RISK TAKING BEHAVIOR ON THE PGA TOUR

A THESIS

Presented to

The Faculty of the Department of Economics and Business

The Colorado College

In Partial Fulfillment of the Requirements for the Degree

Bachelor of Arts

By

Joseph Howe

April 2013

Risk Taking Behavior on the PGA Tour

Joseph Howe

April 2013

Economics

Abstract

This thesis investigates characteristic variables such as wealth and recent wealth of PGA Tour golfers that may affect risk taking behavior during play. This study finds that ’s risk taking behavior on the PGA Tour is affected very little, if at all, by recent and career performances. Additionally it is found that in-tournament performance as well the importance of the tournament will slightly affect their risk taking behavior.

KEYWORDS: (PGA, Risk, Expected Utility, )

TABLE OF CONTENTS

ABSTRACT

1 Introduction 1

2 Literature Review 7

2.1 Importance of Study………………………………………………………..5

2.2 Overview……………………………………………………………………6

2.3 Golf Specific Studies Examined...………………………………………….7

2.4 Theory Studies Examined…………………………………………………..11

3 Theory 13

3.1 Expected Utility in the PGA…………..…………………………………...14

3.2 Measuring Risk…………………………………………………………….21

3.3 Theory Conclusion………………………………………………………...23

4 Data and Methodology 25

4.1 Data and Sources…………………………………………………………..25

4.2 Results: Summary Statistics……………………………………………….27

4.3 Methodology………………………………………………………………30

4.4 Performance and Independent Variables………………………………….31

4.5 Characteristic Variables…………………………………………………...34

4.6 Dependent Variables………………………………………………………36

4.7 Estimation Procedure……………………………………………………...37

4.8 Econometric Problems…………………………………………………….38

4.9 Ordinary Least Squares Results…………………………………………...39

TABLE OF CONTENTS CONTINUED

5 Conclusion 44

6 Works Cited 47

LIST OF CHARTS

1.1 2012 Top 125 Golfers PGA Tour Earnings ……………………………. 3

1.2 PGA Tour Prize Distribution by Placing ………………………………. 3

3.1 Risk Averse Individual Utility Function ………………………………. 17

3.2 Risk Loving Individual Utility Function ………………………………. 17

LIST OF TABLES

4.1 Description of Variables……………………………………………..26

4.2 Summary Statistics…………………………………………………..28

4.3 Expected Signs of Variables…………………………………………35

4.4 OLS Results………………………………………………………….40

CHAPTER I

INTRODUCTION

Professional Golf Association players are a very diverse group of individuals, whose behaviors cannot expected to be the same. This study aims to identify characteristics of PGA golfers which explain their risk taking behaviors on the course in line with expected utility theory.

In the past few years professional golf fans have been treated to some of the greatest uncertainty and competitive balance that the game has ever seen. For one of the first times in quite some time, and arguably ever, there was no single dominant golfer on the PGA Tour. Prior to Tiger Wood’s leave of absence from golf he would dominate the PGA season. When took out his red shirt on Sunday morning you could count on him to win the whole tournament.

From 1999 to 2007 Tiger Woods averaged over six and a half wins per PGA Tour season, including 9 victories in the year 2000 and 8 in 2007. In 2012 Rory

McIlroy enjoyed the most victories with four, two of those coming in the final three weeks of the season. Before Tiger there were the greats like ,

Jack Nicklaus, and so on and so on. By Tiger leaving (and returning in lesser form), it opened the door for young stars like , Rory McIlroy, Jason

Dufner, and among others. In the PGA today it is as big of a mystery as ever who will have a big week and who will not. Chart 1.1 shows this 1

parity, even though it is obvious that there is not a completely even distribution of earnings amongst players. This can be seen by comparing it to chart 1.2, the usual distribution of prize money in any given PGA Tour tournament.

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CHART 1.1

2012 EARNINGS BY PLAYER

6000000.00 5000000.00 4000000.00 3000000.00

Earnings (US (US Dollars) Earnings 2000000.00 1000000.00 0.00 David Hearn PGA Top 125 Earning Golfers Earnings 2012

CHART 1.2

PGA TOUR TOURNAMENT PRIZE DISTRIBUTION 1600000 1400000 1200000 1000000 800000

Earnings (US (US Dollars) Earnings 600000 400000 200000 0 65 T58 T53 T47 T39 T35 T28 T23 T16 T8 T3 Finishing Place in Tournament Prize Money

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Clearly there are still some golfers who are better and win more often than others. Is this only attributed to greater skill?

Shmanske (2007) identifies the PGA Tour as a system that disproportionally rewards one-time, exceptional performances over consistent steady play. In the discussion of his study he asks the question of where the variance and skewness of golfer’s relative scores come from (p. 470). Hood

(2008) found that when golfers are in danger of being eliminated from a tournament they play 0.08 strokes worse, but their standard deviation increases by

0.32 strokes, suggesting an increased level of risk taking behavior. In simulated tournament seasons he found that if players played as previously mentioned they would win more prize money with the exception of Tiger Woods. Woods would however would increase his winning percentage (pp. 515-518). Winning for Tiger

Woods provides a possibly bigger incentive as he is the third top earning athlete in the world.

One of the ways golfers can have a big week is by taking risks on the course. It is not unreasonable to think that to win in any given week in the modern

PGA Tour a player must play exceptionally well because of the chances of another player also playing exceptional golf.

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Importance of this Study

Many golf columnists and journalists have pointed out that in the past four years the PGA has been in a transition period. Popularity of the Tour plummeted in 2009 after Tiger Wood’s sex scandal. Since then the Tour has been looking for a new star, but who should the Tour promote, who should they put in the spotlight? The PGA has tried to replace Tiger Woods with another consistent superstar; the only problem is that there isn’t anyone that dominant currently in the game. In spite of this fact, the PGA Tour must find a way to identify the most exciting players on Tour and focus on that group of players. These exciting players are the ones who are never out of a tournament, who can make a run at first place even if they are behind by a lot on the final day. Additionally these players may or may not be the highest ranked. This research could help the PGA discover a new group of players to promote by providing information or tools that help identify these players.

Additionally, an important contribution from this study, and one that has been identified by Ehrenberg and Bonanno (1990), is the similarity of the PGA

Tour’s prize distribution system to that of the corporate and specifically financial sectors in the business world (pp.74S-77S). The controlled structure and data of a

PGA tournament is much easier to study and the conclusions are useful. Some of the relationships between risk taking and golfer characteristics could possibly lead to identifying behaviors of employees and improve strategies in hiring and compensation.

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Overview of the Paper

This paper will attempt to explore the determinants and characteristics of risk taking behavior of PGA Tour professionals. Chapter two will review the literature of studies that include risk taking behavior and relevant studies on the

PGA Tour as well as the financial sector in the business world. Chapter three will outline a theoretical model for characteristics of risk taking behavior and apply these theories to the PGA Tour golfers. Chapter four will describe the data collected, adjustments, and empirical methodology used to test the theoretical implications of Chapter III. In conclusion, Chapter five will discuss the implications that can be drawn from the results shown in Chapter four and identify for future research as well as possible pitfalls of this study.

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CHAPTER II

LITERATURE REVIEW

The purpose of this chapter is to review the current literature on risk taking and factors that affect earnings in professional sports, especially golf. Professional golf tournaments are often won and lost during the last round of competition.

There is substantial literature on earnings in professional golf, however, most focuses on the skills of a golfer and less on the decision making a golfer exercises in how he plays each shot. Much of this literature compares professional golf earnings to the typical corporate reward and promotion systems, as they are very similar; and also identifies important implications that can be drawn from the

PGA. The main difference between this study and others is that it identifies characteristic variables (such as career earnings, wins, and others) of a golfer and how these may change his play.

Golf Specific Studies Examined

Ehrenberg and Bognanno (1990) studied incentive effects of tournaments using European PGA Tour data, examining the structure and level of prizes and ensuing effect on performance. They found that a when players faced larger marginal returns in the final round of play their scores improved compared to the first three rounds of the competition (pp. 85S-86S). It is important to note that higher marginal returns to score are seen as players’ finishing place increases, or 7

the difference of winnings between first and second place is much larger than last and second to last. It is important to note the top heavy prize structure of PGA

Tour Tournaments. The total prize money and its distribution are known to players before tournaments.

The previously mentioned findings are suggesting that effort is increased with extra incentive. Additionally, Boganno and Ehrenberg (1990) find that when the amount of money won or lost by moving up or down a spot increases, the scores also improve, or more simply stated the higher the stakes the more effort will be expended (as cited in Shmanske, 2004, p. 254). Lastly, a very interesting finding was that when the tournament field contained better golfers the scores on

Sunday were worse. Shmanske expected that with a more skilled field, golfers would know a better score would be required to win and therefore increase effort which in turn improves scores. A possible explanation is not offered by the authors or Shmanske. One reason for this could be that the expectation of an abnormally good score from one of the top ranked golfers would change the risk taking behavior of the other golfers.

In another study of the PGA, Hood (2008) examines the rewards of being consistent, a normally sought after quality, on earnings of PGA Tour golfers. He rated the ability and consistency of the top thirty players on the PGA tour in 2006 and examined their rewards. Hood discusses the difficulty involved in defining and measuring risk taking behavior; however, consistency has been used in financial literature as a quantifiable proxy for risk-taking behavior. Hood (2008)

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finds evidence in support tournament theory suggesting PGA golfers should take more risks and that inconsistent play will increase winnings because the reward system heavily favors excellent performances (p. 518). He also points out that golfers are not homogeneous; some are more skilled than others. This suggests that risk taking would be beneficial for some golfers but not for others. Hood’s

(2008) findings are the opposite, in fact he finds that risk taking would increase winnings of all the golfers studied except for Tiger Woods (p.518). Hood then concludes that essentially everyone in a tournament format is trailing because of the odds of another golfer scoring extremely well throughout the event. There is an expectation then that to win a player must score better than consistent play would allow.

Shmanske (2008) recently identified the importance of using PGA Tour microdata when examining skills, performance and earnings. By using individual tournament data rather than season long averages Shmanske (2008) was better able to account for differences between difficulty relating to specific skills. As a result his specific findings of variance and skewness of scoring distributions improved on other golf related literature. Shmanske (2008) finds small evidence that the variance of scoring distribution per tournament can be explained by skill distribution functions but most of the variation in scoring remains unexplained (p. 660). Part of this unexplained variation could be due to unexamined variables such as players deciding to play with more or less risk. The consistent high ranking and earnings of certain golfers suggests that luck is

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unlikely the main source of score variation and other skill variables must exist.

Much like a financial market investor, golfers can choose when to take risks or to play it safe. This behavior of choosing risk wisely can be thought of as a skill and could be part of the unexplained score variation. Another possible explanation could be that risk taking behavior is affected by valuation of wealth, this will be examined more thoroughly in chapter three.

Callan and Thomas (2007) used a multi-equation approach rather than a single equation model used by most golf research. They do so because studying certain shot making skills will have an indirect effect on earnings; the better shot making skills will lower scores and therefore help golfers finish higher. One of their findings is important to note aside from the effects of shot making skills such as driving distance, putting, iron skill etc. Clearly the better a player’s skills are result in a better ranking for the season (lower numerical value). The better ranking the more a player will earn. Not as clear was Callan and Thomas’s (2007) finding that a player’s experience in the PGA, both short and long term, will favorably affect the player’s average score (p. 409). This is important because experience is a non skill variable that affects a player’s average score. Experience could lead to differing strategies on the golf course, one of these strategies is when to take risks and when not to.

McFall, Knoeber and Thurman (2009) use the PGA to examine a “hot hand” or a player who performs well over time in a grand prize setting where contests are linked together. This type of setting exists in the PGA as players must

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qualify for the end of the year Tour Championships by collecting points in tournaments throughout the year. By collecting the most points throughout the year PGA golfers can win the Tour Championship (one of the highest paying events). Mcfall et al. (2009) examined the PGA tour before and after the grand prize format was introduced. Golfers who won early in the year are expected to have increased incentive to win as the year goes on. Mcfall et al. (2009) confirmed that with 30 tournaments remaining the top ranked players performance is about 0.13 strokes per round better than the thirtieth ranked player

(p. 251). These findings suggest that players who are doing extremely well or poorly will have less incentive to take risks and finish higher in tournaments.

Theory Studies Examined

Kahneman and Tversky (1979) pioneered risk taking behavior studies by proposing an alternative theory to expected utility theory called prospect theory.

An important aspect of prospect theory is that value is assigned to gains and losses rather than to final assets. Instead of only probabilities, weighted values are assigned to probabilities of a gamble. Prospect theory suggests that identifying conditions under which risk aversion or risk seeking are expected to occur will help more accurately predict outcomes (pp. 284-285).

Risk aversion is an accepted concept in modern economics. Varian (2006) defines three different types of consumers when it comes to risk. The first is risk averse, a consumer who prefers the expected value of his wealth rather than face a gamble where wealth could increase or decrease. The second consumer is a risk

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lover, this consumer’s behavior is the opposite of a risk averse individual; they prefer a random distribution of wealth to its expected value. Lastly, if a consumer is risk neutral then the expected utility of wealth is the utility of its expected value

(p. 255). A consumer is more likely to be risk averse if their valuation of current wealth is low. Simply put, a dollar is not necessarily worth the same to a homeless man and Tiger Woods; we could expect that the two would behave differently when it comes to taking risk. Varian (2006) later discusses the measurement of risk. Risk in an asset is not the same to everyone as a consumer’s utility depends on the mean and variance of total wealth, not on the mean and variance of any single asset (p. 240).

In a study of risk taking behavior in mutual funds, Taylor (2003) challenges the previous literature on the subject that towards the end of a financial year a winning fund manager will index and “lock in” his good performance while a losing manager will be more likely to gamble to catch up to the winning managers benchmark. He concludes the winning manager still indexes but now with respect to his expectation that the losing manager will gamble. The result is a higher probability of the winning manager to gamble than the losing manager (p.

374).

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CHAPTER III

THEORY

This chapter will discuss the theories pertaining to PGA Tour golfer variance in performance on the final day of tournaments and specifically expected utility and risk taking behavior. First the theory of expected utility will be examined for PGA golfers with knowledge of the potential earnings of different place finishes. Next, a measurement of risk taking will be outlined. This will create a framework for risk taking decisions of the golfers and how these behaviors influence performance, therefore determining earnings. Lastly other theories of factors effecting risk will be discussed and a specific multivariate equation model will be constructed and empirically tested in Chapter Four. A general equation to summarize the theoretical model can be found in equation 3.1.

Risk taking will be the dependent variable as this study will examine characteristics that may or may not affect changes in the risk taking behavior of the golfers. The variables that will be used to explain the dependent variable are wealth, recent changes in wealth, non-monetary accomplishments (wins, recent wins, and prestigious wins), knowledge of scenario (experience), and finally recent changes to performance. These independent variables will be justified through theory presented in this chapter.

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(3.1)

Expected Utility and the PGA

Expected utility is a theory of utility in which preferences of taking risk

(or betting) with uncertain event outcomes are represented by a function of the payouts. Expected utility also depends on the probability of the payout occurring, risk aversion, and the different utility preferences unique to each individual. At its most basic form the expected utility function is a sum of different periods of consumption, each with a certain probability in which only one of them will actually happen. A simple form of the expected utility theory is shown by equation 3.2 presented by Varian (2006, p. 221). In the equation and represent two separate states’ probability of happening. For example if =1 then that would be a certain state of consumption, and the utility of it could be known as long as the consumers preferences were exactly defined. and

represent consumption in each of the two states and how much utility each gives the consumer.

(3.2)

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The probability of each state of consumption actually happening is represented by the variables multiplying the utilities of each period. This is easily adaptable to any PGA golfer for each that he takes. The golfer has a choice in how to play each situation, either risky with high reward or playing it safe with little reward and little risk. Each state or outcome can be thought of as a different place finish in the tournament, and the probability of the event happening depends on the combined riskiness of the shots the golfer will play.

Golfers cannot have absolute certainty of these probabilities. Experience (years on the PGA Tour) would undoubtedly give the golfer a better objective estimate about these distributions as he has probably been in a similar situation multiple times in the past. For this reason experience will be tested as an independent variable affecting risk taking behavior.

Expected utility was first formally presented by Daniel Bernoulli in 1738 after realizations that the same amount of additional money was more useful to a poor individual in comparison to a wealthy individual. Castelvecchi (2009) records a quote shortly before formulation of the expected utility theory when

Gabriel Cramer wrote a letter pointing out, “The mathematicians estimate money in proportion to quantity, and men of good sense in proportion to the usage that they may make of it” (Economic Thinking section, para. 3). PGA golfers will not take the same amount of risk because their expected utility of different outcomes varies. Additionally the risk required for a top player to place first would be less than the risk a lower ranked golfer would have to take to achieve the same place

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finish. These qualities of the expected utility theory are the underlying goals of the study, attempting to identify other variables that effect risk taking behavior.

Two possible risk taking behavior groups are show in figures 3.1 and 3.2.

The figures illustrate the different utility functions of risk averse and risk loving individuals. The curvature of the consumers utility function demonstrates their attitude towards risk, the more convex the utility function the more risk loving the consumer is, the more concave the utility function the more risk averse. A linear utility function would suggest a risk neutral or indifferent consumer. Von

Neumann, Morgenstern (1947) pioneered expected utility theory and the effects of risk taking behaviors on utilities on which most modern theories of the topic are based off of.

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CHART 3.1

RISK AVERSE INDIVIDUAL UTILITY FUNCTION

SOURCE: Varian, 2006

CHART 3.2

RISK LOVING INDIVIDUAL UTILITY FUNCTION

SOURCE: Varian, 2006

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Although expected utility theory’s strict mathematical application has come under scrutiny by behavioral economists it is still relevant when certain issues are addressed. One of the main and obvious issues with expected utility theory is the concept of loss aversion. Rabin (2000) addresses this concept and points out that consumer’s utility are determined by changes in wealth rather than absolute levels of wealth (p.1288). Loss aversion in the PGA can not only be directly related to a golfer’s earnings, but also the golfers recent placing in tournaments. A golfer who places poorly in several consecutive tournaments will have won a small amount of money, and according to this theory, will be less likely to play risky in order to improve his finish by only a few places.

Additionally a golfer who has performed poorly in a previous round of the tournament he is currently playing in could be expected to have a similar affect.

As alluded to earlier, the outright monetary gambles used by Rabin (2000) and others can be very different than the PGA. Competitive sports create incentive to capture first place in tournaments other than the largest monetary prize. Phil

Mickleson has been one of the top ranked professional golfers in the PGA since turning pro in 1992. However, until 2004 he was known as the best player to never win one of the four major golf tournaments.1 Studying recent earnings and

1 Mickleson won the in 2004, and has since won it two other times along with one other major (the PGA Championship). However many still do not consider him an all time golf great because he has not won the British Open or U.S. Open tournaments. Interestingly he is considered to be one of the most risky golfers on the PGA Tour. 18

recent tournament victories (first place finishes) will improve the empirical model by addressing the concept of loss aversion’s effects on risk behavior in the PGA.

Rabin (2000) identifies several other issues with expected utility theory which must be taken into consideration, especially when studying data sets to determine differences between individuals’ (or groups’) risk taking behaviors.

The first of these problematic research methods is that expected utility theory makes wrong predictions about the relationship between modest stakes and large stakes risks. Rabin concludes that estimates of risk attitude differences will be affected by data sets that contain different levels of risk (p. 1287). The prize structure of PGA tournaments will create larger stakes risks for those golfers near or at the top of the leader board on the final day, possibly affecting risk taking behavior in exactly this way. To control for this, the standings of golfers after the third round of play is completed will be examined. Additionally, the more golfers closely grouped around a certain place finish would most likely increase the stakes of the risk. Observing the risk taking behavior on the final of four rounds results in assessing the most informed decisions golfers can make. They have the most information available to them including, but not limited to, strength of the field, positions of various opposing golfers, course conditions, and their current level of play. Additionally, examining the golfers at this stage eliminates the issue of players who play very risky to try and make the cut of golfers after the first two rounds of play.

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Rabin (2000) also suggests that expected utility is a miscalibrated explanation of modest-scale risk aversion (p. 1286). It would prove difficult to estimate what defines modest-scale risk aversion; however, it is important to realize several unique attributes of the PGA tour as compared to the financial gambles that Rabin examines. First, there is much more at stake than just earnings. Players who do not finish well consistently are in danger of not being able to enter certain tournaments or remain on the PGA Tour itself. Secondly, for the top ranked players, sponsorships as well as standings for the end of the year

PGA championship are at stake. The substantial amount of money awarded in each tournament, in combination with these other important implications for performing well, substantiate the risks being defined as large scale.

Despite the fact that PGA Tour risks could be defined as large scale and therefore be exempt from the previous argument, it may not matter. The findings and theories of Rabin that modest-scale risk aversion will automatically lead to risk aversion of gambles with infinite pay outs for any level of initial wealth. Watt

(2002) argues that Rabin implicitly assert an extremely high degree of risk aversion for modest-scale bets (p. 228). If a consumer has such high risk aversion as to turn down a modest-scale bet that is attractive, Watt (2002) suggests it is intuitive that they would exhibit risk aversion for large-scale bets for any level of initial wealth (p. 229).

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Measuring Risk

Examining and testing the risk taking behavior in the PGA will be an important addition to the current literature. Most of the current studies that involve risk taking and consistency focus on whether or not it is beneficial, but not on the decisions that the athletes make in real tournaments and what factors affect those decisions. Essentially, the current literature asks should the athletes take risk or do they; this study examines why and under what circumstances certain athletes choose risk. Most other risk taking literature is focused on investing strategies and fund managers in particular. Other applications outside of golf are corporate reward and promotion structures as they resemble that of the

PGA.

In any tournament setting where relative performance is rewarded Hvide

(2002) shows that a higher reward going to an agent with the highest output results in a greater incentive for said agent to take risks (p. 892). Intuition may suggest that poor performing funds would take risk to catch up to better performing funds while the funds performing well will eliminate risk to “lock in” their good performance. Busse (2001) found that funds that perform better than the median increase total risk more than funds that have performed below the median (p. 36). An explanation of this behavior is that funds not only need to perform well for the investors they currently represent but also need to attract new investors to their fund. The best performing funds continually attract the lion’s

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share of investor inflow the following year while the CEO of the worst performing fund could be fired.

In the PGA inflow of investors cannot help to explain risk taking behavior; however other incentives may exist that influence which golfers take risk.

Endorsements to the very top golfers can be very lucrative and last the length of a career and even beyond. To sign an endorsement deal will undoubtedly create extra financial gain outright, but also many companies build in bonuses for players performing well. The reasons for these bonuses can vary from brand image to extra television exposure. Expected utility theory would suggest that marginal utility of wealth decreases as wealth increases. It has been shown that fund managers that perform the best will risk more, but it remains to be seen if the best performing golfers on the PGA follow a similar pattern. To examine the behavior of the golfers’ career earnings, career tournament wins and current

World Golf Ranking will be included in the model. The intuition behind including career total earnings is obvious; wins and World Golf Ranking are included for reasons discussed earlier pertaining to non-monetary motivations from winning.

Measurement of risk in the financial sector is more easily observable than in the PGA. Additionally fund managers would have much more time to assess risk of certain decisions than a player on the PGA Tour. Golfers must use a somewhat more Bayesian probability approach by assessing their risks by past experiences and knowledge of their own chances of being successful. Hood

(2008) acknowledges the difficulties in measuring risk taking behavior on the

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PGA tour and uses consistency as a quantifiable measure of risk taking (p. 506).

Shmanske (2007) uses variance and skewness around each golfer’s average score to measure consistency (p.465). Using variance and skewness of the fourth round score compared to the first three rounds for individual golfers will measure the risk behavior exhibited in the final round.

Conclusion

This chapter has provided the theory behind the model that will be tested in the coming chapters. Among the hypotheses to be tested are that professional golfers on the PGA Tour exhibit certain risk taking behaviors based on expected utility theory. If expected utility theory exists then career earnings and wins should positively correlate with higher levels of risk. The theory of loss aversion would suggest that recent earnings and wins will also positively correlate with higher levels of risk. Experience is expected to have a positive effect on risk taking; more experience generates possession of a greater amount of information.

Tournament positions after three rounds of play and number of players close to a golfer in score are both expected to affect the level of riskiness for each shot, and in turn are expected to be positively correlated with risk taking behavior. The empirical model that will be outlined in the following chapter will test these hypotheses regarding the variables that may impact risk taking behavior of PGA

Tour golfers.

This concludes the discussion of the theory behind risk taking behavior of

PGA Tour golfers. The following chapter will give a description of the data sets

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that will be used for empirical analysis of the theory and the necessary adjustments that were made to most accurately and fairly measure the discussed variables.

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CHAPTER IV

DATA AND METHODOLOGY

The purpose of this chapter is to familiarize the reader with the empirical methodology and reasoning used to test the theoretical implications of Chapter III.

The variables introduced in the previous chapter will be discussed in detail in addition to the source and nature of the data. After reviewing the data set, variables, and necessary adjustments made to the raw data, the methodology used to test the model will be explained and constructed. The results will then be presented in Chapter V.

Data and Sources

The data set was obtained with special permission from the PGA TOUR’s

Media Department, all data comes from the PGA TOUR’s online database run by

Shotlink (the PGA TOUR’s data gathering system). Other common data (for example, a golfer’s age) was obtained from the PGA through their website. Data from the 2012 PGA golf tournament season only will be examined. The top 125 money earners are examined in order to control for the large differences in skill amongst the best and worst golfers on tour. Table 4.1 provides the name and definition of the variables that were gathered for the data set

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TABLE 4.1

DESCRIPTION OF VARIABLES IN EQUATION 1

Variable Abbrev. Definition

The number of strokes a player’s final round 18-hole score differs from said player’s adjusted average round 18-hole score in tournament t with course difficulty, weather, and field adjustments

The career earnings on the PGA Tour of a player before the start of tournament t The earnings a player has won on the PGA Tour in that year up to that tournament t

The career total win percentage of a player in official PGA Tour events before the start of tournament t

The number of official PGA Tour event wins a player has had in his 5 events prior to tournament t

The age of a player during tournament t

Number of years a player has been a PGA Tour member

The World Golf Ranking of the player

1 if the tournament being examined is one of the four Major Championships, 0 if it is not one of these

1 if the player has won a Major Championship in their career at the start of tournament t

1 if the player is one of the top 50 off course earning players in the PGA at the time of tournament t

Number of official PGA Tour events played in at the start of tournament divided by years on tour t

Golfer’s third round score of tournament t

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Results: Summary Statistics

Before the OLS results, a look at simple summary statistics is relevant in that it will help examine the data and assure it is representative of a diverse group of golfers. The expected utility theories that are being examined are a comparison of a variety of characteristics; with a diverse group of observations this assures that if the relationships exist they exist across all golfers and not just a special group. Table 4.2 shows the wide variety of players that were used in the data of the study, and that this wide variety is also relevant in the observed tournaments/rounds.

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TABLE 4.2

SUMMARY STATISTICS

Variable Minimum Maximum Mean Std. Deviation .011 11.211 2.490424 1.916616

0 102,000,000 14,000,000 15,300,000

0 7,842,192 1,018,256 995,657.5

0 75 4.031 90109511

0 3 0.1096774 0.3464189

22 50 34.34018 5.954971

2 31 12.43226 5.799184

1 634 105.995 98.70067

0 1 0.0973607 0.2965353

0 1 0.1002933 0.3004787

0 1 0.3313783 0.4108468

27 666 197.566 125.4214

61 82 70.71437 3.040792

There are 45 official money tournaments on the PGA Tour for 2012.

When selecting which tournaments to examine one must be careful as there are several tournaments that cannot be used. The first of these is the Accenture Match

Play Championships. uses head to head matches in a bracket format to

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determine a winner. However this tournament is still an official PGA money- earning event so while the scores from that exact tournament will not be used this study will be using its prize money and final placings data to contribute to the variables of career winnings, recent winnings, career wins, and recent wins. Four alternate tournaments also exist that are on the same weekend as main PGA tournaments. These will be treated the same way as the Accenture Match Play

Championship; only the earnings and win variables will be used, not the scoring data. The PGA also has four fall series tournaments that will not be included because they take place after the playoffs and are generally only played by the golfers who are in danger of not qualifying for the PGA the following season.

Additionally, the , a team event, will not be included and neither will its earnings and win variables. After these exclusions the scoring data will be taken from 37 different official PGA events. All other variables, for example recent wins, will include the other 8 official events for a total of 45.

Golfer was dropped from the data set despite being in the 125 top money earners of 2012 as he only played in one tournament. Of the remaining

124 golfers the average events played was just under 24, with ,

Troy Matteson, and tied for the most at 32 and Peter Hanson with the least at only 11 events. A wide variety of golfers were examined, the oldest of which was (50 years old). Vijay is 28 years senior to the youngest golfer, (22 years old). Age as well as experience data was collected.

Experience is measured by the golfers’ years on the PGA tour as well as their

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career total events played. The players averaged 12.4 years of PGA Tour experience with the maximum being 31 (Vijay Singh) and the minimum being 2 years ().

In the PGA most tournaments reduce the field of golfers after two days.

This is called the cut and generally the lowest 70 scores, including ties, continue to play the final two rounds on Saturday and Sunday. Some players in certain tournaments do not make the cut; therefore they do not play four total rounds of golf and win no prize money. Players who miss a cut in an event were eliminated from the examined scoring data for that tournament.

Methodology

The empirical model used is presented in equation 1. Dummy variables appear in all capital letters while others appear in lower case letters.

(4.1)

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Independent Variables

The independent variables in this study fall into two major categories. The first is a performance variable; these are different however than what has been studied in most other golf literature. The performance variables in this study are the results of past performances and the success (or lack of) that it has brought the individual golfer. The other type of independent variable is non-skill characteristics of the golfers. Some of these have been studied in similar literature however not in the context of risk taking behavior.

Performance Variables

The empirical model mainly consists of variables that are characteristics of individual golfers based on their past performances. The following will explain more in depth how each of these variables are measured and their importance to the study.

The first two variables are carearnpga and recearnpga. They both represent the money a particular player has won only in official PGA Tour money winning events. These were included based on the theory that a dollar does not have the same value to everyone. For example, winning one thousand dollars would be much more beneficial for a poor college student, while Donald Trump may be more inclined to take a risk for more money because one thousand dollars is negligible compared to his enormous amount of wealth. Behavioral scientists criticized expected utility for lacking a reference point. The total earnings over

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ones career, represented by carearnpga, give one reference point. The recent earnings or recearnpga variable creates another reference point to observe. One of the main criticisms of expected utility was that two people both with $1 million may not necessarily approach risk the same way. One of these consumers might have recently had $2 million and lost half of his/her wealth while the other may have just gained $999,500 dollars. By including the golfer’s recent earnings year to date, another reference point is created that augments examination of risk taking behavior on the PGA Tour.

The following two variables are similar in the way they are measured to the previous two. Both recwinpga and carwinpga measure the wins of PGA golfers to add two more observable reference points. By addressing the same issues with expected utility as the winnings variables, measuring the total tournaments won and tournament wins in the ten prior tournaments to the examined contest will account for non-monetary incentives present in competitive sports. In competitive sport monetary reward is not the only incentive for performance. Not only does the glory and prestige of the win provide incentive, but wins on the PGA Tour (especially in certain tournaments) also help a player obtain automatic qualification for other events and points that go towards qualification. The variable carwinpga is a win percentage based on more than just the total number of wins; this is because a golfer that has played 20 years on the

PGA tour and won the same amount of tournaments as a golfer who has only been on tour 2 years will likely have different behavior. All of these incentives and the

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competitive nature of professional athletes provide possible characteristics for differing risk taking behaviors.

Another one of these incentives that will be examined is the World Golf

Ranking of the player going into the tournament, represented in the model as wgr.

These rankings are of significance to golfers because the top fifty ranked players gain automatic qualifying to three of the four PGA Majors as well as the World

Golf Championship events. Also, these rankings are used as criteria for the Ryder

Cup and national teams. If a player is near the cut off line for one of these exemptions it can be expected that the incentive to take risk and improve will be increased as well as an incentive not to drop and possibly take less risk if they are one of the automatic qualifiers.

Lastly two dummy variables are performance related that are included in the empirical model. These are represented by CARMAJWIN and TOP50OFF.

The CARMAJWIN variable is a measure of if the player has won a major in their

PGA Tour career. Besides the larger monetary prize that comes with a major win it is a very prestigious honor to have won; many players measure their career against each other not by their career earnings but number of major titles. Similar to many debates in all athletics about great athletes, the number of championships is usually the deciding criteria. A player with or without a major win may be more or less likely to take risks to win rather than play it safe. The other dummy variable is TOP50OFF, a dummy variable that represents whether the player is one of the top 50 earners from sponsorships and endorsements. Similarly to the

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earnings variables, if a player is one of the top 50 off course earners then they will be more willing to risk on course earnings to move up and go for the win and more prize money.

Lastly is the variable thirdscore. This variable will aim to assess the changes in risk taking behavior with respect to how the golfer performs on the second to last day. The reason this is studied, and not the first two rounds, is because it has been shown that many golfers will play it safe the first two days to make the cut. By the third round the golfers start to get an idea where they are in the standings and maximized effort is expected.

All these variables, except arguably thirdscore, are affected by previous performances and will possibly affect decision making according to expected utility theory as well as current financial and sports economics risk taking literature.

Characteristic Variables

The last four variables are all characteristics of the individual players.

Three of the variables are all measurements of experience of the individual golfers. By examining age, careventsplayed, and yrsonpga the golfers could affect the risk taking behavior by being related to better or worse information. The variable careventsplayed was divided by years on the PGA to create a statistic that measures experience but does not correlate with other variables. With better information of risk taking and other factors that affect PGA Tour golf, one can

34

assume that the player will make different choices than a player with little or no experience.

The dummy variable MAJOR will account for the added pressure and incentive a major championship brings. One might expect the other variables to have different affects on risk taking behavior with a major championship at stake compared to regular PGA Tour events. Table 4.3 shows the predicted signs of the independent variables.

TABLE 4.3

EXPECTED SIGNS OF INDEPENDENT VARIABLES

Variable Abbrev. Expected Signs

(+)

(+)

(+)

(+)

(+)

(+)

(-)

(+)

(+)

(+)

(+)

(-)

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Dependent Variable

Other studies have measured risk-taking behaviors by scoring variance or standard deviation in professional golf. A similarity between these studies and the current one will be the dependent variable. To estimate risk behavior changes this study will compare the final round (4th round) score with the individual player’s average score for a single round throughout the year. The average score must also be adjusted to take into account weather, course difficulty, and other external factors that can differ from course to course and tournament to tournament. The

PGA uses a similar statistic to award the Vardon trophy for the lowest average adjusted score for a PGA Tour season. Initially the study was going to use the difference between third and fourth round but the problem this creates is if, for example, a player decides to play risky on both days the difference won’t be observable. The result of the risk taking behavior could be the same on both days in our example and it would tell us there was no risky behavior. By comparing it to the average scoring over an entire season we can identify if they play riskier or less risky than normal. Much like the scoring average statistic each course that was studied must be adjusted for difficulty and external effects so the fourth round scoring data can be interpreted correctly. For example, if a player shoots four shots lower than his average during bad weather one would assume he had to play riskier than if the same player shoots four shots lower than his average on

36

one of the easiest courses in fair weather. Using adjround4var as the dependent variable for data collected on each player’s scores for each tournament they play in (in which they reach the final rounds) allows the study to determine if there are any non-skill variables that effect risk taking behavior.

Data Adjustment

An important characteristic of the dependent variable is the adjustment made in line with the study first proposed by Shmanske (2007) and also used by

Baer. These studies adjust skill statistics and scoring statistics to account for both course and player field differences across tournaments. Each event is held at a different golf course of varying degrees of difficulty in different areas. The effect of different players in the field must also be adjusted, as some tournaments attract a much more skilled group of golfers than others. The PGA releases the adjusted scoring statistic for season long averages; this study used their numbers.

Estimation Procedure

The equation presented above takes the form of a multiple regression model. This study utilizes the estimation procedure of ordinary least squares

(OLS) regression to measure the effect of non-skill characteristic variables of

PGA Tour golfers on their risk taking behavior in the final round of a tournament.

OLS provides the best approximation of the relationship between two variables.

For the OLS to estimate coefficients that are unbiased and best fit, several

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assumptions must be made. These assumptions are as follows: no correlation of independent variables, homoscedasticity, and normally distributed error terms.

Adjustments must be made if any of the assumptions are not true.

Econometric Problems

The first results immediately led to four corrections from the original model. Four of the original variables were omitted because of correlation amongst variables. This study acknowledges that this leads to omitted variable bias, which will be addressed in the conclusion of this chapter. These variables were recwin, yrsontour, TOP50OFF and carearn. The variables that were omitted were not significant in the original regression or when regressed against the dependent variable by themselves. By leaving these out could affect the validity of the study; these variables were not as carefully selected as they should have been. There is no relevant research that uses these types of variables, so it was difficult to know if they would work or not in the model. After the model was adjusted it now contains no collinearity. The new model now is represented by equation 2.

(4.2)

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Second the model was tested for homoscedasticity (as opposed to heteroscedasticity). The White Test was used; if the White Test statistic is higher than the critical chi-square value, we must reject the null hypothesis of homoscedasticity. The model passed the White Test and therefore no problem with homoscedasticity was found.2

Normality of the error term is the last assumption that was tested using the

Jarcque-Bera statistic, which indicates whether normality poses a problem, or not.

If the JB stat is greater than the critical chi-square value of 5.99, then the error terms are not normally distributed. After adjusting the data for one observation that was an outlier (one of the players was not ranked in the WGR for several of the tournaments) the data passed the Jarcque-Bera test for normality with a chi- square value below 5.99. Additionally the residuals were plotted against a normal density and also suggest that normality is not an issue for the study.

Results: Ordinary Least Squares

After all adjustments were made to fix the model’s econometric problems the OLS regression was run, the results are reported in Table 4.4 below.

2 The returned White Test statistic was 57.75, which was much higher than the chi-square value 39

TABLE 4.4 OLS RESULTS FOR EQUATION 1

Dependent Variable: adjround4var

N=1719

Variable OLS Coefficient t-Statistic -12.43366 -6.74* -0.0146884 0.00

-0.0062362 -0.48

1.008939 3.82*

0.0017614 1.89

2.19E-07 2.40**

0.7986957 2.59**

0.182873 7.28*

-0.0102071 -0.77

R-Squared 0.0526

Adjusted R-Squared 0.0482

F-Statistic 11.87 t-statistics *indicates significance at the 1% confidence level **indicates significance at the 5% confidence level

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Half of the variables had significance at the 5% or 1% level while half did not. Two of the significant variables were the dummy variables CARMAJWIN, and MAJOR. CARMAJWIN measures if a player has won a major in his career or not, however the coefficient tells us that if the player has won a major championship his score in the fourth round will be only about seventh tenths of a stroke more than his adjusted average round score. This behavior makes sense, as a player who has won a major has most likely won quite a bit of money already in his career and made a name for himself by winning said championship, therefore more willing to risk moving down several spots if it means there is a chance of moving up. The variable MAJOR simply measured whether the tournament being observed was one of the major championships. It was significant at the 1% level and had just over a one-stroke increase on risk taking behavior. This makes sense and was expected because despite the larger risk of losing more money in a major by moving down, the prestige, large first prize, and off course implications of winning outweigh the risk.

The other two significant variables were recearnpga and thirdscore. At the 5% significance level recearnpga has the expected sign and therefore effect that expected utility theory would predict. A player who has won more money recently is more willing to take risks, although upon inspection of the small coefficient it seems that it would not affect the risk taking behavior by more than about one and a half strokes. Lastly thirdscore was significant at the 1% level and

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shows that if a player performs poorly in his third round he is more likely to take risks than a player who performs well in the same round. The coefficient is significantly large and could be capturing behavior of a golfer who did very poorly and therefore has little to lose by playing worse or the same. A player who shot a poor round but still is not far off the lead, however, would not be expected to face the same risk as the previously mentioned golfer, so this variable could be capturing the player who returns to playing less risky after playing risky in the third round and having a poor outcome. Additionally if the player plays abnormally well the third round he could be more inclined to take similar risks

(but not as many as the golfer who performed poorly) because they paid off in the previous round. Some of this variation could also be due to other factors such as confidence.

The other four variables are not significant although it is noteworthy that wgr is close to the 5% significance level. Possibly wgr would be significant if only studied for the top 100 spots on the World Golf Ranking as several of the younger golfers may feel that the difference between ranking 500 as opposed to

600 is not important.

The extremely low R-squared and adjusted R-squared are definitely important to note. Even though several of the variables were significant they explain very little of the variation between fourth round score and the players adjusted yearlong average score. This could suggest that a different functional form is more appropriate, or perhaps a different estimator. The scope and

42

resources of this study do not possess the resources to test these hypotheses.

Additionally as noted above there is a problem with omitted variable bias which was not fixed. If the independent variables are redundant then eliminating will fix mulitcollinearity, however it is not clear in this study that this is the case. If the variables are not redundant then valuable information may be omitted from the model. Again, proper econometric fixes were beyond the scope of the study. The

F-statistic for the regression was above the critical value and supports the validity of the model.

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CHAPTER V

CONCLUSION

This study examined whether risk-taking behavior of PGA Tour golfers could be explained by the economic theory of expected utility. The present study attempted to expand on previous golf research that mainly studies place in tournament and skill characteristics. While other studies have showed that risk- taking behavior is beneficial to professional golfers because of the prize distribution system used by the PGA, it was unclear if there are any observable variables that affect their risk taking behavior. With the wide variety of age, earnings, experience and skill on the PGA Tour one might expect the decision making process to be different between the different golfers.

Expected utility theory suggests that there will be a difference in risk taking behaviors for individuals with different characteristics. The low number of significant variables found and their small effect on total variation suggests that while PGA Tour golfers may exhibit some characteristics that change their risk- taking behavior it is not highly explained by the variables identified in this study.

This study suggests that contrary to previous mutual fund studies on risk taking behavior, such as Busse (2001), a golfers risk-taking behavior is effected very little or not at all by past performances. As suggested before in Chapter III, this could be simply because risk taking behavior is much easier to measure in the 44

financial sector as opposed to professional golf. Additionally, these fund managers have more time to assess past performance before actions are taken.

The significant variables that were found in the study are all based on either characteristics or performance of the tournament that is being played or the most recent tournaments. Any long term performance or characteristic variables in this study were not significant in effecting the risk taking behavior of golfers. This lack of long term perspective with respect to risk taking behavior and expected utility suggests that external variables, luck, and personality traits have a large role in risk taking behaviors of golfers and possibly consumers. These findings, if still holding true with econometric improvements suggested in the previous chapter, agree with the literature examined that there are other variables that have a large affect on risk taking behavior and effort of PGA Tour golfers. These variables either have not been identified, are very difficult to measure, or cannot be measured/accurately defined (for example variable representing luck). The lack of information and time spent assessing risky decisions of the average consumer more liken them to the behavior of golfers rather than mutual fund managers.

Some useful implications that can be taken from this study are that for PGA golfers the events that have happened in the most recent rounds and tournaments are the most useful in predicting behavior in the final round.

Future studies may include a ranking of risk taking behavior amongst

PGA golfers that could lead to more observable characteristics that effect said

45

behavior. Additionally a better measurement of risk taking behavior in the PGA could be a useful tool in not only golf but also other sports economics studies.

46

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