 (7.88)  (7.88)
 (7.88) (7.88)   
 .9675!.9675.9675 .9675

" 
 industry possible.   impact of significant non-­‐IPO eventson the regression results; the 30-­‐day period was chosen to capture Equity Volatility 
 across Industries from  IPO Day    to minimizeThe the method impactology of significantfollowed throughout non-This model this study was consists Financials chosen of for(2058)two its ability processes. to break0.0395426 First down is (69.25) volatility the calculation into0.0907731 of two (42.87) types: IPO-­‐related1.769266 volatility (11.59) and .9860 squared as a percentage of closing $Sincebenchmark
& price the was  ' used is # not
instead ( term perfect$ % to ' merely normalize # because
( represents differently the S&Pdeviation 500 priced with includes only stocks respect .large companies  to an average,each that intraday industry. have  trading main
tained range Since$
& the impact' #
o (termf significant$ %merelyimpact' #
o nonrepre f ( significant-­‐IPO- eventsIPOthe full noneventson -­‐ IPO the effect eventson regression ofthe on the regression
the IPO results  regression ; event the
results;!  30 while-­‐day resultsthe period
 ;
minimizing the" 
30 was-­‐day the chosen period Healthcare effectstrends, to was of non-­‐IPO capture the (821) chosen events results to on capture the of0.0575546 this data. The study (25.57)The may regression beEquity0.2345721 skewed Volatility estimates6 (25.97) as a result. average across2.959527 industry Industries (5.58) volatility from.9619 IPO ( ) as Day a function of the number of days from IPO equalsSince t 2he. For  each 
 additional term merely day represents from IPO, thedeviation variable withis incremented respect to an by average, one. The intraday creation trading of this range ConsumerConsumerConsumer Goods Goods Goods (653) (653) (653) 0.03907840.0.03907840390784 (31.01) (31.01) (31.01) 0.13785870.13785870.1378587 (30.74) (30.74) (30.74) 1.4639531.4639531.463953 (8.81) (8.81) (8.81) .9929.9929.9929 squared as a percentage of sents closing deviation price was used thewith full instead respect effect to to normalize ofan theaverage, IPO differently event30-day while pricedperiod minimizing stockswas. Thischosen model the to effects capture was of non-­‐IPO chosen events the impact for Consumer on its ability o thef significant to data Goods. breakThe (653) down non-­‐IPO volatility events0.0390784on into the (31.01) regression two types: IPO -­‐0.1378587related results; the volatility (30.74)
30-­‐day period and 1.463953 was6 chosen(8.81) to capture.9929 consistent  profitability. If The stock regression resilience estimatesor company averagevalue sizess that industry are correlated represent 7 volatility average with ( )IPO as intraday a period baselin function price volatilitye volatility. of volatility theIndustrialsSince for numbereach the (1141) of  
industry dayssecond . from Second IPO 0.0412802 term is rapidly the (47.95) nonlinear decays 0.1061883 as the counter (31.54) variable2.424831 increases, (7.50) its .9740 from IPO. O n 
 
ActualIPO volatility dayintraday, the squared ( ) variable was trading calculated as  aequals range  percentage
 1 squaredfor . On every the ofas day observationa closing percent immediately price- wasusing full used following 
 
effect instead of IPO, the intradayto the IPO normalize variable event trading7 differentlywhile range minimiz priced- stocks. ( ). On IPO day, the term is equal  to 0; this means that average IPO day volatility variable makes  comparison
 ofthe chronologically the scattered full effect IPOthe of period full the s effect for IPO different event ofregressions the whilestocks IPO run in event minimizing each toestimate while the minimizing all effects three of non-­‐IPO thevalues events effects for on of non-­‐ ConsumerIPO eachConsumer theConsumer events index data. The Market Servicesused on Services Services the (S&P (798) following data(798) .500)(798) The 0.0 0.0 model5986040.05986040.0470464 598604given (24.60) known (24.60) (24.60) (20.04) 0.47930990.47930990.47930990.1760342 (47.82) (47.82) (19.88) (47.82) 3.8061893.8061891.9365213.806189 (8.87) (8.87) (5.20) (8.87) .9379.9884.9884.9884 squared as a percentage of closingage of closing price was used price instead was used to instead normalize to nor differently- ing the priced Equityeffects( 5 stocks ) Volatility .of baselinnon-IPO acrosse volatility. events IndustriesMethodology onSince the from the t heConsumer full  
Subsection IPO effect Day second Services I: of Calculating the term (798) IPO rapidly event 0.0decays 598604 while as the (24.60) minimizing counter 0.4793099 the variable effectsimpact of non-­‐ increases,IPO(47.82) of events significant it s 3.806189 on Equity the non-­‐IPO (8.87) data . Volatility The events on across the.9884 regression Industries results from; the IPO 30 Day -­‐ day period was chosen to capture regressions run( toestimate  ). On all IPO three day, the values regression for each of indexvalues term used agaiis the equal nst following time tovalue 0; from this represents model IPO in given means order Oil the known that averageSection to& effectGas estimate (578) IPO of IV: day IPO on volatility stock volatility Methodology0.049487 volatility; trends following (17.32) captures IPO day0.1118282 thein expected (10.66) additional1.686358 volatility (2.93) on an .8142 squared relativemalize trends, to differently closing the results price. priced 
  
stocks. of  this
 study Equityhigh may price data. Volatility be( P skewedThe), low across regressions price as a result. Industries( P ), and run closing to from estimate IPO price Day ( P all) equals 2. For each additional day from IPO, theregressions variable is run incremented regressions toestimate run by all one. three tovaluesestimate The H for values creation all( and 5 )three for of this each L values index: forused each the following indexC used the model following given Technology known model given (890) known 0.1173751 (26.78)is   estimated0.7072644 by (40.15) since !   the2.997637 denominator

(8.57)" .9837 of the second term becomes equal to one. For each day industry possible.     Equity Volatility across Industries   from  IPO
 Day     three values for each index used the fol- regressionsFinancialsFinancialsFinancialsFinancials run (2058) (2058) to (2058) estimate (2058) all three 0.03954260.0395426 0.0395426 values 0.0395426 (69.25) for (69.25) (69.25) (69.25) each  0.0907731 index 0.0907731used 0.0907731the0.0907731 full the (42.87) (42.87) effect following (42.87) (42.87) of 1.769266 the1.769266 model1.7692661.769266 IPO given (11.59) (11.59) event known (11.59) (11.59) while .9860 .9860 minimizing.9860 .9860 the effects of non-­‐IPO events on the data. The values for and  
  :  each industry.value
represents the effectIPO(5 )day of when IPOon stock Telecommunications volatility; is 0 captures and 
  


 
 

the0.0297135 expected (12.20) additional0.1283577 volatility (16.27) on an becomes1.045903 equal (4.98) to1 .9137. is   estimated by lowing model since !   thegiven denominator known

" values ofThe for the andcalculation second term process becomes equal was run toindividually one . For each using day data setsthat include the trading  historyimpact forthe S&P of significant non-­‐IPO eventson the regression results; the 30-­‐day period was chosen to capture   impact of  significant non-­‐IPO eventson the regression results; the 30-­‐day period was chosen to capture Thevariable square makes root comparison ofwere the calculated used of tothe calculate percentagechronologically  volatility  was 
not scattered for taken each . T IPO tradinghe final period day scalculation : for different measuresstocks ( 5 ) in    variance each
  following IPO, volatility 
 decaysas the term g rows and the second regression term values for and values  for (5): and : The methodology followed throughout this study consists oftwo processes. First is the calculation of Section IV: Methodology  impact of  significant non-­‐IPO eventson the regression Healthc resultsHealthcHealthc; theareare (143) 30 are(821) -­‐day (821) (821) period was 0.0575546 chosen0.05755460.0575546 to (25.57) capture(25.57) (25.57) 0.23457210.2345721regressions0.2345721 (25.97) (25.97) run(25.97) to estimate 2.9595272.9595272.959527 all (5.58) three (5.58) (5.58) values .9619.9619 for.9619 each indexused the following model given known   
       
    IPO day when valuesHealthc is for 0 are and and ! 
  


 
 

(821)    :  " 0.0575546 (25.57) (8) 0.2345721becomes (25.97) equal to1 2.959527. (5.58) .9619 ActualThe square volatilityfrom IPO. root ( )O was n of the
 
calculated calculatedIPO for day percentage every, the variable observation was equals not takenusing 1 . On . following 
 
T he the final day IPO, immediately intradaycalculation volatility  trading
 measures decaysfollowing rangeas variance the IPO, the variable 500 term and
eachgTherows of and term the the ten is second selected the value regression industry of the groups term horizontal provided asymptote by above MarketWatch which. theFor all regressionexamined the settles data full sets, as effect of the IPO event while minimizing the effects of non-­‐IPO events on the data. The  the full effect of the IPO event while minimizing Utilities the (206) effects of non-­‐IPO events 0.0276752 on the (33.32) data. The 0.0460092 (13.93) 2.732502 (3.12) .8794 insteadindustry of possible. standard deviation : The  square  root
 of the  calculated   per -    Methodology Subsection I: Calculating(8)  (8) approaches 0. The model effectively !   represents
the
 significant" impact of an IPO event on stock volatility. The square root of the calculated percentagethe full Equity effectwas not Volatility of taken the. IPOT he across final event Industries calculation while minimizing from measures IPO Day the variance effects of non-­‐ IPOvalue eventss that on represent the data. The average intraday price volatility foreach industry. Second  is the nonlinear 
Equity Volatility across The Industries  term (1) from is!    the IPO
 value Day  Industrials  of"
Industrials theIndustrials!Industrials  horizontal (1141)
(1141)   
 (1141) " (1141)
asymptote above0.0412802 0.0412802 which0.04128020.0412802 the (47.95) (47.95) regression (47.95) (47.95) 0.1061883 0.1061883 settles0.1061883values0.1061883 as(31.54) for (31.54) (31.54) (31.54) and 2.424831 2.4248312.4248312.424831: (7.50) (7.50) (7.50) (7.50) .9740.9740.9740 .9740 squaredTheinstead square relative of root standard to of the closingdeviation calculated price.:centage 
  
percentage was not was taken. not high taken The price. T final he ( PH final ), lowcalcula price calculation - ( P L), and measures closing variance price (!P   C)

a "day counterincreases variable and ( the8 ) was second generated regression( for8) each observation term approachesto mark the zero; Equity is number an Volatility indicator of days across that of theregressions a verage had Industries passed   level run from of toestimate IPO Day all three values for each indexused the following model given known equals 2. For each additional day from IPO, the variableapproachesis incremented ! 0. "The by model one.regressions The effectively creation
  run !of  represents this toestimate

 the" significant all three impactvalues for of an each IPO event indexused on the stock following volatility. model given known (8) Equity Volatility acrosstion Industries measuresThe method from varianceology IPO followed Dayinstead of throughout standard' 
 ( thisThe The study regression consists
regression  of estimatestwo estimates processes. average average industry
First  indus is - volatility the calculation ( ) as a of function Table 1. of Regression the number results. of days from IPO instead of standarddeviation : regressions run toestimate all three  values for each index used theregression following of model values given agai known nst time  from IPO in order to estimate   volatility trends following IPO day in Actual volatility ( ) was calculated deviation: for every observationusing 
 
$  intradaytry volatility tradingThe ( ) rangecalculation  as
 a ! function process

 of
" the!  was num run
-individually
"MarketMarketMarketMarket (S&P using (S&P (S&P 500) (S&P data 500) 500) 500) sets that include 0.04704640.04704640.0470464 0.0470464the trading (20.04) (20.04) (20.04) (20.04) This history 0.1760342 model 0.1760342  for0.1760342the 0.1760342 was S&P    (19.88) (19.88) chosen (19.88) (19.88) 1.936521 for 1.936521 its ability1.9365211.936521 (5.20) to (5.20) break (5.20) (5.20) down .9379 .9379 volatility.9379 .9379 into two types: IPO-­‐related volatility and wereinstead used of to standard calculatedeviation volatility : for each tradingThe regression day: estimates averageimpact industry 
of significant(6) volatility  increases (
)  nonas -­‐ aIPO function and events the
on second of the thelong regression -­‐ regression run
number volatility of results term days that ; the stocks approaches from 30 IPO -­‐day will period zero; exhibit is was after an indicator chosen the effects to of capture of the average theIPO period level  of have ebbed. The variable  variable makescomparison ofthe chronologically scattered IPO periodimpacts for of different significantvaluesstocks for non -­‐and IPOin each events on : the regression results; the 30-­‐day period was  chosen
   to
  capture!

" 
values for and : (8) values that represent
 average  intraday price ber volatility of days from foreach IPO industry ( . Second). On is IPO the nonlinear 
impact of significant non-­‐IPO events6 on the regression results; the 30-­‐day period was chosen to capture Microsoft Corporation hadThe its regression initial publicThisThe offering estimates regression model on average was March estimates ( chosen industry 13, average for) . 1986.On O volatility its abilityn IPO its industry day, first to ( break) theas day a volatility down function of trading, ( volatility) as of a its the function term into numberis equal two of types: of the to IPO days 0; -­‐related number this from IPO volatility of means days
that average from and IPO IPO day volatility  Equityvalues(6) Volatility day, for the and ( across (6)
Industries: - 1) term from is equal IPO Day to 0; OilOil &Oil & & Gas Gas (578) that Gas (578) each(578) stocks industry. will exhibit 0.0494870.0494870.049487 after (17.32) the (17.32) (17.32) effects 0.1118282of0.1118282 0.1118282comes, (10.66) see (10.66) (10.66) Appendix 1.6863581.6863581.686358 II. For (2.93) (2.93) graphs (2.93) of the.8142.8142 .8142  squaredfrom relative IPO. O n to 
 
closingIPO price. day 
  
, the variable  equals high 1  price. On the( PH) day, low immediately price ( thePL) , full and following 500 effect closing and of IPO, each long price the the ( ofP-­‐runC IPO variable) the volatility ten event selected that while stocks industryThe minimizingOil regression & will groups Gas exhibit (578) the provided estimates after effects the of non-­‐ IPO by average effects events MarketWatch0.049487 industry of on theIPO the. For (17.32) period volatility data all. The examined have baselin ( ) as 0.1118282 ebbed a e data function volatility.. The sets, (10.66) Since of variable the the1.686358  
number (2.93) ofsecond days term from IPO .8142rapidly  decays as the counter variable increases, its industry possible. ( 
). On  IPO day, the term is equal to 0; this meansrepresents(6) that average stabilization IPO day volatility rate  the larger the value of , the quicker stock volatility converges  to its   
  
!

" 
the fullthis effectmeans ofthat  the average  IPO   IPO event day while volatility minimizing the effectsthe of non-­‐IPO IPO events period on have the dataebbed.. The The vari- regression models with calculated values, regression of values  against time from IPO   in order to estimate volatility!   trends
following
" IPO day in the full effect of the IPO event while minimizing the effects of non-­‐IPO events on the data. The Volatility was calculated adjusted for low stocks price in wasthe $25.50, ten( Dow its Jones adjusted ). On baselin( IPO Sector high day, e Indexes volatility. price the). On provided IPO wasis Sinceday, estimated  $29.25, by the  the (1)   ( 6) MarketWatch  

 term and by its is second equal  adjustedin since term to term the 0; closingis rapidly this equal denominator decays price was means to 0; that asaverage this the of the counter means IPO second day that average variable volatility term IPO increases, day becomes equal volatility its to one . For each day Appendix V (8) Volatility was calculated  for stocks in is estimated a day by counter variablesince the denomi was generated- forTechnology eachTechnologyTechnology observationable (890) (890) represents(890) to mark stabilization the 0.1173751 0.1173751 number0.1173751 rate of(26.78) days (26.78) – (26.78) the(8 ) that larger 0.7072644 had 0.7072644The0.7072644see passed regression (40.15) (40.15) (40.15) estimates . 2.9976372.9976372.997637 average (8.57) (8.57) (8.57) industry .9837 volatility.9837.9837 ( ) as a function of the number of days from IPO were usedequals to 2. For calculate each volatility additional for day each from tradingis   estimated  IPO,! the
 " variable day: by is incremented since !   the by regressions one. denominator
The
" creation run to ofrepresentsestimate of the this second all stabilization three term values ( becomes rate equalTechnology for  the each to ) larger.one On index .(890) IPO For theused day, each value the the day following of , the0.1173751 quicker model (26.78) giventerm stock is known equalvalue volatility0.7072644 represents to 0; converges this (40.15)  the means to effect its 2.997637 that average of IPOon IPO (8.57) stock day volatility; volatility.9837 captures the expected additional volatility on an Volatility was calculated for the stocks ten Dow inthe Jones ten Dow' Sector
Jones ( Indexes Sector provided impact Indexes provided onatorf significant  of by the  MarketWatch Equitysecond non-­‐IPO Volatility term eventsin becomeson across the equal regression Industries tolong -­‐ resultsterm from; the volatility IPO 30 Day the-­‐day Methodology levelvalue period of. For was , all Subsection the industries chosen quicker(8) to I: , stock t his capture Calculating model volatility approximate s values very well with all 
 regressions run toestimate  all three values for each indexused the following model given known    additionActual to the volatility S&P$28.00. 500 ( )which was calculated serveseach as industry.for a every $ market    observation benchmarkvalueis   . estimated using Volatility represents 
 
ratings ! by   following the intraday for effect
stockssince
IPO,! " trading   of the volatility in IPOeach on denominator range stock

 decays
 " volatility;as of the the captures second  the term expected term 
  becomes !g  equalrows additional and to

one  "the . For second volatility each on regression an day term regressions run toestimate all three values for each index  used
 the  following
 ! model

 "given 
known by MarketWatchVolatility was is estimatedin calculated addition by for to  stocksthe S&P since inthe one. the ten Dow denominatorFor each Jones day Sector offollowing the Indexes second providedIPO, termvolatil by -  becomes MarketWatch equal
  toone in . Forconverges each to day
its long-term volatility level In every regression, all three variables  variable makescomparison ofthe chronologically scattered IPO periods for differentstocks in each  is   estimatedTelecommunicationsTelecommunicationsTelecommunicationsTelecommunications2 by  (143) since  (143) !    (143) (143) the 0.0297135 0.0297135 denominator
0.0297135 0.0297135
" (12.20) (12.20) (12.20) (12.20) of the 0.1283577 0.1283577 second0.1283577(0.1283577 (16.27) term (16.27) ) .(16.27) On (16.27) becomes IPO equal1.045903 day, 1.045903 1.045903 to 1.045903 theone (4.98) . (4.98) For (4.98) (4.98) each .9137 day.9137  term .9137 .9137 is equal to 0; this means that average IPO day volatility 500 which servesfollowing as a market IPO, volatility benchmark.
the decays full ityas effectvalues thedecays of for as the the and IPO ( long event term -­‐term: - while g 1)rows volatility term and minimizing grows the  level
 second  ! the. For regression effects all

industries " of non-­‐IPO events . termFor, t his all on model industries, theapproximate data. The this models values approxiIPO day very - when well were with statistically6 all  significant is 0 and 
  


 
 

at the 1% level. becomes equal to1 . MicrosoftVolatilityaddition Corporation to was the calculated S&P 500 had which for its stocks initial serves in publicthe as offering ten a Dow market on Jones benchmark March Sector. 13,Volatility Indexes 1986. O n provided ratings values its first for for by day and stocksThe MarketWatch of regression trading, ineach : its in estimates  
average  industryregression volatility R values 
( ) as above a function 0.8100 and of theseven number ofeleven of above days from 0.95 IPO 0. In addition, all estimatedThe regression estimates average industry volatility ( ) as a function of the number of days from IPO Volatility ratings for stocks in each 
indus - and 
the secondimpact(1) regression of significant term approaches non-­‐!IPO   events
on
 the" regressionmatesThe calculation values results; the very 30 process well-­‐day with period was all regression run wasindividually chosenvalues Since to using for capture all data and stock sets pricesthat include change: the regularly, trading base history- forthe S&P industrysquared group relative were then to divided closing additionby price. the 
  
number to thefollowing S&P of stocks 500 IPO, which high followingIPO volatility in price day serves the when( decaysP IPO,The indexH ( )N, as ) low regression volatilityto aas approaches calculate price the market ( decaysP L) estimates, and an benchmark 0. averageis as The 0 closing the and. average modelVolatility 
  


 
 

term price effectively industry (g ratingsProwsC) and volatilityterm for representsthe stocks g secondrows ( ) the as in and each a regression significant functionthe second impact of term regression becomes the of an number IPO equal term event of to 1 days . on from stock IPO volatility.    !  

" industry possible. Methodology Subsection '!
"( I: Calculating !   
  
" 2 followingUtilitiesUtilitiesUtilitiesUtilities IPO, (206) (206) volatility (206) (206)2 
 decaysas 0.0276752 the0.0276752 0.02767520.0276752 (33.32) (33.32) (33.32) (33.32) The term 0.0460092 0.0460092 term g 0.0460092rowsis0.0460092 estimated is !and (13.93)    the (13.93) the (13.93) value(13.93) second by 2.732502 of " 2.732502 regression2.732502 the2.732502 since (3.12) horizontal (3.12) the (3.12) (3.12) term denominator asymptote.8794.8794 above.8794 .8794 of which the the second regression term settles becomes equal as toone . For each day addition to the S&P 500 which servestry group as were a marketthenapproaches divided benchmark 0. by. The Volatility the model numberregressions ratings effectively 0. Thefor run stocks represents tomodelestimate in each effectively the all regression significant three represents ( values 2 R ) impact values for the above of eachsig an-coefficie IPO 0. index 81 event00ntsused and were the on seven R stock significant following values of volatility.eleven above at model above the0.8100 given 1% 0.9 known and5 level.0 . In seven addition, of eleven all estimated line volatility was( expected). to On be IPO positive day, the term is equal  to 0; this means that average IPO day volatility adjustedindustry low group price were was then $25.50, divided its adjusted by the number high price$ of stocks was in $29.25, the and index (N) itsto calculate adjusted  ( an    closing average). On price was IPO day, the term is equal  to
0; this means that average IPO day volatility of stocks in the index (N) to calculate'
 an !(    nificant impact"the full of !an effect   IPO of event
the
 " on IPO stock event while minimizingabove500 and0.950. the each effects In of addition, of non-­‐IPO the ten events selected all ( estimated8 on) the industry data co. The - groups and provided statistically     by significant MarketWatch from. For zero. allexamined The data sets, compositewere measure used to calculate ofindustry volatility volatility industry for groupfor eachapproaches each were tradingday then relative 0. day divided approachesThe:The model to term by IPO(. the Where 0. effectively is The number the N model) . is valueOn the !    of represents IPO effectively of stocks number day, the
the inof horizontal
 significant stocks " the represents index (N) the to impact asymptote calculate significant above term of anis which IPO an equal impact average event the to of 0; regression an on IPO this stock event means settles volatility. on that average as stock IPO volatility. (8 ) day volatility   
 average composite measure Equityof industry  Volatility volatility.This across model Industries was chosen from for IPO its ability Day to breakapproaches down volatility  0. The efficients into model two effectively were types: IPOsignificant-­‐related !   represents volatility at
the
 significantincreases "1% and level. followingand consistency impact the second IPO, of an IPOof volatility increased regression event decays onvolatility term stockas the approaches volatility.on IPO zero; is term an indicatorg rows and ofthe the second average   regressionlevel (8 of) term Microsoft Corporation had its initial public offering on March$ 13, 1986. O n its$  first day of trading,coefficie its nts were significant at the 1% level.    !  

" $28.00.industry group were then divided by the number of stocks in the values index (N) to for calculate and    an average: !   

"   is estimated by since the denominator of the second term becomes equal toone . For each day compositeActual measure volatility ofindustry ( ) was volatility calculated volatility The calculation for for for every This eacheach model day day observation process relativerelative was wasusing chosen toto run IPOIPO. individually 
 
. Where for its abilityN is intraday using to theis break estimated data number trading down setsof that stocks range volatility by include into the since trading two the
 types: denominator IPO history -­‐related
  for!the volatility of S&P
the
"  second and
term becomes equal toone . For eachdates day means that IPO-driven volatility  As a result,  
volatility rating for IPO daywas 0 .5022321. A higher regressions calculated run to estimate represents  all  three
! values

 " for a each day counter indexused    variable the following was generated model given for each known observation to mark the number of days that had passed in an index with an available Where value composite :N is the measure number of ofindustry stocksincreases in volatility an and is    in estimated- the for second eachThis byday regressionmodel relative since was ! to    termchosen the IPO. Where denominator approaches
for 
its
N " is ability the zero; of number is the an indicatorof second stocks term
ofAll the a veragecalculations becomes equal level toone ofand. For regressions each day were was expected to be positive and nonzero,!    as

 !
"

"  adjusted low price was$25.50, its adjustedThis high model price was wasThis chosen model $29.25, for was and its ability baselin its chosenThe to regression adjustede break volatility. for its ability down closing estimatesSince to volatility break price was the average  
down into industry volatility second two types: term IPO volatility into-­‐ relatedrapidly two ( ) as volatility types:decays IPO a function-­‐related as the and volatility of counter the and variable number of increases, dayslong its from-­‐ run IPO volatility approaches that 0. stocks The model will exhibit effectively after  the
represents effects  the of significant theIPO period  impact
have ebbed of an IPO. The event variable on stock volatility. composite measure ofindustry dex volatility with an 
for available eachday value: relative to IPO. WheretoN is break the   numberdown of volatility(1) stocks  into
 two types: ForFor Fortables tables tables orderedrun ordered ordered using by Stataregression by byregression regression version outcomes, outcomes,11.1. outcomes, For see a see Appendix discus seeAppendix Appendix - well.II . II For .II For .Finally, For graphs graphs graphs since of of the ofthe following the the levels regression regression regression of IPO, volatility volatility models  models modelsob
 - decays with with with as the term g rows and the second regression term in an indexsquared with relative an available to closing value 500 : price. and 
  
each of the ten highselected impact price o industryf( P significantHThe), low regression groups price non ( followingprovided P-­‐IPOL) , estimates and events by closing IPO, on average volatility MarketWatch the price regression industry (P decaysC) . For as all volatility results theexamined This ; theFor ( model) as tables 30 data -­‐ aday function ordered was period sets, term chosen of was byg rowsregression the for chosen and its ability number the to outcomes, to second break of capture days down regression see fromAppendix IPO volatility term II . intoFor graphs two types: of IPO the-­‐related regression volatility models and with increased volatility. baseline volatility.' !
"( Since the  
second values term rapidly for and decays as the: counter variable increases, its (8) The regression estimates average industry volatility ( ) as a function of the number of days from IPO in an index with an availablelong -­‐value run volatility :following  IPO-related that IPO, stocks volatility(2)  volatility
will decays exhibit and afteras thebaseline the effects volatil of- the IPO term period g rows have and sion ebbedthe of secondStata-specific. The regression variable methodology, term see Ap- served on IPO dates are typically expected 6  $28.00. baseline volatility. baselin Since e volatility. the  
value(Since secondrepresents the )  
. On term IPO the rapidly second day, effect the decays term of rapidly as IPOon the stock decays counter volatility; term  as the variable is equal counter captures increases, to 0; variable the this its expected increases, means that average additional its IPO volatility dayrepresents on volatility an stabilization rate  the larger the value of , the quicker stock volatility converges to its in an index with an available value :  '
  $( (7) ity. Since the(7 )model’s second term rapidly !    calculatedcalculatedcalculated

 pendix" values, values, values, I see. see Appendix see Appendix Appendix V. V . V . Thisto modeldecline over was time, chosenapproaches stabilization for its ability 0. The to rates break model down effectively volatility !   represents into
two the
 significant types:" IPO-­‐related impact volatility of an IPO and event on stock volatility. were used to calculate volatility a day counterfor each variable trading daythe was: full generated effect( for each of the) . observationOn approaches IPO IPO day, eventto the 0. mark while The the model minimizing number  effectively term of the days baselin effectsis represents calculated that equal of non-­‐IPOe had volatility. to events the values, 0; passed significant this Since on see the means t Appendixhe impact data  
. that averageThe  V of.second an IPO IPO day event term volatility rapidly on stock decays volatility. as the counter variable increases, its 9   value represents the effect ofdecays IPOon stock as the volatility; counter  captures variable    
 theincreases,   expected
 !  additional

" 
volatility on an  ( were also). On expected IPO day, theto be positive nonzero term is equal to 0; this means that average IPO day volatility Microsoft Corporation had its initial$ public offering  $ on represents March approaches 13, stabilization 1986. O n its 0. firstThe rate ( model7 the day) larger of effectively trading, the its value !   represents of , the
the
 significant quicker" stock impact volatility of an IPO converges event to on its stock volatility.  This calculationFor is based example, on

   

  

  


  

value on represents Day 1 thevalue theS&P represents effect 500 ofits IPO the is IPO   on value estimated day effect stock when represents of volatility; by IPOon stockthe captures effect since volatility;! is    0 the of the andVolatility IPO denominator 
  


 
 


expectedcaptures
on" the additional of  expected the second volatility additional on term an volatility becomes equal on becomes an to one . For equallong each to-­‐(term81 ) . day volatilityvalues. The level regression. For allindustries results , confirmed this model approximate s values very well with all  
The regression estimates average industry volatility ( ) as a function of the number of days from IPO baseline volatility.9Since the  
second term rapidly decays as the counter variable increases, its As a result,  
volatility rating for IPO daywas  0 .5022321.regressions A higher is run   estimated calculated toestimate by represents all three since  !values    the for denominator
each
" indexvalueused ( of7) the therepresents following second the term  effect model given becomes equal of known IPO on to one stock . For volatility; each day captures the expected additional volatility on an index containedIPO 500 day stocks when with available is stock 0 and volatility; 
  


 
 

(2) captures the expected becomes 6 equal to1 . is   estimatedthese expectations by onThis since all ! model   counts. the denominator was
Further
 chosen" - for of its ability the second to break term down becomes volatility equal to intoone . For two each types: IPO day-­‐related volatility and For example,adjustedon low Day price 1 the was$25.50, S&P 500 index its adjusted contained  
 high 500 price stockslong was-­‐term with $29.25, volatility available and level its data. The This ( .7 sum adjusted For ) model all ofindustries all closing was chosen, price was this model for its abilityapproximate to break downs  values volatility very well into with two all  types: IPO-­‐related volatility and   !   (1)   "  
  
 !
Section
" 
V: Results 2  2 10 10 10 10  Trading ( 2008,data. p. The 16).   
    sumIPO 'of  day all
 when values ( , IPO where divided day when N by defines is additionalThe 0following the and 
  


 
 

term number  volatility IPO,  is is 0  the volatility  of and on 
  


 
 

value periods
 an decays ofIPO the sampled, as is: day the  horizontal when  asymptotebecomes above term which g equalrows becomes the and to1 .the regression second equal to settles regression1 . as regression term R more, values the above high 0. R81 00values and seven associated ofeleven with above 0.950. In addition, all estimated For example,on Day 1 the S&P 500 index contained 500 ! stocks" with( This available model). On   IPO was
data. The  day, sum chosen the
of for all its ability to break term down is equal volatility to 0; into this two means types: IPO that average-­‐related IPO volatility day volatility and value represents  the  effect of IPOon stock volatility; captures the expected additional volatility on an increased volatility. 500 was 0.2221825 on Day' 1 and!values  
 0.114652( for following and " ( IPO,:  volatility - 1) is 0 decaysand theas denominator the of IPO day term when g rows and the second is 0 regression and 
  


 
 

term  the regressions indicate
 becomes that the equal model to1 . de - values divided by 500 was 0.2221825 on Day $ The 1
  and 0.114652 term is$ on the Day value 2.2 of This suggests the horizontal  thatThea n average regression asymptote above which estimates the average regression industry settles  volatility as ( ) as a function of the number of following days from IPO IPO, volatility baselin decayseas volatility. the Since the  
term g secondrows and term the rapidly second decays regression as the term counter variable increases, its $28.00. on DayFor example,2. Thison suggests Day $ 1 that theregression an S&P 500 average index R values the contained above model’s baselin 0. 50081second00e stocks volatility. and term seven with becomesSince of availableeleven the equal  
above data. The to second sum 0.950 . of In term all addition, rapidly The alldecays estimated results as the of counterthe regressions variable for increases, each itscribeds by Equation (8) captures the typical As a result,  
volatility rating for IPOThe day term was 0 is.5022321.The!    the value term is   A estimated higher  is of"!    the theincreases approachescalculated value horizontal by and  of" 0. therepresents The since asymptote ! second horizontal   model above the denominator regression
effectively which
asymptote" the above ! term    represents regression of which the approaches
the the second
 settles significant " regression zero; term as is impact an becomes settles equal indicator of as to an IPOone of . For event the average each on   level stock day coefficie of volatility.nts were significant at the 1% level.  Forvalues example, divided on by Day 500 1 was the 0.2221825 S&Plarge-cap 500 index on stock’s contained Day 1 volatility and 0.114652 500 stocks decreases on Day with baselin 2. availablebyapproaches This suggests1.e   volatility.The data. The 0. that sum The termSince a n model of average is t allthehe  
effectivelyvalue ofsecond the !   represents horizon term
rapidly the- The
 significant" decays term is as impact!    industry the counter value of an and IPO  of" the variable the event market horizontal on increases, benchmark stock it s asymptote volatility. above are in which IPOtrends day the whenin regressionprice volatility settles exhibited is as 0 and by 
  


 
 

stocks  becomes equal to1 . Microsoft Corporation had its initialincreases public offering and on the March second 13, regression 1986. O n its term first( day approaches of ). trading, On IPO zero; its day, is an the indicator of the average term    level is equal  of to 0; this means that average IPO approaches day volatility 0. The modelvalue effectively represents !   represents the effect
the
 significant " of IPOon stock impact volatility; of an IPO captures event on the stock expected volatility. additional volatility on an Thislarge calculation-­‐

 
is based on

   

  

  


  

decreasesaboutvalues 50% by divided aboutafter its by 50% firstafter 500 wasday its first coefficieof 0 .2221825 trading. daynts of on were trading. Daytal significant asymptote 1 value and 0.114652 at represents aboveVolatility the on 1%which Day the level. 2. the( effect3 This) suggests regression of IPO on that stocka n average volatility; Table  captures 1 with ( the8) corresponding expected additional sample volatilitysizes onin an each sector very accurately. At the 10%            increased volatility. increases and theincreases second following and value regression the represents long IPO, second-­‐run volatility term volatility  the regression
 decays effect approaches that as of term stocks the IPOon zero; approaches stock willis an exhibit volatility; indicator after zero; term is the an of captures  g effects indicatorrows the average and the of level the of expected theIPO second the of a periodverage regression additional have level ebbed of volatility term. The on an variable valueslarge -­‐divided 

 
by 500 was 0.2221825decreases on by Day about 1 50% and 0.114652after its first on Day day 2. of This trading. suggestssettles thatas increasesa n average (2 )and the second regres-  and t-statistics in parentheses. Thelevel, term sample is!    size the had value an insignificant of"    the horizontal effect asymptote above which the regression settles as adjusted low price was$25.50, its adjusted high price was  $29.25,  This and model its adjusted   was chosen closing for price was its ability to! break   increases down

 and volatility" the second into two regression types: IPO-­‐related term volatility approaches and zero; is an indicator of2 the average level of Regression Modellong-­‐run volatility $
&that  stocks' #sion will
( term exhibit afterapproachesis estimated the effects zero;  by of is the
IPO an!  periodindica since the-
have 
" denominator ebbed . The of variable the second term becomes equal toone . Foron each fit dayquality R (seeIPO Appendixday when III); this is 0 and 
  


 
 

 becomes equal to1 . Trading ( 2008, p. 16).   
    large,-­‐ 

 
where N ' defines
 decreases the( number byThis of about model periods 50% IPOafter was sampled,day is: its chosen when first  for day
 its ability of  trading. to break is 0 down and 
  


 
 

volatility
into two types: IPO-­‐related volatilitybecomes and equal to1 . Methodology Subsection II: Regression Model long-­‐run volatility represents that stocks stabilization will exhibit after rate  the the larger effects the of the valueIPO  period of , the have quicker ebbed . stockThe volatility variable converges to its This model was chosen for its ability to break down volatility into two types: IPO-­‐related volatility and large-­‐

 
decreases by aboutlong 50%$after -­‐run volatility its  first daythat $  approaches of stocksIPO trading. day tor will when of 0. exhibit theThe average after model the level effectively effects ofis 0long-run and of !   represents 
  


 
 

theIPO volatility period
the
 significant "have  ebbed impact. The of Forvariable an IPO tables event orderedbecomes on stock by equal regression volatility. to1 . out-  implies that variations in sample size be-    $28.00. For the purposes of this study, N is equal The to 1 because regression volatility estimatesbaselin is e measured average volatility. on industry Since a day -­‐ tby he volatility-­‐ day  

basis  ( )second :as a functionlong term-­‐run rapidly volatility of thedecays  that  number as stocks the of counter will days exhibit from variable IPO after the increases, effects its ofincreases theIPO period and have the second ebbed. The regression variable term approaches zero; is an indicator of the average level of MethodologyThis calculation Subsection is based on II: Regression

   

  

  


  

Modelrepresents stabilization rate  the larger thefollowing valueVolatility of IPO,, the volatility quicker decays stockas the volatility converges term to its g rows and the second regression term The term is!    the value  of" the horizontal asymptote above which the regression settles as As a result,  
volatility rating for IPO daywas 0 .5022321.baselin A higher e volatility. calculated The Since term represents t he is!    the  
value second  of" the term horizontal rapidly decays  asymptote as above the counter which the variable regression increases, settles its as    baseline volatility.Since the  
second term rapidly decays  as the counter variable increases, its Methodologyrepresents Subsection stabilization II:represents Regression The rate stabilization Model  the long term larger -­‐term is ! rate    the the volatility  the value value larger  level of " of the, the. For horizontal value quicker all industries of  , stock the asymptote quicker, volatility above this model which stock convergesapproximate the volatility regression to its s converges values settles very to its as well with all   9 AfterTrading calculating ( 2008, p. 16)values .   
    forevery day from, where IPO in each N defines industry( the (represented number). On IPO of value using day, periods therepresents a( 3 ) sampled, is: the   effect term of is IPO equalon stock torepresents volatility; 0; this!   stabilization means captures
that average
" the rate IPO expected  the day larger volatility additional the value volatility of , on the an long quicker -­‐run volatility stock volatility that stocks converges  will exhibit to its after the effects of theIPO period have ebbed. The variable Methodology Subsection II: Regression Model long -­‐term volatility levelThis model. For all industries was chosenapproaches, this for model its ability 0.approximate The to break model down s effectively values volatility very represents intowell with the two all significant types: IPO-­‐related impact volatility of an IPO and event   on stock volatility. increases and the second regression term approaches zero; is an indicator of the average   level of increased volatility.   value represents increases the2 and effect the of second IPOon stock regression volatility; term captures approaches the expected zero; is an indicator additional9 of volatility the average on an level of After calculating values forevery day from IPO in each industry (represented regression using a R values ( 2 )above   0.81(4)00 and  seven ofeleven above 0.950. In addition,  all estimated value represents the effect of IPOon stock volatility; captures the expected additional volatility on an long-­‐term  volatilitylong -­‐term level increases volatility . For all and levelindustries the . For second, t allhisindustries model regressionapproximate , this term model s approaches approximate values very zero; s well is values an with indicator very all well of with the a allverage    level of   $
& ' #
2 (is   estimated by since   !   the denominator

" of the second term becomes equal toone . For each day  represents stabilization rate  the larger the value of , the quicker stock volatility converges to its variable), a nonlinear regression After was calculating used toregression model' values  as  R a
 values function for  every ( above baselin day of day  0. from from81e volatility.00IPO IPO and IPO day in. No seven each whenSince values  of industry t heeleven besides  
(represented above second is 0.9 5 00 term using. and In addition, 
  


 
 

rapidly  a long decays -­‐ term all estimated volatility as the counter level . variableFor allindustries increases,becomes, it tshis equal model toapproximate 1 . s values very well with all      IPO day when long -­‐run volatility is that 0 and stocks 
  


 
 

will exhibit after the effects of theIPO periodbecomes have ebbed equal. toThe 1 . variable long-­‐run volatility that stocks  will exhibit after the effects of theIPO period have ebbed. The variable ForAfter the calculating purposes of values  this for studyevery , N is day equal from to 1 because IPO in $ each volatility$
industry&2 is (represented ' measured$ #
 (2 on$ using a% day' -­‐ #by a
-­‐   day ( This basis model : was chosen for its ability to break down volatility into two types: IPO-­‐related volatilityIPO day and when is 0 and 
  


 
 

 becomes equal to1 . variable) , a nonlinear regression was used toregression model as aR functionvalues regression above of day R 0. values from81coefficie00 IPOand above . No seven nts 0.values 81 were( 3 of00) eleven besides and significant seven above of at eleven 0.9 the50. In above 1% addition,  level. 0.950 all. In estimated addition,  all estimated  This calculation is based on

   

  

  


  

 followinglong IPO,-­‐run volatility volatility 
 decays that as stocks the Volatility will exhibit after term the g effectsrows and of the the2IPO second period regression have  ebbed term. The variable long-­‐term volatility  level . For allindustries , this model approximate s values very well with all one value As a for result, each  
volatilityvalue were rating required coefficie for IPO tonts run day werewas the significant 0 .5022321. regression. To atA investigate higher The the 1% calculated term level. the is ! IPO    the represents period value in  of" the horizontal  regression asymptote aboveR values which above the 0. 81 regression00 and seven settles ofeleven as above  0.950. In addition, all estimated  variable), a nonlinear   regression value was used represents to model the !    as a effect function of " IPOon of day stock from volatility; IPO. No values 7 captures besides the expected additional volatility on an  represents stabilization rate  the larger the value of , the quicker stock volatility converges to its  The term represents is the value stabilization of the horizontal rate  the larger asymptote above the value which of the, the regression quicker stock settles volatility as converges to its !   " variable)one value , a nonlinear for  each regression value was were used required to  model to as   a run function the regression of day . from To investigate IPO. No    values thebaselin besides IPOe volatility. period in Since the  
second term rapidly decays as the counter variable increases,The itterm s is the value of the horizontal asymptote above which the regression settles as Trading ( 2008, p. 16).   
    $coefficie
&, wherents ' N were # definescoefficie
( significant thentsrepresents were number at significant the stabilization of 1% periods level. at the rate sampled, is: 1%  the level. larger the value of , the quicker stock volatility converges to its 2   isolation  , o bservations   for any day past 30 were droppedapproaches from the 0. The regression in model order to effectivelyminimize !the    represents
the
 significant" coefficie impactnts of were an IPO significant event on at stock the 1% volatility. level.    regression R values above 0.8100 and seven ofeleven above 0.950. In addition, all estimated increased volatility. one value for each value IPO were day required whenincreases to (4 )and run the the secondis regression 0 and . 
  


 
 

regressionTo investigate term the approaches IPO period zero; in  is an indicatorbecomes of equal the average to1 level . of long-­‐term volatility level . For allindustries , this model approximate s values very well with all For the purposes of this study, N is equal to 1 because volatility is measuredincreases on a and daylong -­‐ theby-­‐-­‐termday second basis volatility : regression level term. For all approachesindustries , zero; t his is model an indicatorapproximate of s the a verage values    level very ofwell with all     one value  for each    value were  required to  run the regression. To investigate thevalue IPO represents period in the effect of IPOon  stock volatility; captures the expected additionalincreases volatility on and an the second regression term approaches zero; is an indicator of the average level of isolation, o bservations for any day past 30 were dropped from the regression in order tominimize the     long-­‐term volatility level . For allindustries , this modelapproximate s values very well with all coefficients were significant at the 1% level. &      long!-­‐   run volatility  "that stocks will exhibit after the effects of theIPO period have ebbed. The variable 2  $isolation
, o 'bservations #
( $ for%' This any#
model day (The past was term 30 chosen is were the for dropped value its ability of2 to from the break horizontal the down  regression in volatility order asymptote to above minimize into which two the types: the IPO regression-­‐related volatility settles  as and regression R values above  0.8100 and  seven ofeleven above 0.950. In addition,  all estimated  This calculation   is based on

   

  

  


  

long-­‐run volatility regressionIPO that day ( stocks3R ) when values Volatility will 8 above exhibit 0. after8100 the and is 0 seven effects and 
  


 
 

of ofeleven theIPO above period have 0.950. ebbedIn addition,. The all estimatedvariable becomes long equal-­‐run to volatility 1 . that stocks will exhibit after the effects of theIPO period have ebbed. The variable isolation, o bservations for any day past 30 were dropped from the regression in order2 tominimize  the    regression R values above 0.81700 and seven ofeleven above 0.950. In addition, all estimated  9 increases  and represents the second ( stabilization4) regression rate8  term the larger approaches the value zero; is of an, the indicator quicker of stock the average volatility   level of converges  to its $
& 'baselin  #
(e volatility.representsSince stabilization the  
ratesecond  the term larger rapidly the decays value of as , the the counter quicker stock variable 9 volatility increases, it convergess  to its coefficients were significant at the 1% level.  Trading ( 2008, p. 16).   
      , where  N defines the number ofcoefficie periodsThents wereterm sampled, is: significant is !    the value at  of the" the 1% horizontal level. asymptote above which the regression settles as represents stabilization rate  the larger the value of , the quicker stock volatility converges to its   8 $
& ' #
( $ %' #
coefficie ( nts were significant at the 1% level.   9 9 For the purposes of this study, N is equal to 1 because volatilitylong is -­‐run measured volatility long on-­‐term a that day volatility -­‐ stocksby-­‐day levelbasis will8 : exhibit . For after all industries the effects, this of model  theIPO approximate period have ebbeds values . The very variable well with all 9 value represents long-­‐term the volatility effect of level  IPOon  stock. For all volatility;industries captures , this model theapproximate expected additionals values very volatility well on with an all     increases and the second regression term approaches zero; is an indicator of the averagelong level -­‐term of volatility level . For allindustries , this model approximate s values very well with all 2 7 regression R values above  0.8100 and  seven ofeleven above 0.950. In addition,  all estimated 9 represents stabilization2 rate(3 ) the  larger the value of , the quicker stock volatility converges to its IPO day whenregression R values long is above 0-­‐run and volatility 
  


 
 

0.8100 and that seven stocks of eleven will exhibit above after 0.9 the50. In effects addition, becomes of theIPO all equal estimated period to1 .have ebbed. The variable 2      (4) regression R values above 0.8100 and seven ofeleven above 0.950. In addition, all estimated     $
& ' #
long ( -­‐term coefficie volatilitynts level were . significant For allindustries at the, this 1% model level. approximate s values very well with all  The term coefficie is!     thents value were  of" significant the horizontal at the asymptote 1% above level. which the regression settles as  9 $
& '  #
( $ %'  #
( represents stabilization rate  the larger the value of , the quicker stock volatility convergescoefficie to9 its nts were significant at the 1% level. For the purposes of this study, N is equal to 1 because volatility is measured on a day-­‐by-­‐day basis :  2  9  regression R values above  0.8100 and seven ofeleven above 0.950. In addition,   all estimated   increases and the second regressionlong-­‐term volatility term approaches 7 level . For zero; all is industries an indicator, this model of the averageapproximate level ofs values very well with all  coefficients were significant at the 1% level.   long-­‐run volatility that stocksregression will( 4 exhibit) R 2 after values the above effects 0.81 of00 and theIPO seven period of have eleven ebbed above. The 0.9 50 variable. In addition,  all estimated      $
& '  #
represents ( $ %'  # stabilization
( rate  the larger the value of , the quicker stock volatility converges to its 9 coefficients were significant at the 1% level. 9 9 7  long-­‐term volatility level . For allindustries , this model approximate s values very well with all

 regression R 2 values above  0.8100 and seven ofeleven above 0.950. In addition,  all estimated 9

coefficients were significant at the 1% level. 9

9

Equity Volatility across Industries from IPO Day

impact of significant non-­‐IPO eventson the regression results; the 30-­‐day period was chosen to capture

the full effect of the IPO event while minimizing the effects of non-­‐IPO events on the data. The Equity Volatility across Industries from IPO Day regressions run toestimate all three values for each indexused the following model given known Equity Volatility across Industries from IPO Day impact of significant non-­‐IPO eventson the regressionEquityEquity results Volatility Volatility; the 30 across -­‐day across period Industries Industries was from chosen from IPO IPO to Day Day capture values for and :  Equity Volatility across Industries from IPO Day the full effect of the IPO event whileimpact minimizingEquity of significant Volatility the effects across non of non-­‐IPO-­‐IPO events Industries events on on the from the regression data IPO. The Day results; the 30-­‐day period was chosen to capture impact impact    o f o significantf significant non non-­‐IPO-­‐IPO events eventson on the the regression regression results results; the; the 30 -­‐ 30day-­‐day period period was was chosen chosen to to capture capture the full effect of the IPO event whileimpact minimizing of significant the non effects-­‐IPO of non-­‐ IPO events eventson the on regression the ( data8.) The results ; the 30-­‐day period was chosen to capture regressions run toestimate all three values for each indexused the following model given known  impactthethe o f full significant full effect effect of non of -­‐ the IPO the events IPO IPO event on event the while while regression minimizing minimizing results the; the effects effects 30-­‐day of non-­‐IPO of non-­‐ IPO period events events was on on chosen the the data . data The to. The capture 
  
!

" 
 values for and :  regressions run toestimate all three the values full for effect each of index theused IPO the event following while minimizing model given known the effects of non-­‐IPO events on the data. The The regressionthe fullregressionsregressions effect estimates of run run the average to toestimate IPOestimate industry event all all three while three volatility values minimizing values ( ) as for for a each the function each effects index index used of non-­‐ ofIPOused the events the the following number following on the of days model data . model The given given from IPO known known Equity Volatility across Industries from IPO Day     values for and : regressions run toestimate all three values for each indexused the following model given known Equity Volatility across Industries from IPO  Day ( regressionsvalues). valuesOn IPO for run for day, to and estimate and the all :three : values term (8 )is for equal each to index 0; used this the means following that average model IPO given day known volatility impact   of    significant non-­‐IPO eventsvalueson for the and regression : results ; the  30-­‐day period was chosen to capture      !  

" 
is estimatedvalues
impact! for by o fand significant

 " 
since       : non the -­‐IPO denominator events on the of regression the second results term; the 30 becomes-­‐day equal period toone (8. was ) For chosen each day to capture      (8()8 ) The regression estimates average industry volatilitythe ( full) as effect a function of the of IPO the event number while of days minimizing from IPO the effects of non-­‐IPO events on the data. The  
 
  
!

"
followingthe IPO, full volatility  effect   decays of theas IPO the event while minimizing term g rows  the and effects the of non-­‐ IPO second events regression on the term data. The (8)  



!!

"
 " 

  (8) ( ). On IPO day, the The term regressionregressions is equal  estimates to run 0; to thisestimate average means industry all that average three volatility IPOvalues day ( for) as volatility each a function indexused of the the following number of model days given from known IPO approaches 0. The modelEquity effectively Volatility !    represents across Industries
the
 significant" from impact IPO Day of an IPO
  event 
  on!  stock
 volatility.
" 
 -40- ECONPress regressionsTheTheEquity regression regression runVolatility to estimatesestimate estimates across average all average Industries three industry industry values from volatility for volatilityIPO each Day ( ) ( indexas ) as aused a function function the following of of the the number model number given of-41- of known days days from from IPO IPO Equity Volatility across Industries from IPO Day 
  
 !

" 
is   estimated by since !   the denominator

(" values of). On the for IPO second day, and the term : becomes equalThe regression to term one . Foris equal estimates each to day 0; average this industry means that average volatility IPO ( ) as day a function volatility of the number of days from IPO Thevalues regression( ( for ) . and )On estimates. On IPO IPO day, averageday, the: the industry  volatility term term ( ) is as is equal a equal function to to 0; 0; this of this the means means number that average that average of days IPO IPO day from day IPO volatility volatility   This modelEquityEquity was Volatility Volatility chosenimpact across for across o its abilityf significant Industries Industries to break non from down -­‐ fromIPO events IPO volatility IPO Day Day on the into regression two types: IPO results-­‐related; the volatility 30-­‐day period and was chosen to capture following IPO, volatility 
 decaysas the is   estimated term by g  rows   and since ! the    the second denominator
(
regression" ). On of IPO term the day, second the term becomes equal term toone is equal .  For to each 0; day this means that average IPO day volatility A significant positive correlation ex-  stock’s industry has on the way it behaves ( is   is estimated   estimated). On IPO day, by    by the since since !   !    the the denominator
denominator
term

" "is equal of of to the the 0; second this second means term term that average becomes equal becomes equal IPO to toone (8 dayone ) . For. For volatility each each day day Volatility Relative to IPO (Regression Models) baseline volatility.ists betweenEquityEquitySince the Volatility Volatility  t he full  
and effect across across. second A of linear Industries the Industries term regression IPO rapidly event from from decays while in IPO IPO the Day Day as market. minimizing the counter the variable effects of non-­‐IPO increases, events it s on the data. The approaches 0. The model effectively !   representsfollowing
the impact
 significant IPO,impact" volatility of o significantf significant
impact decays non of as an non-­‐ IPO IPO the-­‐IPO eventsis    event events estimatedon onon the the stock by regression term regression volatility. g rows since results!    and results the; thethe ; the denominator second
30 -­‐ 30day
-­‐day" period regression period of was the was term chosen( 8 second chosen) to term to capture capture becomes equal toone . For each day 0.9 showed that for  every  0.01 increase in is   estimatedfollowingfollowing Equity by IPO, Equity IPO, volatility Volatility volatility Volatility since 
!
   decays decays the across across as denominator
as Industries the the
Industries "
    from of
 from  the!  IPO  IPOterm second Day term Day
 g
 rows"g  rows term
and  and the becomes the equal second second toone regression regression. For each term term day , the valueregressions of is expected run toestimate to increase all three by values  Estimating for each Annualized indexused theVolatility following and model given known valueapproaches represents 0. The impact impact the model effect o off significant significant effectively of IPOon stock following ! non non   represents-­‐-­‐IPOIPO volatility; events events
IPO,
 the 
  significantvolatility on "on  captures
the the
!  regression regression decays impact the
as
 expected" the  of results results
an  IPO;; the the additional event 30 30-­‐-­‐dayday on period period term volatility stock g onrows was was volatility. an chosenand chosen the to second to capture capture regression term 0.8 Thethethe about regression full full effect 0.0757; effect estimates of of this the the indicates IPO average IPO event event industrythat, while as while a volatilitygen minimizing minimizing- an ( ) Optionsas the a the function effects effectsArbitrage of non-­‐IPO of non-­‐IPO of events eventsOpportunity the on number on the the of data . dataThe days. The from IPO This model was chosen for its ability to break downfollowing volatilityeral IPO, rule, volatility intoindustries
 two decays types:with IPOas the-­‐higherrelated IPO-time ! volatility   !  
and
term

" "g rows and the second regression term Technology Theapproachesapproaches regression 0.values 0. The estimates The model for model average and effectively effectively industry : represents represents volatility the the ( significant) significantas a function impact impact of of the a ofn an IPO IPO number event event of on on days stock stock from volatility. IPO volatility. Equity Volatility0.7 across Industries from IPO Day IPO day whenvolatility impactimpact will o falso significant o fis significant 0exhibit and 
  


 
 

nonrelatively -­‐ nonIPO-­‐IPO events events highon on the the regressionThe regression results results !of    results the; the ;study thebecomes
30 -­‐ day 30
have-­‐day" period equal perioda number to was 1 . was chosen chosen to to capture capture Consumer Goods (regressionsregressionsthe)the. On full run full IPO run to effect effect day, estimate toestimate the of of all the theEquity approaches all three IPOthree IPO Volatility event event values values 0. term The whileacross while for for modelis each equal Industries each minimizing minimizing effectively index to indexused 0; fromused the the this the IPO the represents effects effects following Day means following of non-­‐ of non-­‐IPOIPO the that average events events significant model model IPOgiven on on given the the day known impact known data data volatility.. The The of an IPO event on stock volatility. baseline volatility.Since the  
secondThis termapproaches model rapidly long-run was decays 0. chosenThe volatility modelas the forEquity its ability counter(See effectively Volatility Appendix to break variable !   represents across down IV ). increases, Industries True
the volatility
 significant " itsof from applications. into IPO impact twoDay types:Most of IPO an IPO-­‐ practicalrelated event volatility is the on stockpoten and - volatility. 0.6 ( ). On IPOEquity day, theVolatility     across Industries term is from equal IPO to Day 0; this means that average IPO day volatility v Healthcare The term ThisThisto is model! this   model thethe observation,the value full was was full effect  of chosen " chosen effect the ofthe for Equity horizontal of for thetop its ability the its ability IPO Volatilityand IPO to to event bottom break asymptote break event across above while down down while tialIndustries which volatility minimizing to volatility minimizing compare the from into regression into the IPO theindustry two effects Day two effects types: of non-­‐ settlesIPO types: IPO of non-­‐volatilityIPO IPO events-­‐related -­‐ as eventsrelated trends on volatility volatility on the the data . andThe data and. The is   values estimatedvalues forregressions regressions for and by and Equity run run since to to: Volatility estimate !estimate :   the denominator across all
all three three
" Industries values values of from the for for IPO second each each Day index index termused used the the becomes equal following following to one . For model model given given each known known ( day8 ) impact of significant non-­‐IPO eventson the regression results; the 30-­‐day periodMarket was chosen to capturebaselin e volatility.three sectorsSince theby  
are thevolatilitysecondThis same model term ofas their rapidly when was underlying chosen decays with for related as stocks, its ability the countertheoption to regression break prices; variable down models since volatility increases, generatedoption its into in two this types: study IPO-­‐ relatedcan be modified volatility to and 0.5 value represents the effect of IPOon stock volatility; is   estimated captures by theEquity expected since Volatility!   the additional across denominator

Industries" volatility on of from an the IPO second Day  term becomes equal toone . For each day increasesThis model and ordered the wasregressions second byregressions chosen  exceptvolatility regression run for run for its ability to estimate of tothe estimatetheir term toFinancials break underlying all approaches allthree down three sec -stocks, values volatility zero;prices values isthe for an are forregression into each indicator directly each two index index models types:used affected of IPOused the the a-­‐related veragegenerated the followingby    following thelevel volatility involatil of this model - andstudy model given given can known known be modified to Consumer Goods baselinbaselinevaluesvalues e volatility. volatility.   for forvolatility       Since
and and Since tofhe t hetheir  
 
:underlying: secondsecond stocks,  term term rapidly therapidly  regression decays decays 
 !as  modelsas the the counter

generated counter"  variable variable in this increases,study increases, can its it be s modified to the full effect of the IPO event while minimizing the effects of non-­‐IPO events on the data. The followingtor replacing IPO, volatility Telecommunications. decaysvolatilityas the of their underlying  ity
term of stocks, their g rows theunderlying and regression the second stocks, models
regression the generated regres term- in this study can be modified to 0.4 IPO day when is 0 and 
  


 
 

value represents  the effect volatility
 of IPOon of calculate stockbaselin theirbecomes volatility;underlyinge expected volatility. equal stocks, optionSince captures to1 . t hetheprices the  
regression using expectedsecond the models Black-Sc additional term generated rapidly holes volatility model. decays in(8 ()this on8 )This an as study the could can counter be be used modified variable to help to predict increases, its Oil & Gas following IPO,The volatility regression decays estimatesas the average industrysion term models volatility g rows generated and ( ) as the a function second in this regression ofstudy the can number term of days from IPO long-­‐baselinrun volatility valuevaluee volatility. represents represents valuesthat values stocksSince calculate for volatility the calculate for  the  t heand will effect  
and    effect   expected of exhibit expected their of of aftersecond IPO :underlyingon option IPOon : the stock option stock term prices effects volatility; prices rapidly stocks, volatility; using of using decays the  thethe IPO captures regressionthe captures Black-Sc period as Black-Sc the thehave holes the countermodelsholes expected ebbed model. expected model. generated variable. The This additional This additional could increases,in variable could this be volatilitystudy beused it volatility s used tocan on ontohelp an be an help modified predict predict to Volatility Rating The values represent an!    estimation

be" modified to calculate expected option regressions0.3 run toestimate all three values for each indexused the followingTelecommunications model given known approaches 0. The model effectivelycalculate expected represents  option the significant prices using impact the Black-Sc  of an IPOholes event model. on stock This could volatility. be used to help predict The term is!    the value  of" the horizontalIPO day asymptote whenof above how which quickly thecalculate the is regression 0effects and expectedoptionvalue 
  


 
 

of settles represents price!an    option
IPO as movements
 prices on
the 

prices
 effect"using! for! usingnew the of

Black-Sc
IPOs. IPO"the
on " 
stock Black-ScholesFor
holes example, volatility; becomesmodel. when model. This equalcaptures N()could This is to the be1 the. ( (usedcumulative88) ) expected to help distribution predict additional function volatility on of an approaches 0.( The model). On effectively IPO day, the represents the significant term impactis equal  of to an IPO 0; this event  means on stock that average volatility. IPO day volatility Industrials representsvalueIPO represents IPO stabilization day day when when the rateoption calculate effectoption  the price of largerprice   expected    movements IPOon is movements is 0 the stock 0 and option and value 
  


 
 

volatility; 
  


 
 

for forprices of new ,new the IPOs. using captures IPOs. quicker For the For example, Black-Sc theexample, stock expected holeswhen volatility when model. N() additionalN() is converges theis This the becomescumulative becomescould cumulative volatility to its be equal on used equaldistribution an distribution to to to1 help.1 . predictfunction function of of 0.2 TheThevolatility regression regression fade; estimates estimatesthe higher average average the industry value industry of volatility volatility, could ( ) ( as ) beas a aused function function to help of of predict the the number option number of price of days days from from IPO IPO values for and :   option price movements for new

! !IPOs. For



example,""  when N() is the cumulative(8)( 8) distribution function of increases and the secondFinancials regression termThe approachesThis term the model is! faster   the zero; was is valuean an chosenindustry indicator  of" the for regresses horizontal its abilitythe IPO of standard day the a verage totowards when break    asymptote normal level down  its above
of
 distribution,movements volatility which is the 0 into T for– and regressiont is 
  


 
 

new twothe time types:IPOs.

IPO settles to-­‐ relatedmaturity,For as example, volatility S is the spot and price of thebecomes underlying equal to1 .    option price movements!   for new
IPOs.
" For example,  when N() is the cumulative distribution function of 0.1 long-­‐IPOterm day volatilitybaseline when levelvolatilityis ! estimated   !   the. For standardlevel all is industries by  0 " and". normalAlthough 
  


 
 

, tsince his distribution, model thethe approximate denominatorwhen T–t isN() the s istime  of values the theto cumulativematurity, very second well becomes S term withisdistribution the all spot equal becomes equal price to to 1 of.one the. Forunderlying each day Basic Materials This(The(The model Theterm The) term . On ) . regression was regression On is IPO is the the IPO chosen option theday, standard day, value the value estimates price estimates the for of its ability normal ofmovements the average the average to horizontaldistribution, break horizontal industry industryfor term down termnew is asymptoteT IPOs. –is equal volatility asymptote volatilityt equalis above  abovethe For to time example, to ( which ( into) 0;) which as as 0; to this a a this maturity, the function two function thewhen means regression types: means regression IPO N() S of that average of-­‐is relatedis  that average the the the the spot settles cumulative settles IPO volatility number number IPO price as day as day of of of distribution and volatilitythe days volatility days underlying from from IPO IPO function of       the standard normal  distribution,

 

 T!–t! is the

time
"
"
to
maturity, S is the spot price of the underlying increases and three the industries second regressionwith thesecurity,The termquickest term K approaches is the drops is!    thestrike function zero value; price, is  of an "r is of the indicatorthe the risk-free horizontal standard of rate, the a veragenormal asymptote and above    σ level isdistribu the which of volatility - the of regression the underlying settles asset, as the 0 long-­‐run volatility that Utilities stocks (8 ) will exhibit after thebaselin effects2 e volatility. of theIPO Since  periodthe standard the have  
 ebbed normal
second. The distribution, term variable rapidly T – t decays is the time as the to maturity, counter S variable is the spot increases, price it ofs the underlying regressionThe R interm values  volatility  isThe!    theabove Thefollowing regression are regression value 0.security, the 81  IPO,00 ofsame" estimatesand the volatilityK estimates isasseven the horizontalthe average strike of decaysthree averageeleven price, with industryas asymptote industry above the r aboveistion, the volatility 0.9 risk-free which volatilityT–t50. In is  ( addition, the )the rate,as ( ) term aas time regression and function a functiong all toσrows estimated ismaturity, the and of settles volatility of the the theS as second is number ofthe    numberthe   regression underlying of of days days from termasset, IPO from IPO the 1 3 5 7 9 11 13 15 17 19 21  23 25 27 29 baselinis   increases is estimatedincreases   estimatede ( volatility.( and and by the by security, the) theSince).. On On second secondstandard IPO IPO the since K day, sinceis day,  
!   regression the! regression   thenormal the the thestrike second denominator
denominator distribution,price,
term
 term"
 term" r is approaches therapidly approaches of T term ofterm –risk-free t the is thedecays the is is second zero; equal equal zero; secondtimerate, as is is an to the toand to an term maturity, indicator term 0; 0;σ indicator counter is this this the becomes equal becomes Svolatility equal ofis means variable means ofthe to the a to theverageone spot a that average that average verageofone . increases, the Forprice. Forlevel underlying level IPO IPO each of it each of s the of day day day underlying day asset, volatility volatility the the highest and values,security, the K isvalue the strike of spotprice, price r is the of risk-freethe underlying rate, and security, σ is the volatilityK is of the underlying asset,   the  
!
represents
"  stabilization rate  the larger thelong -­‐ valuerunvalue volatility of represents , the that quicker stocks thesecurity, stock effect will volatility exhibitK ofstandardincreases is the IPOon after strike stock Black-Scholes the converges and price,  volatility; effects the r second to is its of the model captures therisk-free IPO regression for period the therate, pricing have term expectedand ebbed ofσ is approachescall the. The options additional volatility variable zero;follows of volatility is the an the underlying on indicator equations: an asset, of the a veragethe level of  Counter
  Day 
 does notapproaches appear to 0. be The significantly model effectively cor- the !   represents strike
price, the 
  significant" r is the risk-free impact rate, of an   IPOand σ event on stock volatility. coefficieincreasesvaluentslonglong were represents -­‐ and run-­‐runisis    significant   ( volatility the estimated estimated volatility ( second standard thesecurity, )standardthat . that On
at effect) by. by
On regression stocks IPO the stocksBlack-Scholes K IPO Black-Scholesday, is of 1% theday, will IPOthe since onsince will level.strike term! the! stock    exhibit    exhibit the the model price, after model approaches volatility; after denominator denominator

forr the is
the
for the"" effectsthe term effectspricingrisk-free zero; captures term pricing of ofis is of  an equal of is of the therate, equalofcall the the indicator IPO the callIPO second secondoptions toand period expected options period to 0; σ is 0; this of termfollows have termthe thishave follows the avolatility additional verage ebbed means ebbed the becomes becomes means equal equalthe equations:. that averagelevelThe .of equations: The that average to volatility tothe ofone one underlying variable IPO on. variable . For IPO For an day each each day asset, volatility volatility day day the The regression estimates average industry volatility ( ) as a function of the number of days from IPO followingfollowingrelated IPO, with IPO, volatility volatilityeither decays decays orstandard as ;as thefor the Black-Scholes example, is model the term term volatility for g rows theg rows pricing and of and the the the ofunderlying second call second options regression regressionasset, follows the termthe term equations: represents stabilization rate  the largerlong the-­‐run volatility value of that , the stocks  quicker will stock exhibit volatility after the converges effects of to its theIPO period have ebbed. The variable tween the industries studied are no reason Gaminglong Corp,-­‐term a casino volatility operator. level On. For some allindustries , thisIPO model day the Utilities whenapproximate sectorstandards has values the Black-Scholesis fourth very 0 and well 
  


 
 

highest with model all forstandard the pricing Black-Scholes of call options model follows forbecomes the the pricequations: equal- to1 .         !   !  


"
"   longIPO-­‐representsrunrepresents day volatility whenfollowingfollowingis estimated stabilizationis stabilizationthat estimated standard IPO, IPO, stocks volatility volatility by rate by Black-Scholes will rate
is 
 the 0 decays exhibit decays the and since larger larger after 
  


 
 

since !   as as ! the   model the the the the denominator
effects valuefor denominator
value
the"
 of " pricing of , the , the ofIPO term ofterm of quicker the period quicker call the g g secondrowsoptionsrows have stock second stock and and ebbed follows term volatility the the term volatility second.becomes second The the becomes equal becomes equations: converges equal regression converges regressionvariable equal to one toone to. For its to1 . . its term For term each each day day (9) ( for )concern.. On IPO day, the term is equal level, tohowever, 0; this their means performances that average IPO are day all volatility approachesapproachesvalue but 0. This the 0.The The modellowest model model was effectively and effectively chosen values. represents for represents its ability As the to theing significant break significantof call down options impact impact volatility follows of an of IPO an into IPOthe event equations: two event types: on IPO on stock -­‐related stock volatility. volatility. volatility and  2   ି௥ሺ்ି௧ሻ (9)(9)  correlatedregression with both R values the availability above  0. 81of00 con and - seven long of-­‐termeleven The volatility a aboveresult, term is levelwe 0.9!    the5 can0 . In . value concludeFor addition,  all  of"industries represents the that all estimated horizontalIPO, this stabilizationperiod model asymptoteapproximate above rate  which the s larger values the the regression very valueଵ well with of settles, the allଶ as quicker stock volatility converges to its (9) ݁ܭሺܵǡݐሻ ൌ ܰሺ݀ ሻܵെܰሺ݀ ሻܥ       In every regression, all three variables werestatistically significant at the 1% level. Since all stock The sectors with the highest baseline sumers’ disposable income in addition to representsstabilization stabilizationfollowingfollowing!   rate IPO, rate and IPO, volatility  the volatility " larger
 decays
 decays magnitude theas value theas ! the!      of , the

quicker

 "" term term stock g rows g rows volatility and and the ି௥ሺ்ି௧ሻ the ି௥ሺ்ି௧ሻ second converges second  regression to regression its term term(9) Thelonglong -­‐term term -­‐termapproachesapproaches volatility is volatilitybaselin the 0.e value 0. level volatility. The levelThe of model model . For . the For Since all effectively all effectively horizontalindustries tindustries he  
, represents represents t ,his asymptote thissecond model above model the the termapproximate which significantapproximate significant rapidly ଵ theଵ decays impacts regression impact s values ଶ values as ଶ of of the very an an very settles IPO IPO counter well well event event as withି௥ሺ்ି௧ሻ with variable all on on all stock stock increases, volatility. volatility. it s  ݁ܭሻ݁ܭǡݐሺܵǡݐሻ ൌሻ ܰൌሺ ܰ݀ሺሻ݀ܵെܰሻܵെܰሺ݀ሺ݀ሻܵܥሺܥ 
" of the second term becomes equal toone . For each day 2
the denominator    estimated by since !   is volatility are technology,
consumer ser- consumers’ constantly-shifting preferences; regressionThisThis R are model values modelnot closely above was was  chosen 0.linked chosen8100 forand when for long its ability seven its ability observing-­‐term to of to break eleven volatility break in down - above down level volatility volatility 0.95. 0For . In all ሺ into addition, intoindustries  ሻ two two ሺ all types: , estimated ଵ t types: IPOhisሻ IPO -­‐ modelrelated-­‐relatedି௥ሺ்ି௧ሻሺ ଶapproximate ሻ volatility    volatility (9) and s and values (9) very well with all (level of (10 ݁ܭ is ܵǡݐ an indicatorൌ ܰ ݀ ܵെܰೄ of the average഑݀మ ܥ ;prices change regularly,baseline volatility wa s expectedto becoefficie positivents and werestatistically significant significant at the 1% level. increases and the second regression term approaches zero  2 2   !   !  


"
" ଵ ଶ . event all event on on stock stock volatility. volatility    well ofି௥ሺ்ି௧ሻ an of IPO మ an with൰ሺ்ି௧ሻ IPO ݁ܭ impactሺ୪୬ቀ very ݀ ಼ሻቁା൬௥ା  approximate ሺܵǡݐ theሻ theൌ significant ܰ significantሺ݀s ሻ values ܵെܰ impactܥvices, and healthcare.  Technology, the most the unpredictability of these factors adds to long-­‐termdustry volatilityapproaches averages.approaches level 0. . The 0.For  The  model all modelindustries effectively effectively, this model represents represents increasesregressionregression and R value theR values values second represents above above regression 0. 0. 81 the810000 and effect and term seven seven of approaches of IPOon ofeleven eleven stock above volatility; above zero; is 0.9 an 0.95ଵ 05 indicator.0ೄ In captures. In addition, addition,మ ഑మଶ the of all the a expected a estimatedllverage estimated level additional 9 of volatility(10) on an followingvolatile IPO, volatilityindustry, 
 decays exhibitsas thevolatility  levels uncertainty term g rows for and all the Service second companies. regression term 2 ሺ ሻ  ሺ ೄሻ ഑ ሺ ሻ (10) ( and and all estimated(10 types: types:഑ IPO above IPOమ -­‐-­‐relatedrelated 0.950 volatility. volatility In addition, ݁ܭdownܵǡݐ down 0.81ൌ volatility00 ܰ volatility and ݀୪୬ቀ ܵെܰseven ಼ ቁା൬௥ା intoଵ into of݀మ ൰ሺ்ି௧ሻ twoeleven ೄ two ܥ from zero. The consistency of increased volatility
on IPO dates means that IPO-­‐driven volatility was coefficients wereThisThis significant model model was was at the chosen chosen regression 1% for level. for its ability its ability R values to to break break above longbaselinbaselin-­‐rune volatility volatility.e volatility. that Since Since stocks the the  
 
will exhibitsecondsecond after term the term rapidly effects rapidly decays of decays theIPO ୪୬ቀ as ಼ as periodቁା൬௥ା the the݀ counterൌమ counterhave ൰ሺ்ି௧ሻ ebbed ఙ variable ξ variable்ି௧. The increases, increases, variable its it s that are equal to nearly double those seen 2  ೄ ୪୬ቀ഑మ಼ቁା൬௥ା మ ൰ሺ்ି௧ሻ (10) (10) regression R values above  0.8100 and seven ofeleven above ଵ 0.95ଵ0. In addition,  ఙ ்ି௧ all estimated longcoefficiecoefficie-­‐run volatility ntsnts were were that significant significant stocks at will at the exhibit the 1% after 1% level. level. the effects of݀ theൌIPO ୪୬ቀ periodఙቁା൬௥ା்ି௧ξ have మ ൰ሺ்ି௧ሻ ebbed. The variable approachesin the 0. runner-up The model Consumer effectively Services !   represents sec
the -
 significant" The three impact stocks of an IPOexhibiting event the on lowest stock volatility. IPO day when is 0 and 
  


 
 

݀ ൌ ೄ ಼ଵξ ഑ మ becomes (10) equal to1 . expected to bepositive and nonzero, as well. Finally, since the levels of volatility observed on
IPO dates baselinbaselinThisThis modelee model volatility. volatility. was was Since Since chosen coefficie chosen t thehe for  
 
nts for its ability were its abilitysecondsecond to significant break to break term term down down rapidly rapidly at volatility the volatility decays decays 1%݀ ൌ level. into as as into the the two counterఙ counter twoξ ்ି௧ types: IPO types: IPO -­‐ variablerelated variable-­‐related volatility increases, increases, volatility it its ands and representsvaluevalue represents represents stabilization the the effect rate effect  the of of larger IPO on IPOon stock stock the volatility; value volatility; of , thecaptures captures quickerଵ ୪୬ቀ the ಼ theቁା൬௥ା stock expected expectedమ ൰ሺ்ି௧ሻ volatilityೄ additional additional഑మ converges volatility volatility toon its on an an tor. For the Technology sector, this can be amount of baseline volatility – basic materi- Section VI: Conclusion ݀ ൌ ఙξ்ି௧  (11) coefficients were significant at the 1% level. ଵ ୪୬ቀ಼ቁା൬௥ି మ ൰ሺ்ି௧ሻ represents stabilization rate  the larger the value of , the quickerೄ stockఙξ்ି௧మ ഑ మ volatility converges to its (11) areexplained typically expected by the tounpredictability decline over time,of stabilization earn- als, rate telecommunications,s were also expected and to utilities be positive – are The term is!    the value  of" the horizontal  ݀ ൌ asymptoteೄ above഑ which the regression(11) settles as (11) valuevaluebaselinbaselin represents represents e volatility.e volatility. the the Since effect effectSince the t he of  
of  
IPO IPOon on stock stocksecondsecond volatility; volatility;  term term rapidly rapidly captures captures ୪୬ቀ decays ಼ decays ቁା൬௥ିଶ the theas మ theas ൰ሺ்ି௧ሻ ೄ expected expected the counter ഑ counterమ additional additional variable variable increases, volatility volatility increases, on on it s an an it s (11) ings linked to the dynamic, rapidly-evolv- all characterized by relatively stable revenue longIPOIPO-­‐ termday day The when volatility when models level used in. For thisis allis 0 0study’sindustries and and 
  


 
 


  


 
 

regres, this- modelapproximate ୪୬ቀ಼ቁା൬௥ିs݀ values ൌమ ൰ሺ்ି௧ሻ very ఙξbecomes்ି௧ well becomes with equal all equal to 1 to. 1 . This model was chosen for its ability to break down volatility into two types: IPO-­‐related volatility and 9 ೄ ୪୬ቀ഑మ಼ቁା൬௥ି మ ൰ሺ்ି௧ሻ (11) ing nature of the industry and the uncer- streams and predictable earnings. Respon- sions provide both the tools to predict  Havingଶ݀ଶ greaterൌ insightఙξ்ି௧ into the motion nonzero values. The regression results confirmedthese expectations
on all counts. Furthermore, the long-­‐term volatilityincreases level and . the For Having all secondindustries greater regression insight, this model into term theapproximate ݀ motion approachesൌ ୪୬ቀ ofೄ ಼ఙs ଶσቁା൬௥ିξ ்ି௧ zero;in values ഑thisమ మis ൰ሺ்ି௧ሻ anmodel very indicator well given with a ofcompany’s all the average    industry level (11) of will allow for more valuevalue represents represents  the the effect effect of of IPOon IPO on stock stock volatility; volatility; captures captures ݀ ൌ the the expectedఙ ξ expected்ି௧ additional additional volatility volatility on onan an tainty surrounding the future profitability sible for functions earlier in the production TheThetrends term IPOIPO term in2 day day isstock! is    the when! when    the price value value volatility  of"  of" the the around horizontal is horizontalis 0 0 and and the 
  


 
 


  


 
 

asymptoteof asymptote σ above in above this whichଶ whichmodel୪୬ቀ the಼ ቁା൬௥ି thegiven regression regressionమ a൰ሺ்ି௧ሻ company’s settles settles indus as becomesbecomes as - equal equal to to1 1 .. baseline volatility.Since the  
second term rapidly decays as the counter variable increases, its regression R values HavingHaving above greater 0.greater8100 insight and insight seven into into the of the eleven motion motion above of ofσ in ݀σ 0.9thisinൌ5 this0 model. In model addition, ఙ givenξ்ି௧ given a allcompany’s a estimated company’s industry industry9 will will allow allow for for more more of 2technological innovations. For similar line, companies in the Basic Materials in- 30-day IPO2 period as wellHaving as greateran effective insight intotry willthe motionallowଶ for of moreσ in this accurate model forecastgiven a company’s of industry will allow for more high R values associated with the regressions indicate that the model described by Equation (8) regression R values above  0.81accurate00 and forecastseven of ofeleven d and above d ݀and, ൌ 0.9 as50 .a In result, addition,ఙ ξ ்ି௧ a recent all estimated IPO’s call options. This information can also be reasons, the healthcare industry ranks in dustry deal with a customer pool with less breakdown  IPOIPO longday of day -­‐ whenIPOrunHaving when volatility ! !period      greater volatility that insight stocks"" is into 0 intois 0 and will its the and 
  


 
 

exhibit motion 
  


 
 

d1 and after 2dof the and,σ in effects thisas a model result, of givena theIPO recent period a company’s IPO’s have callbecomes ebbed industry becomes. The equal will9 equal 9 allow variable to1 to. for 1 . more increasesincreasesTheThe and and the term term the accurate second is second is the the regression forecast value value regression of of of thed term the termand horizontal horizontal d approaches approachesand,1 as a asymptote asymptoteresult, zero;2 zero; above above is is a an recent an which which indicator indicator IPO’s the the call of regression regression of options. the a verage the average   This settleslevel settles   level information of as as of can also be value represents the effect of IPOon stock volatility; captures the expected additional volatility on an coefficients were accurate significantHaving greaterforecast at the insight of d 1%1 and into 1 level. d the2 and,2 motion as a result, of σ in a this recent model IPO’s given call a options. company’s This industry information will allowcan also for bemore 9 capturesthe top the three typical most trends volatile in price industries. volatility exhibited For elastic by stocks demand in each sector than thosevery accurately in other. A indust the - two main components: accurateIPO-fueled forecast volatil of- d1 options.and d2 and, This as ainformation result, a recent can IPO’s also callbe options.ap- This information can also be coefficients wererepresents significant stabilization atapplied the to 1% rate put  level. optionthe larger pricing the using value the of Black-Scholes, the quicker model: stock volatility9 converges to its pharmaceutical companies, profitability is tries. For Telecommunications businesses, ity andThe baselineThe term accurate term volatility. is!    is the!    theforecast The value value results  ofof"  ofd " the1 and indi the horizontal d- 2 horizontal and,plied as to a result, asymptoteput  asymptote aboveoption abovea recent which pricing which IPO’s the using thecall regression options. the regression Black- This settles settles information      as as can also be  longlong-­‐run-­‐runincreasesincreases volatility volatility and that and that the the stocks stocks second second will will regression exhibit regression exhibit after after the term term the effects effects approaches approaches of of theIPO theIPO zero; zero; period period is is an an have indicatorhave indicator ebbed ebbed . ofThe of . The the the a averageverage variable variable level level of of IPO day determined when by the approval is 0 and (or 
  


 
 

rejection) client contract2 volume is notbecomes typified equal by to1 . cate which industriesappliedaccurateapplied to have forecasttoput put theoption option most of pricingd1 volatilepricingand dusing2 and,usingScholes the as the Black-Scholesa result, Black-Scholes model: a recent model: model: IPO’s call options. This information can also be 10% level, sample sizehad an insignificant effect on fit quality R ( see Appendix III ); this implies that applied to put option pricing using the Black-Scholes model: of drugs by the FDA; the future cash flows sharp drops or big spikes. Utilities, the sec- IPOs, whichlong stabilize-­‐term volatility the fastest, level and . aboutFor all industries , this model approximate s values very well    with   all longlongincreasesincreases-­‐-­‐runrun volatility volatility appliedand and the that thethat to second put stocks second stocks option regression will will regression pricing exhibit exhibit using after term after term the the the approaches Black-Scholes approaches effects effects of zero; of zero; the the IPOmodel:IPO is an is period period an indicator indicator have have ebbed ebbed of of the a verage.. the The aThe verage level variable variable level of of Thevariations generated term in is!    sample theby a valuedrug size  ofawaiting " between the horizontalapproval the industries can asymptote tor above studied with which are the no thelowest reason regression baseline for concern. settlesvolatility, as is representsrepresentswhere each stabilization stabilization industryapplied stabilizes; rate to rate put  the  optionthe larger they larger pricingprovide the the using value value the of of , Black-Scholes the, the quicker quicker model: stock stock volatility volatility converges converges(12) to its to its (12) be very large if the drug receives approval or perhaps characterized by the most predict- both ordinal and cardinal2 measures of vola-   ି௥ሺ்ି௧ሻ  (12)(12) longlongregression-­‐run-­‐run volatility volatility R values that that stocks above stocks 0. will 81 will 00 exhibit and exhibit after seven after the of the eleven effects effects above of of theIPO theଶ 0.9IPO period50 period. In addition, have have ebbed ebbed all . estimated The . The ଵ variable variable (12) volatility volatilityെ ൫ͳെܰ converges convergesሺ݀ ሻ൯ܵ to to its its ݁ܭcan be zero if the drug is ultimately reject- able future cash flows; profits seen in this tilityrepresents representsfor all sectors stabilization stabilization examined. rate rateWhile   the the no larger larger two the the value valueܲሺܵǡ ݐ of of ሻ ൌ,, the the൫ͳെܰ quicker quickerି௥ሺ்ି௧ሻሺ݀ ሻ ൯ stock stock increases and the second regression term approaches zero; is an indicator of the average   level of longlong-­‐term-­‐term volatility volatility level level . For . For all allindustries industries , this, this model modelapproximate approximate ି௥ሺ்ି௧ሻs s values values very very well well with with all all (12) ሺ ሻ ൫ ଶሺ ଶሻ൯ ି௥ሺ்ି௧ሻ൫ ଵሺ ଵሻ൯ 9 with ଶmoreെ ൫െ accuracyͳെܰͳെܰሺ݀ acrossሻ݀൯ܵ ܵ industry,ଵ  put(12) options can be better ݁ܭ݁ܭed. Consumer Services is a very broad sec- sector are usually stabilized by both steady stocks can be expected to Oncebehave again, exactly if dܲ 1theሺ andܲܵǡ ݐܵǡሻ d ݐൌ2 can൫ൌͳെܰ beͳെܰ predictedሺ݀ ݀ሻ൯  ܵ െ ൫ͳെܰሺ݀ ሻ9൯ ݁ܭcoefficients were  significant at the 1% ܲ level.ሺ ܵǡ ݐሻ ൌ ൫ͳെܰሺି௥ሺ்ି௧ሻ݀ ሻ൯ tor and includes companies ranging from 4 consumer demand and heavy regulation in samelong longregardlessrepresentsrepresents2-­‐-­‐termterm2 volatility Once volatilityof stabilization their stabilization again, commonalities, level level if d rate1 .and . For rateFor  the d all  all2 the can industries larger industries the largerbe predicted the , the, Once t t hishis value model value model with again, of more of ,approximate approximate ଶ the ,if the accuracyd quicker  quickerand ss d across stock values values can stock industry, volatilitybe very very volatilitypreଵ well well - put converges with with options converges all all tocan its to its be better In addition,ି௥ሺ்ି௧ሻ 1 addition, acrossെ 2 all ൫ estimated all ͳെܰindustry, estimatedሺ݀ ሻput ൯ܵ options can be better ݁ܭ. long-­‐run volatility that stocks will exhibit after the effects of theIPO period have ebbed. The variable regressionregression R R values values Once above again,above 0. if 81 0. d81001 and00 and and d 2seven can seven be ofܲ predicted ofeleven ሺܵǡeleven ݐሻ ൌ above൫ abovewithͳെܰ more 0.9 ሺ݀5 0.905.ሻ 0accuracy൯In Kids Entertainment, a children’s film and cases where monopolies are allowed. 11 industry volatility forecastsOnce found again, here if d1 canand d2dicted can be with predicted moreଶ withaccuracy more across accuracy industry, acrossଵ industry, put options can be better more accuracy accuratelyെ across൫ͳെܰ. Most industry,ሺ݀ important,ሻ൯ܵ put options however, can beis simply better the use of݁ܭ Once again,valued if d and dtheir canܲ priceሺ beܵǡ ݐpredictedሻ trendsൌ ൫ͳെܰ predicted withሺ݀ moreሻ൯ television production company, to Boyd help to lend insight22 into the impact1 2that a put options can be better valued and their  regressionregressionlonglong-­‐termvalued-­‐termOnce Rvalued R volatility values values volatility again,and and their above above level iftheir d level price and 0. 0.price 81.81 For trendsd00.00 For trendscan all and and all industries bepredicted seven seven industries predictedpredicted of of, eleven more televen his, morewith this model accurately model above abovemore accuratelyapproximate accuracy approximate 0.9 0.9. 55Most00.. .Most In In across addition,important, addition,s  important,s values industry,values all allvery however, estimated estimated very however, wellput well options with is simplywith is allsimply can all the be the use better use of of represents stabilization rate  the larger the value of , the quicker stock volatility converges to its coefficiecoefficientsnts were were significant significantvalued at at the1 and the 1% their 2 1% level. level.price trends predicted more accurately. Most important, however, is simply the use of the regressions to identify typical volatility trends by industry and, as a result, predicted directional valued2 2 and their price trends predicted more accurately. Most important,  however, is simply the use of  coefficiecoefficieregressionregressionthentsntsvaluedthe wereregressionsR were regressionsvaluesR and significantvalues significant their above toabove pricetoidentify 0. identify at at81 0. trends the0081 the typical 00and typical 1% and 1%predicted seven volatility level. level.seven volatility of moreeleven of trendseleven trends accurately above by above byindustry industry 0.9. 5Most 0.90.5 In and,0. important, addition,and,In as addition, asa result, a result, all however, estimated allpredicted estimated predicted is simply directional directional the use of long-­‐term volatility level . For allindustries , this model approximate s values very well with all the regressions to identify typical volatility trends by industry and, as a result, predicted directional the regressionsoptions to price identify movement. typical volatility trends by industry and, as a result, predicted directional coefficiecoefficientsnts were were significant significant at at the the 1% 1% level. level. 9 2   optionstheoptions regressions price price movement. movement. to identify typical volatility trends by industry and, as a result, predicted directional regression R values above 0.8100 and seven ofeleven above 0.950. In addition, all estimated options price movement. options price movement. Determining the precise effects on option price movement provided by the regression results exceeds coefficients were significant at the 1% level. options price movement. 9 9 DeterminingDetermining the the precise precise effects effects on on option option price price movement movement provided provided by bythe the regression regression results results exceeds exceeds Determining the precise effects on option price movement provided by the regression results exceeds the scope of this study. A starting point, however, would be to estimate annualized volatility using the Determining the precise effects on option price movement provided by the regression results99 exceeds theDeterminingthe scope scope of ofthis the this study. precise study. A starting effectsA starting on point, optionpoint, however, however, price movement would would be be toprovided toestimate estimate by annualized the annualized regression volatility volatility results using usingexceeds the the the scope of this study. A starting point, however, would be to estimate annualized volatility using the the scoperegression of this study. results A starting – the Black-Scholespoint, however, model would uses be volatility to estimate on anannualized annualized volatility basis. Assumingusing9 9 the that the regressiontheregression scope results of results this –study. the – the Black-Scholes A Black-Scholes starting point, model model however, uses uses volatility would volatility be on toon an estimate anannualized annualized annualized basis. basis. Assuming volatilityAssuming that using that the thethe regression results – the Black-Scholes model uses volatility on an annualized basis. Assuming that the regression results – the Black-Scholes model uses volatility on an annualized basis. Assuming that the ߥҧ 9 ߥҧ ߥҧ regression results – the Black-Scholes model uses volatility on an annualized basis. Assuming that the ߥҧ 14

14ߥ 14ҧ ߥҧ 14

14 14

Equity Volatility across Industries from IPO Day

Equity Volatility across Industries from IPO Day was meant to reflect the real effects of dividend payments on shareholder value. For example,Microsoft

was meant to reflect the real issued effects a of one dividend-­‐time special payments dividend on shareholder of $3.00 value. on November For example, 15, 2004Microsoft ; because the price drops associated

issued a one-­‐time special dividendwith dividend of $3.00 payouts on November do not 15, affect 2004; because shareholder the value, price 3 was drops associated added to the closing prices, low prices, and

Equity Volatility across Industries from IPO Day with dividend payouts do not high affect prices shareholder for allMicrosoft value, 3 was observations added to on the or closing after the day prices, the low dividend prices, and was issued. This does not lead

high prices for allMicrosoft observationsto a perfect adjustment on or after the for daydividend the dividend payouts. S ince was issued no. This stocks does paid not out lead dividends within their first thirty Equity Volatilityratings across represent Industries variance, from that IPOany Day given year includes 252 trading days, and that volatility levels to a perfectadjustment fordividend days of payouts. trading, S however,ince no stocksno observations paid out dividends used in regression within their were first affected; thirty as a result, this inaccuracy remain close to after IPO, estimated annualized volatility as variance for any industry could be was meant to reflect the real effects of dividend payments on shareholder value. For example,Microsoft ଶ days of trading, however,no observationsdid not affect used results. in regression were affected; as a result, this inaccuracy ଵ calculated using:߮ ߪ issuedEquity a one Volatility-­‐time special across Industries dividend from of IPO $3.00 Day on November 15, 2004; because the pricedid drops not associated affect results. The data is subject to some level of selection bias. All of the companies chosen were still trading as of with dividendratings represent payouts variance, do not that affect any given shareholder year includes value, 252 3 wastrading added days, and to that the volat closingility levels prices, low (13) prices, and ଶ ଷ଴ ఝమ The data is subject to someDecember level of 31, selection 2009 bias.; All as a of result the, companies companies taken chosen were private still trading for reasons as of including bankruptcy and issued߮ଵ could.ሻ This be does not lead כ ሺ ௜ିଵ dividend ሻ ቁfor൅ሺʹʹʹ any industry wasכhigh pricesremain for close all toMicrosoft after IPO, observations estimated annualizedߪ onൌ orσ ௜ୀଵ aftervolatility theቀ߮ଵ day൅ asଵାఝ variance theయ ଶ December 31, 2009; as a result, companies taken private for reasons including bankruptcy and The correspondingଵ annualized standard deviation , which is also a component of the Black-Scholes acquisition may be underrepresented. Furthermore, the accuracy of the S&P 500 as a true market to a perfectcalculatedadjustment using:߮ fordividend payouts. S ince no stocks paidߪ out dividends within their first thirty model, can be calculated using: ߪ acquisition may be underrepresentedbenchmark. Furthermore, is not perfect the accuracy because of the the S&P S&P 500 500 includes as only a true large companies market that have maintained days of trading, however,no observations used in regression were affected; as(13) a result, this inaccuracy ଶ ଷ଴ ఝమ benchmark is not perfect becauseconsistent the profitability. S&P 500 includes If stock only large resilience companiesor company that have sizes are main tcorrelated ained withIPO period volatility ߮ଵሻ כ ʹʹʹሺ௜ିଵሻቁ ൅ሺכdid not affect results. ߪ ൌσ௜ୀଵ ቀ߮ଵ ൅ ଵାఝయ (14) The corresponding annualized standard deviation , which is also a component of the Black-Scholesconsistent profitability. If stock trends, resilience theor results company of sizes this are study correlated may be with skewedIPO period as a result. volatility ଷ଴ ఝమ ߮ଵሻ כ ʹʹʹሺ௜ିଵሻቁ ൅ ሺכߪൌටσ௜ୀଵ ቀ߮ଵ ൅ ଵାఝయ The data model, is subjectcan be calculated to some using: level of selection biasߪ. All of the companies chosen were stilltrends, trading the as results of of this study may be skewed as a result. The resulting value represents the sum of all daily expected daily volatility ratings – the first term Section IV: Methodology December 31, 2009; as a resultଶ , companies taken private for reasons including bankruptcy and represents theߪ 30-day IPO period as modeled by the regression results (14)while the second term represents ଷ଴ ఝమ Section IV: Methodology of߮ theଵሻ S&P 500 as a true market כ ʹʹʹሺthe ௜ିଵሻ accuracy ቁ ൅ ሺ כacquisition may be underrepresentedߪൌටσ. Furthermore, ௜ୀଵ ቀ߮ଵ ൅ ଵାఝయ The methodology followed throughout this study consists oftwo processes. First is the calculation of The resultingthe remaining value represents222 trading the days sum ofin allthe daily 252-day expected trading daily volatility year. Additional ratings – the adjustments first term could be made to benchmark is not perfect because the S&P 500 includes only large companies that have maintained ଶ The methodology followed throughout this study consists oftwo processes. First is the calculation of 
representsthis estimation; theߪ 30-day IPO for period example, as modeled the long-run by the regression volatility results term while could the be second adjusted term representsto account for unforeseen values that represent average intraday price volatility foreach industry. Second is the nonlinear consistent profitability. If stock resilienceor company sizes are correlated withIPO period volatility values that represent average intraday price volatility foreach industry. Second is the nonlinear 
the remainingvolatility 222 spikes trading over days the in the course 252-day of thetrading trading year. Additionalyear. Using adjustments some percentage could be made ρ to to represent the effect of regression of values against time from IPO in order to estimate volatility trends following IPO day in trends, the results of this study may be skewed as a result. this estimation; for example, the long-run volatility term could be adjusted to account for unforeseenregression of values against time from IPO in order to estimate volatility trends following IPO day in abnormal volatility spikes on long-run volatility, we can calculate: each industry.
Equity Volatility across Industries from IPO Day volatility spikes over the course of the trading year. Using some percentage ρ to represent the effect of 
eachEquity industry. Volatility across Industries from IPO Day -42- Section IV: Methodology ECONPress Methodology Subsection I: Calculating -43- abnormal volatility spikes on long-run volatility, we can calculate: (15) impact of significant non-­‐IPO eventson the regression results; the 30-­‐day periodEquity was Volatility chosen across to capture Industries from IPO Day ఝమ ଶ ଷ଴ Methodology Subsection I: Calculating  ሺͳ ൅ ɏሻ כ ߮ଵሻ כ ʹʹʹሺ௜ିଵሻቁ ൅ሺכߪ ൌσ௜ୀଵ ቀ߮ଵ ൅ ଵାఝయ the fullprice effect trends of the predictedThe IPO m ethod event moreology while followedaccurately. minimizing throughout the effects this of non-­‐IPO study events consists on of thetwo processes. data. The First (15) is the calculationrately predict of the motionThe of calculation values from process tion sector was runexhibitindividually total IPO-time using data volatility setsthat include the trading history forthe S&P impact of significant non-­‐IPO eventson the regression results; the 30-­‐day period was chosen to capture Most important, however, is simply the useଶ ଷ଴ ఝమ IPO day, it cannot be assumed that these of about 0.16 while their baseline volatil- ଵ ଵ (16) ,ሺͳ ൅(16) ɏሻ The calculation trends can
processbe used to was 500effectively run individually and
each predict of using the tenity data selected levels sets that are industry closeinclude to groups the 0.03. trading provided If a portfolio history by MarketWatch for the S&P . For allexamined data sets כ ߮ ሻ כ ʹʹʹሺ௜ିଵሻቁ ൅ሺכ൅ ଵାఝయ of the regressions to identify typical volatilߪ- ൌσ௜ୀଵ ቀ߮ regressions run toestimate value alls that three represent values average for each intraday indexused price the ଷ଴volatility following foreach ఝ modelమ industry given known . Second is the nonlinear ity trends by industry and, as a result, pre- ଵ the full effect of the IPOଵ event whiletrends minimizing in individual the stocks effects of non-­‐ IPOwithout events further on the manager data. The wants to wait until the stock has ሺͳ ൅ ɏሻ כ (߮ ሻ(16 כ ʹʹʹሺ௜ିଵሻቁ ൅ ሺכߪ ൌටσ௜ୀଵ ቀ߮ ൅ ଵାఝయ dicted directional options price movement. 500 andanalysis.
each of the ten selected industry groups provided stabilized by and MarketWatch volatility . hasFor dropped allexamined below data sets, values for and regression: of  values against timeଷ଴ from IPO in ఝ orderమ to estimate volatility trends following IPO day in a day counter variable was generated for each observationto mark the number of days that had passed by the ሺͳ to ൅price estimate Black-Scholes ɏሻ all three model, values and for values each indexcan used the following model 0.05given toknown evaluate it, this study’s regressionכ ߮withଵ runሻ כ ሺ ௜ିଵcompatibilityfurtherሻቁregressions൅ ሺʹʹʹ scaled כAfter being furtherߪ ൌ scaledටσ௜ୀଵAfter byቀ߮ ଵprice ൅beingଵାఝ forయ Determining the precise effects on for compatibility with the Black-Scholes ଶOther Applications suggests that the manager should wait until     each industry.After being
further scaled by price for compatibility2 with the Black-Scholes model, and valuesa day can counter variable was generated for each observationto mark the number of days that had passed option price movement beprovided used to byestimate the themodel, fair value σ and of options σ valuesvalues for IPO can for stocks; be and used estimated to : prices can beߪ comparedߪ with real after day 7. 6 Equity Volatility across Industries from IPO Day (8) ଶ regression results exceeds the scope of this estimate the fair value of options for IPO ߪ ߪ Stock price volatility on and follow- Equity Volatility across Industriesstudy. A from starting IPO Daypoint, be usedhowever, to estimate would the befair valuestocks; of options estimated for IPO pricesstocks; estimatedcan be comparedprices can be compared with realing IPO date is also relevant for companies It is surprising that the effects of indus- 6 prices to lend insight into pricing efficiency and, when  studied   using historical discrepancies, can be used Equity VolatilityEquity across Volatility Industries acrossto Industriesfromestimate IPO Day annualizedfromMethodology IPO Day volatility  Subsection
 using  the
 I:  ! Calculatingwith real

 " prices
to lend insight into pricing trying to launch their own IPOs and the tries and the IPO period on stock volatility Equityratings Volatility represent across Industries variance, fromthat any IPO given Day year pricesincludes to lend 252 insight trading into days, pricing and efficiency that volat and, ilitywhen levels studied using historical discrepancies, can be used (8) The regressionregression estimates results – average the Black-Scholes industry volatility mod- ( )efficiency as a function and, of when the studied number using of days histori - from IPO investment banks helping them to do so. have not been studied previously. Although ratings represent variance, that any given year includesto develop 252 trading an arbitrage-based days, and that volat optionsility tradinglevels strategy for IPO stocks.  el uses volatility on toan develop annualized an arbitrage-based basis. cal options discrepancies, trading strategy can for be IPO used stocks. to develop an Having access to a model that can help to volatility trends were successfully modeled ratingsremain representratings close representvariance, to after that variance, IPO, any estimated given that yearany annualizedgiven Theincludes yearcalculation 252 includesvolatility trading process 252as days, variance trading and was thatdays, runindividually for volat and anyility that industry levels volat using ilitycould data levels setsbe that include the trading history 
 forthe   S&P 
  !

" 
ratings represent variance,( thatAssuming any). On given IPO yearthat day, includesthe the ratings 252 tradingrepresent days,term vari is and- equal thatarbitrage-based volat to 0;ility this levels options means that averagetrading strategy IPO day for volatility predict a company’s volatility after IPO during this study, much work is left to be remain close to after IPO,ance, estimated that any annualized given year volatilityincludes as252 variance trad- IPOଶ for stocks. any industry couldThe be regression estimates average industrycan help volatility to guide ( ) as a decisions function on of whether the number a done of daysto fully from IPO understand the impact of remain close to after߮ଵ IPO, estimated annualized volatility
as variance forߪ any industry could be remainEquitycalculated close Volatilityremain to using: acrossclose after toIndustries IPO, estimatedaftering from IPO,days, IPO estimatedannualized andDay that500 annualized andvolatilityvolatility each as of volatilitylevels variance the ten remain asselected variance for anyଶ industry industry for any groups could industry provided be could by be MarketWatch . For allexamined company data sets, should sell equity in the public these factors on volatility and the applica- ଵis   estimated by since !   the denominator

" of the second term becomes equal toone . For each day ߮ close to after IPO, estimated annualizedଶ ߪ Althoughଶ such (further )investigation. On IPO day, the market term in is addition equal  toto how 0; this its shares means should that average tions IPO of day a volatilitydeeper understanding; further calculated using:ଵ 2 ଶ 15 ߮ଵ ଵ σ ߪ 15 calculated calculatedusing:߮ using:߮ volatility as variancea day counter for any variable industry ߪ was generatedexceedsߪ for the each scope observation of this study,to mark some the high- number of days thatbe hadpriced. passed These findings on volatility are study into these relationships will certainly calculated using: following IPO, volatility 
 decaysas the term g rows and the second regression term ratings represent variance, thatcould any given be calculatedyear includes using: 252 trading days, and that volatlevel ility hypotheses levels (13) can is    be estimated fairly formulated by since !   the denominator
most
" relevant of when the second value preservation term becomes equal is a toprovideone . For valuable each day insight for both academics ఝమ without further analysis. While options key objective for the IPO candidate; dis- and profit-seeking arbitrageurs. ଶ ଷ଴ (13) 6 any
 significant" industrytradersଵ could impactare beprobably of an IPO eventforward-thinking on stock volatility. covering that its share prices may be more representsሻ for
(13) the   varianceሺ௜ିଵ ! כ σ model௜ୀଵ volatility ଵ effectivelyଵାఝ asయ remain close to afterapproaches IPO, estimated 0. The annualized
 decaysas the term g rows and the second regression term ߮ ሻ (13) (13)following IPO, volatility כ ʹʹʹߪ ൌ ቀ߮ ൅ ఝమ ቁ ൅ሺ ଶ ଷ଴ ଶ enough to(13) recognize that volatility will de- volatile than expected in the public market ௜ୀଵ ଵ ఝమ ଵ ߮ ሻ of the Black-Scholes R כ ሺ௜ିଵఝሻమቁ is൅ሺʹʹʹ alsoߪ a componentכThe corresponding߮ଵ annualizedଶ ߪ standardଷ଴ൌσଶ deviationቀ߮ଷ଴ ൅ఝଵାఝమ ,య which calculated using: ଶ ଷ଴ cline following the IPO period, the drop may lead a more conservative company to ሺଵ௜ିଵሻ ଵ ଵכ௜ୀଵ ଵ ௜ୀଵଵାఝయ ߮ଵ ሻ כ ሺ௜ିଵሻכߪ ൌσ௜ୀଵ ቀ߮ଵ ൅σ య ଵାఝቁ ൅ሺʹʹʹయ .
 significant" sources impact of capital. of an IPOFor ex event- on stock volatility representsseek alternative
the   volatility߮ ሻ of into the theyBlack-Scholes two expect types:approaches IPO -­‐mayrelated be 0. volatilityunder- The model or and effectively ! כ ቁ a߮൅ሺʹʹʹ componentሻ volatilityinכ its abilityሺ ௜ିଵannualized൅, whichሻቁ to൅ሺʹʹʹ break is also standard  down כThe correspondingThis annualized modelߪ ൌThe standardσ was ߪcorresponding ቀ chosen߮ൌ deviation൅ ଵାఝ forቀ ߮ ߪ The correspondingmodel,The can corresponding be annualized calculated annualized standard deviationusing: deviation standardσ, which deviation ,,is whichwhich also aisis component alsoalso, which aa componentcomponent is also of a componentoverestimated. ofof thethe Black-ScholesBlack-Scholes of the For Black-Scholes example, the study’s ample, companies in the Technology and model, can be calculatedbaselin using:ethe volatility. Black-Scholes Since the model,  
ߪ cansecond be calculated term rapidly results decays (13) suggest as the that counter stocks variablein the Technol increases,- its Consumer Services sectors may decide not మ model, canmodel, be calculated can be calculatedusing:using:ଶ using:ଷ଴ ߪఝ ߪ ogy sector typically exhibitThis model about was7.5 times chosen for its ability toto break issue down common volatility stock into to raise two capital types: IPO -­‐berelated- volatility and ߮ଵሻ their long-term volatility levels on IPO day. cause their industries can be characterized כ ʹʹʹሺ௜ିଵሻቁ ൅ሺכmodel, can be calculated using:ߪ ൌσ௜ୀଵ ቀ߮ଵ ൅ ଵାఝయ value represents the effect of IPOon stock volatility; captures the expected(14) additional volatility on an The corresponding annualized standard deviation , which is also a component(14) of theIn Black-Scholesthe case of an underestimated drop, the by above-market volatility during both the మ baseline volatility.Since the  
second term rapidly decays as the counter variable increases, its ଷ଴ ఝ market may forecast(14) that IPO volatility for IPO period and the long run. ሺ௜ିଵሻ ଵכ௜ୀଵ ଵ ଵାఝయ . ߮ ሻ (14) becomes equal to1כ ʹʹʹ
ቁ ൅ ሺ 
 
 


  
IPO day whenߪൌ ටσ ቀ߮ ൅ is 0 andమ model, can be calculated using: ଷ଴ ߪ ఝ Technology (14) stocks is(14) valuetypically represents 4 times thelong- effect of IPOon stock volatility; captures the expected additional volatility on an ௜ୀଵ ଵ ఝమ ଵ -߮runሻ volatility and that volatility will ulti- When attempting to manage any port כ ʹʹʹሺ௜ିଵఝሻమቁ ൅ ሺכߪൌଷ଴ටσ ቀ߮ଷ଴ ൅ఝଵାఝమ య The resulting value representsଷ଴௜ୀଵ the sumଵ of allయ daily expected dailyଵ volatility ratings – the first term ߮ଵ ሻ ଵ כ ʹʹʹሺଵ௜ିଵሻቁ ൅య ሺכ ߪൌටσ ቀ߮ଵ ൅ ଵାఝ௜ୀଵ -߮ whichሻ drop theby 75% regression by the end settles of the as IPO folio, minimizing risk is of utmost impor כ ቁ߮൅ asymptote ሺʹʹʹሻ abovematelyכ ሺ௜ିଵሻכʹʹʹሺ the௜ିଵ൅ሻଵାఝ ቁ horizontal൅ ሺכଵାఝ  of"ቀయ߮ theߪൌቀ߮ ට value൅σ    The ߪൌ term ට σ is!௜ୀଵ The resulting ଶ value representsThe the resulting sum of σall2 dailyvalue expected represents daily the volatility period; ratings using – theour first results,IPO term day we when forecast that is 0 and 
  


 
 

tance. In “How Relevant is Volatility Fore-becomes equal to1 . The resultingrepresents valuetheߪ 30-day represents IPO period the sum as modeledof all daily by expected the regression daily volatility results while ratings (14)the – secondthe first term term represents The resultingThe resulting valueଶ represents value sum represents the of sum all daily of the all expected dailysum ofexpected all daily daily volatility daily expected volatility rat daily- ratingsvolatility volatility – the ratingswill first actually term– the firstbe reduced term by about casting for Financial Risk Management?” ଶ increases and ଷ଴ the second ఝ regressionమ term approaches zero; is an indicator of the average   level of representsଶ theߪ 30-dayଶ IPOings period – ௜ୀଵthe as modeledfirstଵ term by representsthe regression the ଵresults30-day while 85%. the As second a result, term associated representsThe term put or is! call   the op value-  of" the horizontalChristoffersen asymptote above and which Diebold the observe regression that settles as ߮ ሻ while the second term represents כ ሺ regression௜ିଵሻቁ ൅ ሺʹʹʹ resultsכrepresents theߪ 30-day IPO periodߪൌ asට σmodeledቀ߮ ൅ byଵାఝ thయe representsthe remainingrepresents theߪ 30-day 222 the IPOߪ trading 30-day periodIPO daysIPO as modeled periodperiod in the 252-dayasas by modeledmodeled the regressiontrading by by th year.thee regression results regression Additional while results adjustmentsthetions second while could the term could besecond representsoverpriced be madeterm represents to because of inac- the ability to forecast volatility of a security long-­‐run volatility that stocks will exhibit after the effects of theIPO period have ebbed . The variable Thethe resulting remaining value 222 representstradingresults days the insum while the of 252-day allthe daily second expected trading term year.daily represents volatilityAdditional the ratings adjustmentscurate – the firstvolatility termcould beforecasting. madeincreases to Given and the market second regression is term incredibly approaches useful zero; for is risk an indicator management of the average   level of the remaining 222ଶ trading days in the 252-day trading year. Additional adjustments could be made to the remainingthis estimation;the remaining222 trading for 222 example, days tradingremaining in the the days 252-day long-run in222 the tradingtrading volatility252-day year. days tradingterm Additionalin couldthe year. 252-day be Additionaladjustments adjusted nonrecognition adjustmentsto couldaccount be formade could of unforeseen industry-based to be made to volatility purposes (2000, p. 12). The new insight represents theߪ 30-day IPOrepresents period as stabilization modeled by th ratee regression  the larger results the while value the second of , the term quicker represents stock volatility converges to its  this estimation; for example,trading the long-run year. Additional volatility adjustmentsterm could be could adjusted trends, to account industry-based for unforeseenlong arbitrage-­‐run volatility opportuni that - stocks will exhibitthat after this the study effects provides of theintoIPO periodindustry-based have ebbed . The variable this estimation;volatility spikes for example, over the the coursebe long-run made of theto volatility tradingthis estimation; term year. could Using for be some adjustedexample, percentage to accountties ρexist to representfor and unforeseen can bethe identified effect of with further IPO volatility forecasting can advance risk thisthe estimation; remainingthis estimation; for222 example, trading for days the example, in long-run the 252-day the volatility long-run trading term year. volatility couldAdditional term be adjusted adjustmentscould be to adjusted account could be to formade account unforeseen to for unforeseen long-­‐termthe volatility long-run level volatility . For term allindustries could be, this ad model- study.approximate s values very well with all management proficiency. For example, the  volatility spikes over the coursejusted ofto the account trading for year. unforeseen Using some volatility percentage ρ to represent the effectrepresents of stabilization rate  the largervalues the of value the of , variables the quicker lend stock insight volatility into converges to its volatilityabnormal spikes overvolatility the coursespikes ofon the long-run trading volatility, year. Using we cansome calculate: percentage ρ to represent the effect of volatilitythis estimation; spikesvolatility over for spikes example,the course over the the of long-run the course2 trading volatility of the year. trading term Using could year. some be Usingadjusted percentage some to account percentage ρ to represent for unforeseen ρ to therepresent effect ofthe effect of regressionspikes R values over the above course 0.81 of00 theand tradingseven of year.eleven aboveRegardless 0.950. In of addition, whether all significant estimated arbi- the rate of regression from IPO volatility abnormal volatility spikes Usingon long-run some volatility,percentage we ρcan to calculate: represent the trage opportunities dolong exist,-­‐term it is volatility important level . For allindustries levels to, this baseline model volatility.approximate Whens values deciding very well with all abnormalvolatility volatilityabnormal spikes over spikes volatility the courseon long-run spikeseffect of the on tradingvolatility,of long-run abnormal year. we volatility, Using canvolatility somecalculate: we percentagespikes can calculate: on long- ρ to represent to note the that effect the of final values and associated whether to invest in the stock of a recent coefficients were significant at the 1% level.  run volatility, we can calculate: regression coefficients(15) regression reflect R only2 values trends above in  0.8100 and seven IPO, oftheeleven regression above values 0.950 . canIn addition, help port all- estimated మ abnormal volatility spikes on long-runଶ volatility,ଷ଴ we can calculate:ఝ average industry(15) volatility; no regressions folio managers decide when prices have ሺ௜ିଵሻ ଵכ௜ୀଵ ଵ ଵାఝయ .were ሺͳ ൅ run ɏሻ using(15) values for individual stocks. stabilized enough to buy the stock safelyכ ߮ ሻ(15)כ ʹʹʹቀ߮ ൅ మ ቁ ൅ሺ ߪ ൌσ ଶ ଷ଴ ఝ (15) (15)coefficie nts were significant at the 1% level. మ -ሺ௜ିଵఝሻమ ଵ Although the regression models do accu- For example, stocks in the Telecommunicaכଶ ଷ଴ ௜ୀଵ ଵ ఝଵାఝయ ሺͳ ൅ ɏሻ כ ߮ ሻ כ ʹʹʹଶ ߪ ଷ଴ൌσଶ ቀ߮ଷ଴ ൅ఝమ ቁ ൅ሺ (ሺଵ௜ିଵሻ ଵ ଵ (15) (16כ௜ୀଵ ଵ ௜ୀଵଵାఝయ ሺͳ ൅ ɏሻ כ ߮ଵ ሻ כ ሺ௜ିଵሻכߪ ൌσ௜ୀଵ ቀ߮ଵ ൅σ య ሺ ሻଵାఝቁ ൅ሺʹʹʹయ ሺͳ ൅ ɏሻ כ ൅߮ ɏሻሻכ ሺͳ כ ቁ߮൅ሺʹʹʹሻכ ʹʹʹ௜ିଵ൅ ቁ ൅ሺ כߪ ൌσ ߪቀ߮ൌ൅ ଵାఝఝቀమ ߮ ଶ ଷ଴ ଷ଴ ఝమ ௜ୀଵ ଵ య ଵ (16) (ሺͳ ൅ ɏሻ (16 כ ߮ ɏሻଵሻ כሺͳ ൅ כ ൅߮ ሺʹʹʹሻכ ሺ௜ିଵሻቁכ൅ሺ௜ିଵଵାఝሻቁ ൅ሺʹʹʹయכߪ ൌߪσ ൌටቀ߮σ௜ୀଵ൅ ଵାఝቀ߮ଵ ଷ଴ ఝమ (16) (16) 9 ௜ୀଵ ଵ ఝమ ଵ ሺͳ model, ൅(16) ɏሻ and values can כ ߮ ሻ כ ሺ௜ିଵ withఝሻమቁ ൅ the ሺʹʹʹ Black-ScholesכAfter being further scaledߪ ൌbyଷ଴ ටpriceσ forቀ߮ ଷ଴compatibility൅ఝଵାఝమ య ଷ଴௜ୀଵ ଵ య ሺ ሻ ଵ ሺͳ ൅ ɏሻଵ כ ߮ଵ ሻ כ ሺ௜ିଵሻכʹʹʹଵ௜ିଵ ଵାఝቁ ൅య ሺ כ ߪ ൌටσ௜ୀଵ ቀ߮ଵ ൅ ଵାఝ௜ୀଵ మ ሺͳ ൅ ɏሻଶ כ ൅߮ ɏሻሻכ ሺͳ כ ቁ߮൅ ሺʹʹʹሻכ ʹʹʹሺ௜ିଵ൅ሻቁ ൅ ሺכߪ ൌටσଷ଴ߪቀ ൌ߮ ට൅σଵାఝఝቀయ߮ After being further scaled by௜ୀଵ priceଵ for compatibility with theଵ Black-Scholes model, and values can ሺͳ ൅ ɏሻ model, andߪ valuesߪ can 9 כ ߮ ሻ כ ሺ௜ିଵሻ withቁ ൅ ሺʹʹʹ the Black-ScholesכAfter being further scaledߪ by ൌ priceටσ forቀ߮ compatibility൅ ଵାఝయ After beingbe usedAfter further to being estimate scaled further bythe price scaled fair valuefor by compatibility price of options for compatibility for with IPO the stocks; Black-Scholes with estimated the Black-Scholes model, prices can model,and beଶ compared values and can with values real can After being further scaled by price for compatibility with the Black-Scholes model, and ଶ values can be used to estimate the fair value of options for IPO stocks; estimated prices canଶ beߪ comparedଶߪ with real be usedprices tobe estimate to used lend to insightthe estimate fair into value the pricing offair options value efficiency offor options IPO and, stocks; when for IPO estimatedstudied stocks; using estimatedprices historical canଶ pricesbeߪ discrepancies,compared canߪ beߪ comparedwith can realߪ be with used real be usedbe used to toestimate estimate the the fair fair valuevalue of optionsoptions for for IPO IPO stocks; stocks; estimated estimated prices prices can be canߪ compared be comparedߪ with real with real prices to lend insight into pricing efficiency and, when studied using historical discrepancies, can be used pricesto to develop lend insight an arbitrage-based into pricing efficiency options and, trading when strategy studied for using IPO historicalstocks. discrepancies, can be used pricesprices to tolendprices lend insight insight to lend into into insight pricing pricing into efficiency pricing and, and,efficiency when when studied and, studied when using using historicalstudied historical usingdiscrepancies, discrepancies, historical can discrepancies, be canused be used can be used to develop an arbitrage-based options trading strategy for IPO stocks. toto developdevelopto developto anan developan arbitrage-basedarbitrage-based arbitrage-based an arbitrage-based optionsoptions trading tradingtrading options strategy strategystrategy trading for forfor IPO strategy IPOIPO stocks. stocks.stocks. for IPO stocks.

15 15 15 15 15 15

Equity Volatility across Industries from IPO Day

All calculations and regressions were run usingStata version 11.1 . F or a discussion ofStata -­‐specific

methodology, see Appendix I .

Section V: Results

-44- ECONPress EquityThe results Volatility of the regressionsacross Industriesfor eachindustry from and IPO the Day market benchmark are as follows with -45-

corresponding sample sizes and t -­‐statistics in parentheses:

Variable Name Value Sector R2 counter Day from IPO    total Sum total of all values for a given counter Sector (Baseline(Baseline
Volatility ) (IPO-Driven(IPO-­‐
Driven (Stabilization(Stabilization
Rate) R2 value Equity Volatility across Industries from IPO Day Volatility) Volatility)Volatility) Rate) permno CRSP-assigned permanent identification Technology (890) 0.1173751 (26.78) 0.7072644 (40.15) 2.997637 (8.57) .9837 number for company EquityEquity Equity VolatilityAll Volatility calculations ConsumerBasic Volatility across Materials across Services across and Industries (548) Industries regres (798) Industriessions from 0.05986040.0303853 from were IPO from IPO Day run (47.53) (24.60) IPO Day using Day Stata 0.47930990.0632364 version (27.65) (47.82) 11.1 . F or3.8061891.496436 a discussion (7.88) (8.87) of Stata .9884.9675-­‐specific denominator Number of companies for a given counter Healthcare (821) 0.0575546 (25.57) 0.2345721 (25.97) 2.959527 (5.58) .9619 Consumer Goods (653) 0.0390784 (31.01) 0.1378587 (30.74) 1.463953 (8.81) .9929 value methodology,Oil & Gas (578) see Appendix I .0.049487 (17.32) 0.1118282 (10.66) 1.686358 (2.93) .8142 All calculations All calculations All calculations and and regres and regressions regressions weresions were run were run using run usingStata usingStata version Stata version version 11.1 11.1 . F 11.1or . F aor .discussion F aor discussion a discussion ofStata ofStata of-­‐specificStata -­‐specific-­‐specific vbar Calculated value of industry volatility rating for MarketConsumer (S&P Services 500) (798) 0.04704640.0598604 (24.60) (20.04) 0.17603420.4793099 (47.82) (19.88) 1.9365213.806189 (8.87) (5.20) .9379.9884 a given counter value Industrials (1141) 0.0412802 (47.95) 0.1061883 (31.54) 2.424831 (7.50) .9740 methodology,methodology,methodology,Financials see see Appendix see (2058) Appendix Appendix I . I . I . 0.0395426 (69.25) 0.0907731 (42.87) 1.769266 (11.59) .9860 SectionFinancialsFinancials V: (2058) (2058) Results 0.03954260.0395426 (69.25) (69.25) 0.09077310.0907731 (42.87) (42.87) 1.7692661.769266 (11.59) (11.59) .9860.9860 Table 2. STATA variables. ConsumerHealthcare Goods(821) (653) 0.03907840.0575546 (25.57) (31.01) 0.13785870.2345721 (25.97) (30.74) 1.4639532.959527 (5.58) (8.81) .9929.9619 SectionSectionSection V:Basic V: ResultsMaterials V: Results Results (548) 0.0303853 (47.53) 0.0632364 (27.65) 1.496436 (7.88) .9675 TheTelecommunications Industrials results of (1141) the regressions 0.02971350.0412802for eachindustry (47.95) (12.20) and 0.12835770.1061883 the market (31.54) (16.27) benchmark1.0459032.424831 are (7.50) (4.98) as follows .9137.9740 with Appendix I: Description Of Nonlinear sion, all other variables can be dropped. Regression Process For Stata (143)Market (S&P 500) 0.0470464 (20.04) 0.1760342 (19.88) 1.936521 (5.20) .9379 correspondingMarket (S&P sample 500) sizes and0.0470464 t -­‐statistics (20.04) in parentheses0.1760342: (19.88) 1.936521 (5.20) .9379 Nonlinear regression models can be TheThe resultsThe results results ofUtilities of the of the regressions(206) the regressions regressionsfor for each for each0.0276752industry eachindustry industry and (33.32) and the and the market 0.0460092 the market market benchmark (13.93) benchmark benchmark are 2.732502 are as are as follows as follows (3.12) followswith with with .8794 To calculate the values for a given in- specified using Stata’s nl command. Repre- Oil & Gas (578) 0.049487 (17.32) 0.1118282 (10.66) 1.686358 (2.93) .8142 dustry data set pulled from CRSP, the value senting using C1, using C2, and using correspondingcorresponding sample sample sizes sizes and t and-­‐statistics t -­‐statistics in in parentheses parentheses: : 2 of all volatility ratings were added into one C3, the regression is generally run using: correspondingTechnologyTable Sector3. sample Regression (890) sizes results and ordered 0.1173751t -­‐statistics by (26.78) in values. parentheses 0.7072644: (40.15) 2.997637 (8.57) .9837 R total sum using:    nl (vbar = {C1} + {C2}/ Telecommunications (143) 0.0297135(Baseline
(12.20) Volatility 0.1283577) (IPO (16.27) -­‐
Driven 1.045903 (Stabilization (4.98)
.9137 Rate) 2 2 2 by counter:egen total=sum(v) (1+{C3}*(counter-1))) SectorSector Sector R R R Utilities (206) 0.0276752 (33.32) 0.0460092 (13.93) 2.732502 (3.12) .8794 Because the regression requires the esti-     Volatility)    2 The number of individual companies in mation of three coefficients withEquity only Volatilitytwo across Industries Sector from IPO(Baseline Day (Baseline(Baseline
Volatility
(Baseline Volatility
Volatility) ) ) (IPO (IPO-Driven(IPO-­‐
Driven(IPO-­‐
Driven-­‐
Driven (Stabilization (Stabilization(Stabilization(Stabilization

Rate)
Rate) Rate)R

the industry was then determined using: given variables, however, initial value esti- Basic Materials (548) 0.0303853Volatility) (47.53) Volatility)0.0632364 (27.65) Rate)1.496436 (7.88) .9675 mates for all three variables must be passed Volatility)Volatility)Volatility) Technology (890) 0.1173751 (26.78) 0.7072644 (40.15) 2.997637 (8.57) .9837 by permno counter:generate in order generate the desired results.All calculations After and regressionsFor tables were ordered run using byregression Stata version outcomes, 11.1 . see F orAppendix a discussion II . For graphs ofStata of-­‐specific the regression models with denominator=_N ConsumerConsumerFor tables Goods ordered Services (653) by(798)regression 0.05986040. outcomes,0390784 (24.60) (31.01) seeAppendix 0.4793099 0.1378587II . For graphs(47.82) (30.74) of 3.806189 the regression1.463953 (8.87) models (8.81) .9884 with .9929 experimentation, it was discovered that BasicBasic MaterialsBasic Materials Materials (548) (548) (548) 0.03038530.03038530.0303853 (47.53) (47.53) (47.53) 0.0632364 0.06323640.0632364 (27.65) (27.65) (27.65) 1.496436 1.4964361.496436 (7.88) (7.88) (7.88) .9675.9675 .9675 0.05, 0.2, and 1.75 can be used methodology,as initial see Appendix Healthcarecalculated I . values, (821) see Appendix0.0575546 V. (25.57) 0.2345721 (25.97) 2.959527 (5.58) .9619 To calculate the average volatility rat- values for C1, C2, and C3 respectively in ConsumerMarket (S&P Services 500) (798) 0.04704640.0598604 (20.04) (24.60) 0.17603420.4793099 (19.88) (47.82) 1.936521 3.806189 (5.20) (8.87) .9379 .9884 ConsumerConsumerConsumer Goods Goods Goods(653) (653) (653) 0. 03907840.03907840.0390784 (31.01) (31.01) (31.01) 0.1378587 0.13785870.1378587 (30.74) (30.74) (30.74) 1.463953 1.4639531.463953 (8.81) (8.81) (8.81) .9929.9929 .9929 ings for the data, set, a simple average of every industry to produce the regression Consumer Goods (653) 0.0390784 (31.01) 0.1378587 (30.74) 1.463953 (8.81) .9929 these values was taken: results with the best fit: Financials (2058) 0.0395426 (69.25) 0.0907731 (42.87) 1.769266 (11.59) 10 .9860 Section V:Consumer Consumer Results ServicesTelecommunications Services (798) (798) 0.0 5986040.05986040.0297135 (24.60) (24.60) (12.20) 0.47930990.47930990.1283577 (47.82) (47.82) (16.27) 3.8061891.0459033.806189 (8.87) (4.98) (8.87) .9137.9884.9884 Consumer Services (798) 0.0598604 (24.60) 0.4793099 (47.82) 3.806189 (8.87) .9884 generate vbar = total/denominator nl (vbar = {C1} + {C2}/ Healthc(143)are (821) 0.0575546 (25.57) 0.2345721 (25.97) 2.959527 (5.58) .9619 (1+{C3}*(counter-1))), initial FinancialsFinancialsFinancials (2058) (2058) (2058) 0.03954260.03954260.0395426 (69.25) (69.25) (69.25) 0.0907731 0.09077310.0907731 (42.87) (42.87) (42.87) 1.769266 1.7692661.769266 (11.59) (11.59) (11.59) .9860 .9860 .9860 (C1 0.05 C2 0.2 C3 1.75) Oil & Gas (578) 0.049487 (17.32) 0.1118282 (10.66) 1.686358 (2.93) .8142 After using these commands, all stocks The results of the regressionsIndustrialsIndustrialsfor each (1141) (1141)industry and the0.04128020.0412802 market (47.95) (47.95) benchmark 0.1061883 are 0.1061883 as (31.54) follows (31.54) with 2.424831 2.424831 (7.50) (7.50) .9740 .9740 have the same “vbar” rating on any given HealthcHealthcHealthcare are(821) are (821) (821) 0.05755460.05755460.0575546 (25.57) (25.57) (25.57) 0.2345721 0.23457210.2345721 (25.97) (25.97) (25.97) 2.959527 2.9595272.959527 (5.58) (5.58) (5.58) .9619.9619 .9619 counter day so duplicates can be dropped Financials (2058) 0.0395426 (69.25) 0.0907731 (42.87) 1.769266 (11.59) .9860 by counter: Appendix II: Ordered Regressioncorresponding Results sample sizesMarketBasic and (S&P Materialst -­‐statistics 500) (548) in parentheses0.03038530.0470464: (47.53) (20.04) 0.06323640.1760342 (27.65) (19.88) 1.496436 1.936521 (7.88) (5.20) .9675 .9379 IndustrialsIndustrialsIndustrials (1141) Utilities (1141) (1141) (206) 0.04128020.04128020.04128020.0276752 (47.95) (47.95) (47.95) (33.32) 0.1061883 0.10618830.04600920.1061883 (31.54) (31.54) (13.93) (31.54) 2.4248312.732502 2.4248312.424831 (7.50) (3.12) (7.50) (7.50) .8794 .9740.9740 .9740 duplicates drop counter, force For all regression tables, relevant sample Oil & Gas (578) 0.049487 (17.32) 0.1118282 (10.66) 1.6863582 (2.93) .8142 sizes and t-statistics are listed parentheti- SectorMarket Market Market (S&P (S&P 500) Table(S&P 500) 4. 500) Regression 0.0470464 results0.04704640.0470464 ordered (20.04) (20.04) by (20.04) values. 0.1760342 0.17603420.1760342 (19.88) (19.88) (19.88) 1.936521 1.9365211.936521 (5.20) R (5.20) (5.20) .9379.9379 .9379 The leftover observations represent in- cally. Technology (890)  0.1173751 (26.78) 0.7072644 (40.15) 2.997637 (8.57) .9837 dustry volatility with vbar and use counter Oil Oil & Oil & Gas (578) & Gas (578) Gas (578) (Baseline
Volatility0.0494870.049487) 0.049487 (17.32) (IPO(17.32) (17.32) -­‐
Driven 0.1118282 0.11182820.1118282(Stabilization (10.66) (10.66)
(10.66) 1.686358 Rate) 1.686358 1.686358 (2.93) (2.93) (2.93) .8142.8142 .8142 to show how much time has passed from Telecommunications (143) 0.0297135 (12.20) 0.1283577 (16.27) 1.045903 (4.98) .9137 IPO. Before running the nonlinear regres- TechnologyTechnologyTechnology (890) (890) (890) 0.11737510.11737510.1173751 (26.78) Volatility)(26.78) (26.78) 0.7072644 0.70726440.7072644 (40.15) (40.15) (40.15) 2.997637 2.9976372.997637 (8.57) (8.57) (8.57) .9837.9837 .9837 Utilities (206) 0.0276752 (33.32) 0.0460092 (13.93) 2.732502 (3.12) .8794 Basic MaterialsTelecommunications (548) TelecommunicationsTelecommunications 0.0303853 (143) (143) (47.53) (143) 0.0297135 0.0297135 0.02971350.0632364 (12.20) (12.20) (12.20) (27.65) 0.1283577 0.1283577 0.12835771.496436 (16.27) (16.27) (16.27) (7.88) 1.045903 1.0459031.045903.9675 (4.98) (4.98) (4.98) .9137.9137 .9137

Consumer GoodsUtilitiesUtilities (653) Utilities (206) (206) (206)0. 0390784 (31.01) 0.02767520.0276752 0.02767520.1378587 (33.32) (33.32) (33.32) (30.74) 0.0460092 0.0460092 0.04600921.463953 (13.93) (13.93) (13.93) (8.81) 2.732502 2.7325022.732502.9929 (3.12) (3.12) (3.12) .8794.8794 .8794

Consumer Services (798) For tables 0.0 ordered598604 (24.60) byregression 0.4793099 outcomes, (47.82) seeAppendix 3.806189 II . For (8.87) graphs of .9884 the regression models with

Financials (2058) calculated0.0395426 values, (69.25) see Appendix 0.0907731 V. (42.87) 1.769266 (11.59) .9860 For Fortables Fortables orderedtables ordered ordered byregression byregression byregression outcomes, outcomes, outcomes, see Appendix see Appendix seeAppendix II . For II . For graphsII . For graphs graphs of of the of the regression the regression regression models models models with with with Healthcare (821) 0.0575546 (25.57) 0.2345721 (25.97) 2.959527 (5.58) .9619 calculatedcalculatedcalculated values, values, values, see Appendix see Appendix see Appendix V. V. V. 10 Industrials (1141) 0.0412802 (47.95) 0.1061883 (31.54) 2.424831 (7.50) .9740

Market (S&P 500) 0.0470464 (20.04) 0.1760342 (19.88) 1.936521 (5.20) .9379 10 10 10

Oil & Gas (578) 0.049487 (17.32) 0.1118282 (10.66) 1.686358 (2.93) .8142

Technology (890) 0.1173751 (26.78) 0.7072644 (40.15) 2.997637 (8.57) .9837

Telecommunications (143) 0.0297135 (12.20) 0.1283577 (16.27) 1.045903 (4.98) .9137

Utilities (206) 0.0276752 (33.32) 0.0460092 (13.93) 2.732502 (3.12) .8794

For tables ordered byregression outcomes, seeAppendix II . For graphs of the regression models with

calculated values, see Appendix V.

10

EquityEquity Equity Volatility Volatility Volatility across across across Industries Industries Industries from from IPO from IPO Day IPO Day Day

All calculations All calculations All calculations and and regres and regressions regressions weresions were run were run using run usingStata usingStata version Stata version version 11.1 11.1 . F 11.1 or. F aor .discussion F aor discussion a discussion ofStata ofStata of-­‐specificStata -­‐specific-­‐specific methodology,methodology,methodology, see see Appendix see Appendix Appendix I . I . I .

SectionSectionSection V: V: Results V: Results Results

TheThe resultsThe results results of of the of the regressions the regressions regressionsfor for each for eachindustry eachindustry industry and and the and the market the market market benchmark benchmark benchmark are are as are as follows as follows followswith with with Equity Volatility across Industries from IPO Day correspondingcorrespondingcorresponding-46- sample sample sample sizes sizes and sizes t and-­‐statistics t and-­‐statistics t -­‐statistics in in parentheses in parentheses parentheses: : : ECONPress -47-

2 2 2 SectorSector Sector R R R Appendix III: Correlation Between R2 And Industry Sample Size          2 Equity Volatility across Industries from IPO Day Sector (Baseline(Baseline(Baseline
Volatility
(Baseline Volatility
Volatility) ) ) (IPO (IPO-Driven(IPO-­‐
Driven(IPO-­‐
Driven-­‐
Driven (Stabilization (Stabilization(Stabilization(Stabilization

Rate)
Rate) Rate)R Volatility) Volatility) Rate) Volatility)Volatility)Volatility) Consumer Services (798) 0.0598604 (24.60) 0.4793099 (47.82) 3.806189 (8.87) .9884 All calculations and regressions wereEquity runEquity usingEquity Volatility VolatilityStata Volatility version across across 11.1 across Industries . Industries F or Industries a discussion from from IPO from of IPO Day Stata IPO Day Day-­‐ specific Technology (890) 0.1173751 (26.78) 0.7072644 (40.15) 2.997637 (8.57) .9837 BasicBasic MaterialsBasic Materials Materials (548) (548) (548) 0.03038530.03038530.0303853 (47.53) (47.53) (47.53) 0.0632364 0.06323640.0632364 (27.65) (27.65) (27.65) 1.496436 1.4964361.496436 (7.88) (7.88) (7.88) .9675.9675 .9675 methodology, see Appendix I . Healthcare (821) 0.0575546 (25.57) 0.2345721 (25.97) 2.959527 (5.58) .9619 All calculations All calculations All calculations Utilities and and (206) regres and regressions regressions weresions were 0.0276752 run were run using run usingStata (33.32) usingStata version Stata version 0.0460092 version 11.1 11.1 . F 11.1 or (13.93). F aor .discussion F aor discussion a2.732502 discussion ofStata of(3.12)Stata of-­‐specificStata -­‐specific.8794-­‐specific ConsumerConsumerConsumer Goods Goods Goods(653) (653) (653) 0. 03907840.03907840.0390784 (31.01) (31.01) (31.01) 0.1378587 0.13785870.1378587 (30.74) (30.74) (30.74) 1.463953 1.4639531.463953 (8.81) (8.81) (8.81) .9929.9929 .9929 Industrials (1141) 0.0412802 (47.95) 0.1061883 (31.54) 2.424831 (7.50) .9740 methodology,methodology,methodology, see see Appendix see Appendix Appendix I . I . I . Section V: Results ConsumerConsumerConsumer ServicesMarket Services Services (S&P(798) (798) 500) (798) 0.0 5986040.05986040.00.0470464598604 (24.60) (24.60) (24.60) (20.04) 0.4793099 0.47930990.17603420.4793099 (47.82) (47.82) (19.88) (47.82) 3.8061891.936521 3.8061893.806189 (8.87) (5.20) (8.87) (8.87) .9379 .9884.9884 .9884 Financials (2058) 0.0395426 (69.25) 0.0907731 (42.87) 1.769266 (11.59) .9860 FinancialsFinancialsFinancials (2058) Oil (2058) & (2058) Gas (578) 0.03954260.03954260.03954260.049487 (69.25) (69.25) (17.32) (69.25) 0.0907731 0.09077310.11182820.0907731 (42.87) (42.87) (10.66) (42.87) 1.7692661.686358 1.7692661.769266 (11.59) (2.93) (11.59) (11.59) .8142 .9860 .9860 .9860 SectionSectionSection V:Basic V: ResultsMaterials V: Results Results (548) 0.0303853 (47.53) 0.0632364 (27.65) 1.496436 (7.88) .9675 2 The results of the regressionsfor eachindustry and the market benchmark are as follows with The results of a linear regression of sample sizes on R values show that sample size and HealthcHealthcHealthcareare (821) Consumerare (821) (821) Goods (653)0.05755460.05755460.05755460.0390784 (25.57) (25.57) (25.57) (31.01) 0.2345721 0.23457210.13785870.2345721 (25.97) (25.97) (30.74) (25.97) 2.9595271.463953 2.9595272.959527 (5.58) (8.81) (5.58) (5.58) .9929 .9619.9619 .9619 quality of regression fit are not significantly correlated. corresponding sample sizes and t -­‐statistics in parenthesesTelecommunications: 0.0297135 (12.20) 0.1283577 (16.27) 1.045903 (4.98) .9137 IndustrialsTheIndustrialsThe results results (1141) of (1141) of the the regressions regressionsfor 0.0412802 for each0.0412802 eachindustry (47.95) industry (47.95) and and the 0.1061883 the 0.1061883 market market (31.54) benchmark (31.54) benchmark are 2.424831 are as2.424831 as follows follows(7.50) (7.50) with with .9740.9740 TheIndustrials results(143) (1141) of the regressionsfor 0.0412802 eachindustry (47.95) and the0.1061883 market (31.54) benchmark are 2.424831 as follows (7.50) with .9740

2 Appendix Iv: Correlation Between Sector MarketcorrespondingMarketcorresponding correspondingMarket (S&P (S&P 500)Table (S&P sample 500) sample 5. 500) sample Regression sizes sizes and sizes0.0470464 resultst and-­‐0.0470464statistics t and-­‐0.0470464statistics ordered t -­‐statistics (20.04) in (20.04) by in parentheses (20.04) in parentheses values. parentheses0.1760342 0.1760342: 0.1760342: R :(19.88) (19.88) (19.88) 1.936521 1.9365211.936521 (5.20) (5.20) (5.20) .9379.9379 .9379 Long-Run Volatility And IPO Volatility    (BaselineOil
Oil & Volatility Oil & Gas (578) & Gas )(578) Gas (578) (IPO -­‐
Driven0.049487 0.0494870.049487(Stabilization (17.32) (17.32) (17.32)
0.1118282 Rate) 0.1118282 0.1118282 (10.66) (10.66) (10.66) 1.686358 1.6863581.686358 (2.93) (2.93) (2.93) .8142.8142 .8142 SectorSector Sector R2 R2 R2

TechnologyTechnologyTechnology (890) (890) (890) Volatility) 0.1173751 0.11737510.1173751 (26.78) (26.78) (26.78) 0.7072644 0.70726440.7072644 (40.15)  (40.15) (40.15) 2.997637 2.9976372.997637 (8.57)  (8.57)  (8.57) .98372 .9837 .9837 Sector (Baseline(Baseline(Baseline
Volatility
(Baseline Volatility
Volatility ) ) ) (IPO (IPO-Driven(IPO-­‐
Driven(IPO-­‐
Driven-­‐
Driven  (Stabilization(Stabilization(Stabilization(Stabilization

Rate)
 Rate) Rate)R Basic Materials (548) 0.0303853TelecommunicationsTelecommunications (47.53) Telecommunications 0.0632364 (143) (143) (27.65) (143) 0.0297135 0.0297135 0.02971351.496436 (12.20) Volatility) (12.20) (12.20) (7.88) 0.1283577 0.12835770.1283577Volatility).9675 (16.27) (16.27) (16.27) 1.045903 1.0459031.045903Rate) (4.98) (4.98) (4.98) .9137.9137 .9137 Volatility)Volatility)Volatility) Consumer Services (798) 0.0598604 (24.60) 0.4793099 (47.82) 3.806189 (8.87) .9884 Consumer Goods (653) 0.0390784UtilitiesUtilities (31.01) Utilities (206) (206)Financials (206)0.1378587 (2058) (30.74) 0.02767520.0276752 0.02767520.03954261.463953 (33.32) (33.32) (33.32) (69.25) (8.81) 0.0460092 0.04600920.09077310.0460092.9929 (13.93) (13.93) (42.87) (13.93) 2.7325021.769266 2.7325022.732502 (3.12) (11.59) (3.12) (3.12) .9860 .8794.8794 .8794 BasicBasic MaterialsBasic Materials Materials (548) (548) (548) 0.03038530.03038530.0303853 (47.53) (47.53) (47.53) 0.0632364 0.06323640.0632364 (27.65) (27.65) (27.65) 1.496436 1.4964361.496436 (7.88) (7.88) (7.88) .9675.9675 .9675 Technology (890) 0.1173751 (26.78) 0.7072644 (40.15) 2.997637 (8.57) .9837 Consumer Services (798) 0.0598604 (24.60) Industrials 0.4793099 (1141) (47.82) 0.04128023.806189 (47.95)(8.87) 0.1061883.9884 (31.54) 2.424831 (7.50) .9740 ConsumerConsumerConsumer Goods Goods Goods (653) (653) (653) 0.03907840.03907840.0390784 (31.01) (31.01) (31.01) 0.1378587 0.13785870.1378587 (30.74) (30.74) (30.74) 1.463953 1.4639531.463953 (8.81) (8.81) (8.81) .9929.9929 .9929 Consumer Goods (653) 0.0390784 (31.01) 0.1378587 (30.74) 1.463953 (8.81) .9929 Financials (2058) 0.0395426 (69.25) 0.0907731 (42.87) 1.769266 (11.59) .9860 Basic Materials (548) 0.0303853 (47.53) 0.0632364 (27.65) 1.496436 (7.88) .9675 ForConsumer ForConsumertables ConsumerFortables orderedtables Services ordered Services ordered Services (798) byregression (798) by regression (798) by regression 0.0 outcomes,5986040.0 outcomes,5986040.0 outcomes,598604 (24.60) (24.60) see Appendix (24.60) see Appendix see 0.4793099Appendix 0.4793099 II .0.4793099 For II . For graphs(47.82) II. For graphs(47.82) graphs(47.82) of 3.806189 of the 3.806189 of the regression 3.806189 the regression (8.87) regression (8.87) (8.87) models models .9884 models with .9884 with .9884 with Appendix V: Calculated And Regression Results As A Function Of Day From IPO Healthcare (821) 0.0575546 (25.57) 0.2345721 (25.97) 2.959527 (5.58) .9619 Healthcare (821) 0.0575546 (25.57) 0.2345721 (25.97) 2.959527 (5.58) .9619 calculatedFinancialscalculatedFinancialscalculatedFinancials (2058) values,Market (2058) values, (2058) values, see(S&P Appendix see 500) Appendix see Appendix0.0395426 V0.0395426. V0.0395426. 0.0470464 V. (69.25) (69.25) (69.25) (20.04) 0.0907731 0.09077310.17603420.0907731 (42.87) (42.87) (19.88) (42.87) 1.7692661.936521 1.7692661.769266 (11.59) (5.20) (11.59) (11.59) .9379.9860 .9860 .9860 The following graphs were generated by Stata and show both observed values and Telecommunications 0.0297135 (12.20) 0.1283577 (16.27) 1.045903 (4.98) .9137 Industrials (1141) 0.0412802 (47.95) 0.1061883 (31.54) 2.424831 (7.50) .9740 estimated regression models as a function of day from IPO . Observed values are repre- HealthcHealthcHealthcareare (821) are (821) (821) 0.05755460.05755460.0575546 (25.57) (25.57) (25.57) 0.2345721 0.23457210.2345721 (25.97) (25.97) (25.97) 2.959527 2.9595272.959527 (5.58) (5.58) (5.58) .9619.9619 .9619 sented in red and are labeled “vbar” for each industry graph and “average” for the S&P (143) 500 graph. Regression estimates are represented in blue and are labeled “Fitted values” for Market (S&P 500) 0.0470464 (20.04) Utilities 0.1760342 (206) (19.88) 0.02767521.936521 (33.32)(5.20) 0.0460092.9379 (13.93) 2.732502 (3.12) .879410 10 10 all graphs. All graphs were generated using Stata version 11.1. For all graphs, day relative IndustrialsIndustrials (1141) (1141) 0.04128020.0412802 (47.95) (47.95) 0.10618830.1061883 (31.54) (31.54) 2.4248312.424831 (7.50) (7.50) .9740.9740 IndustrialsOil & (1141) Gas (578) 0.04128020.049487 (17.32) (47.95) 0.11182820.1061883 (10.66) (31.54) 1.686358 2.424831 (2.93) (7.50) .8142 .9740 to IPO is measured on the x-axis and average industry volatility is measured on the y-axis. Oil & Gas (578) 0.049487 (17.32) 0.1118282 (10.66) 1.686358 (2.93) .8142 MarketMarketMarket (S&P (S&P Table 500) (S&P 500) 5. 500) Regression 0.0470464results0.0470464 ordered0.0470464 (20.04) by (20.04) R 2(20.04) values. 0.1760342 0.17603420.1760342 (19.88) (19.88) (19.88) 1.936521 1.9365211.936521 (5.20) (5.20) (5.20) .9379.9379 .9379 Technology (890) 0.1173751 (26.78) 0.7072644 (40.15) 2.997637 (8.57) .9837 Oil Oil & Oil & Gas &(578) Gas (578) Gas (578) 0.0494870.0494870.049487 (17.32) (17.32) (17.32) 0.1118282 0.11182820.1118282 (10.66) (10.66) (10.66) 1.686358 1.6863581.686358 (2.93) (2.93) (2.93) .8142.8142 .8142 Telecommunications (143) 0.0297135 (12.20) 0.1283577 (16.27) 1.045903 (4.98) .9137 TechnologyTechnologyTechnology (890) (890) (890) 0.11737510.11737510.1173751 (26.78) (26.78) (26.78) 0.7072644 0.70726440.7072644 (40.15) (40.15) (40.15) 2.997637 2.9976372.997637 (8.57) (8.57) (8.57) .9837.9837 .9837 Utilities (206) 0.0276752 (33.32) 0.0460092 (13.93) 2.732502 (3.12) .8794 TelecommunicationsTelecommunicationsTelecommunications (143) (143) (143) 0.0297135 0.0297135 0.0297135 (12.20) (12.20) (12.20) 0.1283577 0.12835770.1283577 (16.27) (16.27) (16.27) 1.045903 1.0459031.045903 (4.98) (4.98) (4.98) .9137.9137 .9137

UtilitiesUtilitiesUtilities (206) (206) (206) 0.02767520.02767520.0276752 (33.32) (33.32) (33.32) 0.0460092 0.04600920.0460092 (13.93) (13.93) (13.93) 2.732502 2.7325022.732502 (3.12) (3.12) (3.12) .8794.8794 .8794

For tables ordered byregression outcomes, seeAppendix II . For graphs of the regression models with calculated values, see Appendix V. For Fortables For tables tables ordered ordered ordered byregression byregression byregression outcomes, outcomes, outcomes, see Appendix see Appendix seeAppendix II . For II . For graphsII . For graphs graphs of of the of the regression the regression regression models models models with with with calculatedcalculated values, values, see Appendix see Appendix V. V. calculated values, see Appendix V. 10

10 10 10

-48- ECONPress Equity Volatility across Industries from IPO Day -49-

S&P 500 Consumer Services Industrials Telecommunications

Base Materials Financial Services Oil & Gas Utilities

Consumer Goods Healthcare Technology -50- ECONPress Should punitive damages be scaled to wealth? -51-

Works Cited Should Punitive Damages Literature Review Baillie, Richard T. and Ramon P. be Scaled to Wealth? There have been several opinions pub- DeGennaro. “Stock Returns and lished in the literature regarding this issue. Volatility.” The Journal of Finance Harrison A Seitz The first piece of relevant literature is a re- and Quantitative Analysis, Volume sponse paper by A. Mitchell Polinsky, titled, 25, Number 2, pages 203-214. Northeastern University “Are Punitive Damages Really Insignificant, Predictable, and Rational? A Comment Christoffersen, Peter F. and Francis X. on Eisenberg et al.” (1997). In this paper, Diebold. “How Relevant is Volatility R Polinsky rebuffs three assertions made by Forecasting for Financial Risk Man- separate study of punitive damages. First, agement?” The Review of Economics Introduction Polinsky demonstrates that punitive dam- and Statistics, Volume 82, Number ages, although seemingly insignificant on a 1, February 2000, pages 12-22. In cases in which society, and by proxy, trial level because the amount awarded over courts, want to deter future problematic be- a large number of cases is relatively small, Draho, Jason. The IPO Decision: Why havior, punitive damages serve a fundamen- still have significance in the pretrial settle- and How Companies Go Public. tal role. As an additional source of damages ment process and are therefore still a part Edward Elgar Publishing, Inc.: that can be levied upon an injuring party, of an injurer’s decision calculus. Second, Northampton, MA (2004). punitive damages can excise gains that were Polinsky shows that punitive damages are obtained through illegitimate or harmful typically unpredictable not only in when Lowry, Michelle, Micah S. Officer, and means and also prevent future similar ac- they are awarded, but also in determining G. William Schwert. “The Vari- tions from being taken. However, there are their magnitude. For example, he notes ability of Initial IPO Returns.” The many questions that must be resolved in or- that the injurer’s conduct as well as the type Journal of Finance, Volume 65, Issue der for punitive damages to have any merit of misconduct may have varying impacts 2, April 2010, pages 425-465. in our justice system. How large do puni- on whether or not punitive damages are tive damages need to be in order to provide awarded. Finally, Polinsky addresses the ar- Schwert, G. William. “Stock volatil- a socially optimal level of deterrence? How gument that there is a positive correlation ity in the new millennium: how large ought punitive damages be in relation between punitive and compensatory dam- wacky is Nasdaq?” Journal of Mon- to compensatory damages awarded in the ages. He argues that there are cases in which etary Economics, Volume 49, Issue same case? Should the injurer be liable for there may be positive or negative correla- 1, January 2002, pages 3-26. harms that may have occurred to a third tions between the two values, thus assump- party? tions about how punitive damages ought to Schwert, G. William. “Why Does Stock be constrained based on proportionality are Market Volatility Change Over The discussion of punitive damages, es- not rational. For example, he addresses cases Time?” The Journal of Finance, pecially in their relation to tort reform, has in which the injurer may have zero chance Volume 44, Number 5, Decem- been a popular topic in the public discourse of escaping liability. In accordance with ber 1989, pages 1115-1153. in the past couple of years. There are many theory that punitive damages are meant as scholars, supported by legislation and de- a deterrent, in these cases there can be no Simon, David P. “The Nasdaq Volatility cisions at the state and federal levels, who meaningful deterrence from punitive dam- Index During and After the Bubble.” advocate strongly for restricting punitive ages, thus they ought to be lower even if the The Journal of Derivatives, Volume 11, damages or eliminating them entirely. On compensatory damages are high. Number 2, Winter 2003, pages 9-24. the other hand, there are those who would suggest that the extent of punitive damages The second piece of relevant literature Sinclair, Euan. Volatility Trading. John Wi- ought to be modified or increased. This pa- on this topic is a paper titled, “A Theory ley & Sons, Inc: Hoboken, NJ (2008). per will discuss one proposed modification of Wealth and Punitive Damages,” by Keith of punitive damages, which is the inclusion Hylton (2008). In this paper, Hylton ar- of the wealth of the injurer as a factor in gues that wealth should be a consideration considering the magnitude of the damages. in the calculation of punitive damages for some cases. In general, the conclusion that he reaches is, “Where the parameter of in- -52- ECONPress Should punitive damages be scaled to wealth? -53- terest in the determination of an optimal The next piece of relevant literature is damages that exceed the combined amount good (Hylton, 2008). As their wealth in- punitive award, external cost or internal a paper by Robert Cooter titled, “Punitive of the harm caused to the victim and gains creases, they would be more willing to pay gain, is unobservable and correlated with Damages, Social Norms, and Economic that the injurer may have made from com- for that amount of utility. This would tell the defendant’s wealth, the optimal puni- Analysis” (1997). In this paper, Cooter mitting a malicious action. This suggests us, then, that the amount of punitive dam- tive award will be a function of the de- describes the economic reasoning behind that the goal of punitive damages is not to ages shouldn’t be based on the exact mon- fendant’s wealth”. Put simply, this tells us punitive damages and their purpose of ei- internalize costs (as compensatory damages etary harm caused by the injurer, but rather that in some cases, an injurer’s valuation ther internalizing costs or deterring future do this already, assuming they are set at the on how much they would value that harm. of committing a harmful act may increase behavior. In the discussion of how punitive correct amount), but rather to deter future The justification behind this is because in according to their wealth, much like how damages ought to be determined, Cooter malicious behavior. order to achieve deterrence, the punitive a normal good’s value increases with a argues that the criteria for punishment to measures must have some sort of impact in consumer’s wealth. In order to achieve an achieve deterrence should be determined A common theory of how punitive meaningfully changing the injurer’s behav- optimal amount of punishment, Hylton on the basis of the actual harm caused and damages ought to be determined in order ior. If punitive damages were restricted to would argue that punitive damages should the expected liability. In cases in which the to achieve optimal deterrence is the simple proportionality to the harm caused, then be scaled to wealth. harm caused may be unclear, such as when calculation of the cost of the harm multi- wealthier individuals would be able to in- the illicit gain may be satisfaction, Cooter plied by “punitive damages multiplier”, or ternalize the punishments in many cases The third piece of related literature that argues that even though there is no clear essentially the chances that the injuring and would not be deterred from commit- will be discussed is a paper from A. Mitch- standard for how to value that satisfaction, party will actually be held liable for their ting harmful actions in the future. ell Polinsky and Steven Shavell titled, “Pu- courts ought to use aggregate statistical data action (Polinsky and Shavell, 1998). This nitive Damages: An Economic Analysis” to form the amounts of punitive damages, method of deterrence seeks to reach an op- (1998). This article is an extensive look at much like fines for criminal acts. timal level based on a valuation of the so- punitive damages with attempts to explain cial costs of harmful behavior. Proponents Conclusion a formula-based approach to determining The last piece of relevant literature that of this calculation would argue that because optimal awards. Additionally, this piece will be discussed is a study from Theodore this is the only way to achieve a specific, Based on the goal of deterring future covers the issue of wealth in the determi- Eisenberg, et. al, titled, “The Decision to non-arbitrary level of punitive damages, harmful behavior, it would seem as if con- nation of punitive damages. Polinsky and Award Punitive Damages: An Empiri- wealth should not be a consideration. It sidering wealth in punitive damages fulfills Shavell argue that wealth should never be cal Study” (2009). Using cross-sectional can be said that any rational actor will only the philosophical intent as well as provid- a consideration in determining the scale of data from 2005, this study determined a consider taking preventative action based ing an optimal level of deterrence based punitive damages for several reasons. First, model to explain the relationship between on calculations of expected costs. In this on the injurer. However, this is problem- they cite that it discourages corporations how often punitive damages are requested case, only the direct value of the harm that atic for determining legal consistency or a from expanding and taking any sort of risks in civil cases, how often they are awarded, an injuring party causes can be expected. bright line in calculating the magnitude of because greater wealth actually increases and how proportional they are to compen- For example, in a case of an automobile ac- punitive damages. In addition to muddling their liability. Under this point, they also satory damages. They found that punitive cident, the wealth of the driver is irrelevant the standard for acceptable punishment, argue that the deciding factors in determin- damages are very rarely pursued, were likely since they will both presumably take the scaling punitive damages to the wealth of ing the amount of punitive awards ought to be awarded if they were, and were often same measures to prevent an accident from the injurer may discourage individual and to be limited to solely the amount of harm proportional with regards to the compensa- happening and cause the same amount of firm behavior in ways that are unjustified. caused and the chance of escaping liability. tory damages awarded in the case. harm. If the damages were instead scaled to For example, increased liability because In contention with these claims, they note wealth, it would actually cause inefficient of wealth may disincentivize corporations some circumstances in which wealth could over-deterrence since the punishment is from conducting research and develop- be a useful determinant of the magnitude based off a more arbitrary and far less con- ment. In another case, wealthier people may of punitive damages. They first demonstrate Analysis tributory factor. be subject to a disproportionate amount of that injurers who are poorer are more likely risk from punitive damages that they could to be risk-averse since they cannot afford Before analyzing the effects of consid- On the other hand, there are situations not meaningfully be able to prevent in some liability insurance and will take proper pre- ering the injurer’s wealth, it would be use- in which the value of the harmful action cases, causing over-deterrence. Based on the vention measures. In this case, they ought ful to first define what situations should committed by the injuring party may be context, it may be useful for wealth to be to receive lower levels of punitive damages. deserve punitive damages. According to relevant. As a person’s wealth increases, considered in determining the amounts of The next argument they advance is that Cooter, punitive damages are awarded their valuation of nominal amounts of punishment, but it should be restricted to wealthier individuals tend to value money when the injurer’s behavior is determined money decrease due to diminishing mar- some reasonable standard in order to have less, so in order to offset the utility that they “bad enough”, or malicious enough to ginal returns. However, we can consider solvency and to check abuse. gain from causing harm, they must be pun- warrant additional punishment (1997). the utility that an injuring party gains from ished proportional to their wealth. Punitive damages are considered to be any causing harm to be similar to a normal R -54- ECONPress International Collective Action on Climate Change -55-

Works Cited International Climate Change And Uncertainty Cooter, R. (1997). Punitive damages, social Collective Action on Over the last hundred years, the mean norms, and economic analysis. Law and global temperature has risen by approxi- Contemporary Problems, 60(3), 73-91. Climate Change mately .6 degrees Celsius. This change has coincided with a drastic increase in the con- Eisenberg, T., Heise, M., Waters, N., & centration of greenhouse gases (primarily Wells, M. (2009). The decision to Evan Richards Sankey carbon dioxide) in the Earth’s atmosphere. award punitive damages: an empirical Northeastern University Though there is a vocal minority of clima- study. Cornell Law School Legal Studies tologists who deny it, the vast mainstream Research Paper Series. Retrieved from opinion favors the proposition that the http://ssrn.com/abstract=1397587. industrial revolution caused the increase in greenhouse gases (concentrations are Hylton, K. (2008). A theory of wealth R thought to have risen by about 30% since and punitive damages. Widener Law 1750) which in turn is heating the Earth up Journal, 17. Retrieved from http:// Climate change is a negative externality (Barrett, 2007). The basic warming mecha- www.bu.edu/law/faculty/scholar- which afflicts humanity on a global scale. nism is that an excessive level of greenhouse ship/workingpapers/documents/ If it is left unchecked, it is reasonable to gases in the upper atmosphere absorbs ex- HyltonKWealthPunitives2REV.pdf expect that warming will negatively affect cessive levels of infrared radiation from the the diversity of our biosphere, our economy sun and increases the overall temperature of Polinsky, A.M. (1997). Are punitive and our way of life. Any remedy for global the Earth. damages really insignificant, pre- climate change – one which slows or halts dictable, and rational? a comment further increases in the global tempera- Unfortunately, climatologists are far on eisenberg et al. The Journal of ture by curbing greenhouse gas emissions less certain of the future path of warm- Legal Studies, 26(S2), 663-677. – would classify as a pure public good. ing and the consequences it will have. The That is, it would be both non-rival and most reliable climate models predict that Polinsky, A.M., & Shavell, S. non-excludable. On a global level, this has over the next century, the average global (1998). Punitive damages: an huge implications. A welfare improvement temperature will increase by a further 1.4 economic analysis. Harvard Law brought to the citizens of Bangladesh by to 5.8 degrees Celsius (Barrett, 2007). It is Review, 111(4), 869-962. climate change mitigation could be equally widely believed in the scientific commu- enjoyed by Americans and Europeans. Ad- nity that at some point, these temperature ditionally, no body anywhere could be pre- changes could cause catastrophic changes vented from enjoying these benefits. These in climate patterns. The shrinking of the ice characteristics, however, seem to present sheets in Greenland and Antarctica could policy-makers with a problem. The guar- lead to changes in the undersea currents anteed benefits of mitigation to all may in the Atlantic Ocean which might lead to generate a destructive incentive for some drastic cooling in Northern Europe. Melt- to free-ride on its provision by others. This ing ice may also make life very difficult for paper will begin with a brief introduction countries at low elevations like the Mal- to the scientific community’s assessment of dives and Bangladesh. Average sea levels climate change. It will follow with an over- rose by about two tenths of a meter in the view of the literature on collective action last century. Some expect them to rise by and its application to the problem at hand. half a meter in this century. Another pos- Then there will be a critical examination sibility is that changes in rainfall patterns of current and past international efforts to could render large parts of the southwest- address climate change. It will conclude by ern United States uninhabitable. Events suggesting possible alternatives to these ef- such as these could entail huge costs to the forts. global economy. William Nordhaus, an economist at Yale University, has made a widely publicized calculation that unabated -56- ECONPress International Collective Action on Climate Change -57- climate change could potentially lower the is critical for understanding the prospects he will see that the venture will fall apart further augments their capacity to provide gross domestic product of the world by 2% for effective collective action. without his contribution. Contribution be- public goods. Large groups, however, are by 2100. An alternate estimate made the comes a dominant strategy. Smaller groups usually highly heterogeneous. Their mem- British Government that global GDP will also find it easier to coordinate solutions bers have widely divergent priorities, be- take a hit of between 5.3% and 13.8% by to the the problem of verification and en- liefs and levels of knowledge. This variety 2200 (Barrett, 2007). Complicating this Olson And The Collective Action forcement and arbitrate conflicts of interest massively increases the probability that the picture even further is the notion that the Problem between its members. Finally, members of aforementioned problem of anonymity and costs of climate change will not be evenly small groups will tend to engage with one enforcement as well as the scope for deep distributed. Countries at specific latitudes The modern conception of collective another repeatedly over time. The prospect conflicts of interest will make cooperation are expected to benefit from increased ag- action in the context of political economy of repetition can be a powerful incentive to impossible. Surprisingly, the heterogeneity ricultural opportunities which warming is based on the work of Mancur Olson. In cooperate with your peers (Shepsle, 2010). of large groups may sometimes be a bless- will present. The key point here is that the The Logic of Collective Action published in Small groups’ tendency to achieve their ing in disguise. As heterogeneous groups benefits of climate change mitigation – the 1965 Olson mounted a massive critique of stated goals makes them what Olson calls grow, the probability that a small group benefits of attempting to avoid a variety of the prevailing wisdom at the time on group “privileged” groups. of large and highly capable group mem- disastrous possibilities – are highly uncer- behavior. Groups had been conceived as bers will choose to supply the public good tain. perfect embodiments of the common wills Large groups, on the other hand, are grows. The reason for this is that large and of their individual members. Effective col- seen as being much less effective at provid- capable members usually have more to gain A similar pattern holds for the cost side lective action was taken as given (Sandler, ing an optimum level of public goods to overall from the provision of a public good of the equation. Policies which aim to limit 2004). Olson’s model imagines groups as their members. In general, as groups get than the small, less capable members. They greenhouse gas emissions will necessarily existing to provide their members with larger each individual contribution will may decide that their potential gains are so target the sources of those emissions: trans- intra-group public goods – that is, goods count for a smaller percentage of the col- large that they will supply the entire public portation, power generation and industrial which no group member can be prevented lective outcome. Therefore, holding costs good themselves (thereby making the group machines. An otherwise unnecessary in- from benefitting equally from. A classic ex- constant, the probability that the individ- privileged), despite the inevitability that vestment in a massive expansion of nuclear ample is a labor union which wins a wage ual will find contribution worth his while smaller members will free-ride (Sandler, power and low emission vehicles seems in increase from management by striking. declines. Then too, a large group will find 2004). This notion will prove invaluable for the cards. This will undoubtedly be costly, Obviously all union members, even those it difficult to verify and enforce compliance understanding the role of rich countries in but again it is unclear exactly how costly. who did not strike will enjoy the wage in- and reconcile more frequent conflicts of in- climate change mitigation. Drastic action on climate change such as a crease. This tension is the crux of Olson’s terest between its members. Free riders in commitment to cut carbon dioxide emis- contribution. There emerges within groups a large group are anonymous and probably In the absence of a government which sions by 50% has been calculated to lower a gap between the level of a public good (in only identified at a high cost. Furthermore, can force cooperation and public good global output by between 1% and 3% with this case a strike) which is optimal for the it is difficult to prevent them from using a provision through outright coercion, some poorer countries incurring less cost than group as a whole to provide, and the level good which is by definition non-excludable. groups (especially large ones) will remain wealthy countries (because they use energy which is optimal for an individual member Overall, large groups’ size makes them un- perpetually latent with their members more inefficiently). Other estimates are of that group to provide. Since all union likely to be able to surmount these various worse off as a result. Olson refuses to ac- much higher. The models used to generate members benefit from a strike-induced coordination problems and therefore un- cept this sorry state of affairs and proposes these figures necessarily involve certain as- wage hike, each member will try to “free- likely to supply the optimal level of public a remedy. In large groups, the core impedi- sumptions which may not hold in reality. ride” on every other member’s walkout. As goods to their members. As a result, Olson ment to optimal public good provision is, There are always unintended consequences. a result, this particular public good is un- labels them as “latent” groups. as already noted, the fact that individual A further consideration is that the costs of dersupplied. Though Olson considers this members notice that their individual con- action will likely be front-loaded. That is, problem to be endemic to group behavior Another important determinant of the tributions seem to count for less while the the pain will come early, and the benefits in general, he highlights some group char- effectiveness of groups at supplying public costs they incur to contribute remain fixed. of mitigation will take possibly hundreds of acteristics which can variously aggravate or goods is the nature of their membership. Therefore, as the group grows, members’ years to become evident. This makes a di- remedy the free-rider problem. Some groups are highly homogenous. Their willingness to work for the group declines. rect comparison of costs and benefits inher- members are more likely to look alike, talk Olson’s solution is to attach private benefits ently difficult. What should be clear from Small groups are most likely to supply alike and think alike. They are less likely to contribution towards the public good. If this overview is that there is room for rea- an optimal level of public goods. Their most to get caught up in conflicts of interest be- those who contribute (and only those who sonable international policymakers to dis- important advantage stems from the fact cause their members’ preferences are more contribute) are guaranteed a wholly pri- agree about the net payoffs and worthwhile that their members’ contributions to the homogenous. Unsurprisingly, small groups vate benefit like a cash payment, members’ goals associated climate change mitigation. provision of their goal are clear and large. tend to be more homogenous (that is often overall willingness to contribute would be Awareness of this capacity for disagreement If a member is contemplating free-riding, why they form in the first place). This status greatly enhanced (Shepsle, 2010). It would -58- ECONPress International Collective Action on Climate Change -59- be a challenge, of course, to determine the noted there is scope (even if just based on mate change mitigation for the world. of an international environmental agree- optimal level of private payments to confer the uncertainty in the data) for reasonable ment which achieved its stated intentions. on contributors. Too low and the public countries to come to quite different conclu- There are two other factors working in It is therefore important to understand why good will remain undersupplied, but too sions about the costs and benefits of climate favor for these major countries (like those it worked so well. high and the group may exhaust its collec- change mitigation and therefore about the in the G20) possibly supplying the public tive resources making excessive payments emissions targets which will play a huge good of climate change mitigation. The first In the 1970s and 1980s a number of sci- to its members. The payments must come part in any mitigation agreement. At a concerns the nature of mitigation itself. This entific studies were published which made from somewhere! glance then, it would seem that cooperation small, but weighty group of countries might it abundantly clear that emissions of CFCs on supplying the public good of climate be thought of as a “k-group” – a grouping of from industrial processes and aerosol cans change mitigation is not forthcoming and actors whose full participation is necessary were drifting into the upper atmosphere, that the world is not a privileged group. to supply the public good (Shepsle, 2010). interacting with sunlight and causing seri- International Collective Action On The smaller countries’ free-ridership can be ous damage to the earth’s ozone layer. The Climate Change On closer examination, however, our tolerated because they do not matter very ozone layer is important because it protects prospects are not so terrible. The heteroge- much to mitigation. However, if even one the surface of the Earth from harmful ul- The first, most obvious observation to neity of the world is also a major strength. large country free-rides, the goal (the emis- traviolet rays from the sun. Ultraviolet rays make about the international community There are severe inequities in wealth, popu- sions target) cannot be reached (McGinnis are known to cause damage to plant life and is that it is mostly comprised of sovereign lation size and carbon emissions amongst & Somin). This fact serves as an incentive sea life and well as skin cancer in humans nation states which are fiercely protective of those 193 countries. The United States for each nation to contribute lest the pub- (Barrett, 2007). Like carbon dioxide, CFCs their rights to self-determination. There is alone comprises approximately 20% of lic good not be provided at all. However, drift around in the atmosphere far from no world government with unlimited coer- global output and 16% of global carbon as noted by Kenneth Shepsle in Analyzing where they are emitted. As a result CFC cive powers which can be expected to save dioxide emissions. Similarly, a relatively Politics, this will be no consolation if even emissions by multiple emitters combine to the day simply by mandating global cuts in small number of countries have most of the some of the countries involved believe that make everyone worse off. Ozone damage carbon emissions. There are (depending on Earth’s population and wealth and gener- the costs of contribution outweigh the ben- mitigation can therefore be considered a the definition) about 193 sovereign states ate most of its carbon emissions. In fact, efits. The dominant strategy will turn to de- public good, suffering from the same osten- in the world. On their own, many of them a formal organization of states which fits fection. Secondly, these major players, the sible problems of international collective have succeeded in providing public good this description already exists. It is called G20 members, tend to interact frequently. action as climate change mitigation. Yet, solutions to various regional externalities the Group of Twenty or G20. It includes This is not a one-shot game. Life will go the treaty was successful. like excessive water and air pollution. How- (among others) China, India, the United on and there will be future issues (like this ever, at a global level, the community of States, the United Kingdom, Russia, Ger- one) which many of these countries will The Montreal Protocol as well as the nations is not so different from a group of many, and Japan – countries which are all have to cooperate with each other on in dozen amendments which followed and self-interested individuals. Since there is no major players on the world stage. Precisely order to solve. In contemplating torpedo- strengthened it has led to a sharp decline known other civilization to compare it to, because of this, however, these nations have ing the provision of climate change mitiga- in the concentration of CFCs in the atmo- it is unclear exactly how large and heteroge- significantly more in common with each tion, a large country may find the prospect sphere and a recovery in the strength of the neous we can consider our global commu- other than with the majority of small and of future reprisals by its peers too costly to ozone layer which is expected to continue. nity to be. However, in order to proceed, relatively less influential states in the world. be engaging in intransigence. Given all of How was the Montreal Protocol so fantasti- this analysis will consider it to be large and Each of these countries would sustain big these favorable factors, it seems odd that we cally successful at solving a problem which heterogeneous. This seems reasonable. loses to their economies (if only because don’t already have an effective mitigation seems so similar to climate change? There is they have more to lose) were some or all of agreement. some disagreement on this question, but it There are many more countries now the disastrous climate scenarios predicted by seems the single biggest reason is that there than there were at the close of World War climate models to come true. None would was far less uncertainty in the cost-benefit II and their interests seem to be as diver- gain from climate change, as some small analyses provided by the scientific commu- gent as ever. The weaknesses of large het- agriculturally dependent countries would. Montreal nity at the time. In addition to being more erogeneous groups correspondingly apply. This is not to say, however, that their in- certain, most studies confirmed that the The countries of the Earth will attempt to terests are perfectly aligned. As we will see, Before considering the results of the benefits of acting to limit CFC emissions free-ride on the provision of climate change there is considerable disagreement between most important climate change mitigation outweighed the costs by very large mar- mitigation by others and there will be little the developed and developing wings within treaty, it is instructive to examine the Mon- gins (Sandler, 2004). Unlike with climate to keep them from doing so because global this group of major players over what to treal Protocol of 1987 which imposed lim- change, no countries benefited from the verification and enforcement is quite dif- do about climate change. As a result, it is its on the consumption and production of deterioration of the ozone layer. As a result, ficult (as evidenced by our nuclear prolif- unclear whether these commonalities are chlorofluorocarbons (CFCs) internation- more countries’ preferences were aligned. eration problems). Furthermore, as already enough to encourage them to provide cli- ally. It is often held up as the prime example There were fewer conflicts of interest. Many -60- ECONPress International Collective Action on Climate Change -61- countries (like the United States) had start- ber states (under the auspices of the UN) mate Change. At Copenhagen, imposition work. As already noted, small groups suf- ed limiting CFC emissions even before the in 1997. It entered force in 2005. It was of binding targets wasn’t even attempted. fer from fewer coordination problems and treaty was signed. Another important factor intended to force binding cuts on carbon Most developed countries made incredible so are more likely to be privileged. More which helped the Montreal Protocol suc- dioxide emissions sufficient to keep global promises of further emissions cuts and af- substantial cooperation from developing ceed was the extreme concentration of CFC temperature increases at or below 2 degrees firmed their general commitment to some nations could potentially be secured in a emissions amongst a relatively small num- Celsius. Though Kyoto only entered force kind of climate change mitigation. Devel- small group and enforcement and verifica- ber of countries. In 1987, it was estimated recently, it has not yet had any noticeable oping nations, meanwhile, skated by with tion would be easier. that 12 countries accounted for more than effect on carbon dioxide emissions and it is promises to reduce the “carbon intensity” 78% of emissions (Sandler, 2004). This not expected to. Earlier, it was noted that of their economies – to lower the carbon Ultimately, though, the cold reality made the relevant “k-group” of major understandable disagreement over the costs emissions per dollar of output they pro- boils down to the fact that the net benefits countries smaller and easier to coordinate. and benefits of climate change mitigation duce. Even if they kept these promises, of climate change mitigation are not nearly It also meant that those countries which may be enough to scuttle the whole enter- the speed of their economic growth means as high as the net benefits of ozone layer had the most to lose from CFC emissions prise (even within a smaller k-group). This that their emissions would continue to rise. protection were (Sandler, 2004). Addition- were also the ones who produced the most is precisely what has happened (Sandler, Most observers have concluded that Co- ally, there are more big carbon emitters than CFCs. This made it relatively easy for the 2004). penhagen was a bigger failure than Kyoto. there were big CFC emitters at the time the major players to make the world a privi- What is to be done? Montreal Protocol entered effect (the rel- leged group. Though most small nations In order to secure an agreement, the evant k-group is bigger). These differences did sign the treaty, their participation was drafters of the treaty at Kyoto had to ex- One possibility would be an incentive may make the climate change compliance not strictly necessary to achieve the favor- empt a number of major developing coun- mechanism analogous to the one proposed gap unbridgeable – at least until there is able outcome we have today. tries (like China and India) from binding by Olson and similar in form to the one more certainty about its costs and benefits emissions cuts. These countries effectively implemented in the Montreal Protocol. and the net benefits are shown to be unam- Finally, some observers have drawn at- concluded that the costs of the requisite However, given the wide divergence of biguously positive. tention to the role that external incentives massive cuts exceeded the benefits (espe- opinion on the costs and benefits of climate (not unlike Olson’s private benefit remedy cially in the context of rapid economic change mitigation (as opposed to in the idea) played in compliance with the Mon- development). The problem is that those Montreal Protocol) and already weak par- treal Protocol. The treaty provided two countries are massive and necessary mem- ticipation levels, it seems unlikely that rich R types of incentives – one positive, one neg- bers of any k-group coalition of major pow- countries would be willing to pay enough ative. First, developed countries agreed to ers which might decide to provide climate compensation to developing countries and make payments to developing countries to change mitigation. China now generates that potentially noncompliant countries help defray the cost of compliance with the more emissions overall than the United would find noncompliance too costly due treaty. Second, punishments were imposed States. Since major developing polluter na- to trade restrictions. Trade restrictions tend on countries which judged the optimal tions whose contributions are necessary to to be more effective when there is already level of emissions reductions to be below provide the public good of mitigation effec- high compliance (Barrett, 2007). what the treaty demanded. These punish- tively defected, it became a dominant strat- ments came in the form of trade restric- egy for other otherwise cooperative nations An alternative solution would be to tions. Compliant countries were permitted to defect (McGinnis and Somin, 2007). As provide a decision making environment to impose severe restrictions on imports of a result, the United States never ratified the which excluded the interests of small coun- products containing CFCs from noncom- treaty. Despite, the obvious disincentives, tries. One problem with the United Na- pliant countries. Since participation in the Europe did adopt it – perhaps because of tions decision-making apparatus is that it treaty was so high, these restrictions proved some vague unifying notion of “European demands absolute unanimity for an agree- to be highly costly to noncompliant coun- values.” A further problem is that com- ment to enter force (Barrett, 2007). Given tries (Barrett). pliance by countries which had agreed to the large scope for conflicts of interest binding cuts is not enforceable. As an ex- over climate change mitigation (especially ample, Canada has missed its targets by amongst the smaller countries), the una- considerable margins and will not face any nimity requirement tends to unnecessarily Kyoto And Copenhagen sanction for doing so. What incentive does water-down treaties and prevent the big it now have to comply anyway? countries from cooperating more effectively The Kyoto Protocol is an international with each other. The appropriate k-group environmental agreement which was signed Similar problems plagued the more of nations could assemble under the Group and ratified by many United Nations mem- recent 2009 Copenhagen Summit on Cli- of Twenty (a ready-made k-group) frame- -62- ECONPress -63-

Works Cited

Barrett, Scott. Why Cooperate? The Incentive to Supply Global Public Goods. New York, New York: Oxford University Press, 2007. Print.

McGinnis, John O. and Ilya Somin. “Should International Law be Part of our Law?” Stanford Law Review. 59.5 (2007): 1175-1247. Print.

Olson, Mancur. The Logic of Col- lective Action: Public Goods and the Theory of Groups. nd2 ed. Cambridge, Massachusetts: Harvard University Press, 1971. Print.

Sandler, Todd. Global Collective Action. Cambridge, the United Kingdom: Cam- bridge University Press, 2004. Print.

Shepsle, Kenneth A. Analyzing Politics: Rationality, Behavior and Institutions. 2nd ed. New York, New York: W. W. Norton & Company Inc, 2010. Print R -64- ECONPress

Submissions Process and Guidelines

ECONPress is a peer reviewed journal where anonymized papers are reviewed mul- tiple times and may undergo several rounds of revisions before the paper is accepted for publication. All potential authors should visit our website to submit their papers(s). Peer Review Process

When an Author submits a paper to ECONPress, it is initially assigned to two or more Reviewers. These Reviewers make a recommendation to the Section Editor who then communicates a decision to the author: • Accept Submission • Revisions Required • Resubmit for Review • Decline Submission

Accept Submission - The paper will be reviewed by a Copy Editor and after the small errors are corrected, the paper will undergo a final proofread before it is put in a queue for publication. Revisions Required - The paper is suitable for the journal but some revisions are nec- essary to become ready for publication. The author will receive feedback related to the paper and will be required to upload a revised copy of their paper. The paper will again be reviewed by at least two reviewers, one having read the paper in the previous round. This process may continue for several rounds and if it is ultimately deemed fit for publication, it will be marked Accept Submission. Resubmit for Review - The paper is suitable for the journal but requires significant revisions. The author is suggested to make extensive changes to the paper and complete a new submission. Decline Submission - This paper is not suitable for this journal. This may be for many reasons, including the paper not relating to economics, the paper is discovered to have been plagiarized, etc. Submission Information

Authors should submit their papers through our web site, www.ECONPress.org We welcome all papers related to the study of Economics from students enrolled as an undergraduate at an accredited university. This includes (but is not limited to) interviews with economists, research papers and opinion papers. Submissions are accepted on an ongoing processes, with the selection process occur- ring twice per year: once in the Spring and once in the Fall.