Stock Market of Students: Using Financial Models to Peer Into the Risk-Return Universe of College Admissions Officers

STOCK MARKET OF STUDENTS: USING FINANCIAL MODELS TO PEER INTO THE RISK-RETURN UNIVERSE OF COLLEGE ADMISSIONS OFFICERS

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

Logan Dahl

May 2012

STOCK MARKET OF STUDENTS: USING FINANCIAL MODELS TO PEER INTO THE RISK-RETURN UNIVERSE OF COLLEGE ADMISSIONS OFFICERS Logan Dahl

May 2012

Economics

Abstract

Operating a college is expensive, and the cost of attendance is rising higher every year, easily surpassing inflation. What if part of the cause of this rising cost is poor “investment” by admissions officers. Are they admitting people that they a priori know will not give back to the college after graduation? Using data provided by the advancement and admissions departments of Colorado College, this paper aims to identify whether students can be grouped into asset classes based on inherent characteristics, and whether those assets behave like stocks in the stock market (i.e. is there a risk-return relationship present). To do this, students from the past 40 years have been grouped according to their shared characteristics (race, sex, etc.). Each group has a mean expected per year donation, and a variance measurement from that mean. These risk and return values are plotted and a regression line is fitted to the groups.

KEYWORDS: (CAPM, Admissions, Donations)

TABLE OF CONTENTS

ABSTRACT ii

1 INTRODUCTION 1

2 LITERATURE REVIEW 5 2.1 Academia...... 6 2.2 Inherent Characteristics...... 10 2.2.1 Capital Asset Pricing Model (CAPM)……...... 12 2.2.1.1 Traditional CAPM...... 12 2.2.1.2 Multi-factor CAPM...... 14

3 THEORY 18 3.1 Mean-Variance Optimization………………………………………………. 18 3.2 Efficient Market Hypothesis……………………………………………….. 20 3.3 Traditional Single Factor CAPM…………………………………………... 21 3.3.1 Beta………………………………………………………………….... 24 3.4 Multi-factor CAPM…………………………………………………………. 27

4 DATA 29

5 METHODOLOGY 31

6 RESULTS 36

7 CONCLUSION 42

WORKS CONSULTED 45

LIST OF TABLES

4.1 Data Summary……………………………………………………………. 30

5.1 Asset Class Definitions…………………………………………………... 32

5.2 Skewness/Kurtosis Tests for Normality………………………………….. 35

LIST OF FIGURES

3.1 Securities Market Line of the CAPM……………………………………. 23

3.2 Capital Allocation Line of the CAPM…………………………………… 26

3.3 Capital Market Line of the CAPM……………………………………….. 27

5.1 Diminishing Marginal Diversifiable Risk………………………………... 34

5.2 Histogram of Residuals…………………………………………………... 35

6.1 Linear Regression Results Table…………………………………………. 37

6.2 Graph of Regression Line on Asset Classes……………………………... 37

6.3 Graph of Investment Weights……………………………………………. 39

6.4 Asset Classes with Highest Absolute Values of Residuals………………. 40

CHAPTER 1

INTRODUCTION

One of, if not the fundamental tenant of economics is that absolutely everything has a cost. Whether it is monetary or opportunity, any action has an associated price tag.

For the most part, humans internalize this fairly well, for instance, we would all agree that one should purchase an item before being able to use it, or that one should not store the entirety of their wealth under their mattress. In the former example, they would be stealing, in the latter, sub optimizing (which is like stealing time and/or money from oneself). Going along with this widely agreed upon idea that time is money and that everything has a cost in time, academics have spent a fair bit of time trying to find the associated costs and benefits of various activities. The most obvious is investment theory, but there are other more arcane topics. Investment theory here is meant to be the study of how to maximize the return on one’s investment in the stock and bond markets. However, why should this be so narrowly defined? We as humans invest much time and money in many other activities, yet we seemingly intentionally ignore the tradeoff aspects present. For example, the investment a college or university makes in its students.

Though most higher education institutions are non-profits in the US, they still require money from somewhere to finance themselves. Larger state schools can depend more on state and federal funding to cover the cost of providing their services, but

2 smaller private schools may not have that particular revenue stream available to them.

Instead, they must use their endowed funds, along with the tuition each student pays, to cover their expenses. The endowment of a school gains capital in two ways. One is that the endowment is invested in various marketable securities (stocks and bonds) which make an annual return. Treat it just like any other kind of invested funds an individual might have, the returns are reinvested into the corpus of the endowment. The second way the endowment makes money is through additional injections of capital from donors. Donors tend to be parents of students and alums, along with some charitable institutions.

There has been much research done on what kinds of investments to make in the market for various risk preferences and investment goals. There has also been some amount of research done at what compels people to give to charity and even more specifically, what makes alumni give back to their alma mater. These studies all look to provide advice to colleges and universities on what kinds of actions they can take during the student’s tenure to increase their likelihood of giving back once they graduate. While this is both useful and interesting, it assumes all the behavior of a donor is based on their experiences at the college. This is likely true to some degree, but what if the donor behavior is more ingrained in a person’s psyche than that. What if we can predict how much they will give before they even get to college? If so, a college looking to increase its endowment could use financial modeling techniques to optimize the “return” (the amount given back by a student) they receive from their student body. 3

While portfolio optimization is obviously not the stated goal of most higher learning institutions, as discussed earlier, ignoring the financial side of the college completely is short-sided and foolish. We live in a world of scarcity. Even if people do not feel comfortable changing admissions policy to maximize endowment growth, they should know what they are doing so that they may accurately price the tradeoff they are making. Without a modestly growing endowment, inflation would eventually overrun colleges’ operating budgets and no education would be provided. So there are two main questions posed by this study, one, can students be grouped into meaningful “asset classes” akin to securities in a stock market, and two, if so, what does the investing universe an admissions officer operates in look like in terms of return to the college.

To answer these questions, I will use data provided by Colorado College, a small private liberal arts college. This data includes the age, sex, race, test scores, and athletic status of thousands of graduates of the college. Note these are all inherent characteristics of individuals that they cannot change, rather than basing it on a questionnaire which students could game or lie on. An admissions officer at the college would have all of this information about a prospective student and therefore this analysis will have predictive power. With the data, students will be broken down into several different asset classes. For instance, Asian-American females with mid-range

SAT scores who were admitted to the college at 18 years old, who were not division 1 or 3 athletes. The data also has the amount each individual has given back to the college since graduating. Therefore each asset class will have a mean expected return, as well as variance away from that mean return. So now there are several assets, each with expected return and variance. These can be plotted on the relationship proposed 4 by the Capital Asset Pricing Model (CAPM), which asserts that for stocks, there is a positive relationship between the amount of risk taken (measured by variance) and the expected return one would need.

This paper is not intended to be an investor’s guide for admissions officers.

This is merely to test whether colleges face a similar environment to other areas of the world, like the stock market. And if so, how is it similar? How is it different? What can we learn from any relationship that is present? This is meant to be more descriptive than prescriptive. The portfolio balancing can be left up to the individual admissions officers as they wish.

CHAPTER 2

LITERATURE REVIEW

Because most colleges are non-profits, their activities, on the revenue side, are largely focused on soliciting donations. However this is ignoring (perhaps intentionally due to ethical concerns) an obvious fact: the college has a say in who becomes potential donors in the first place. So the question that is posed here is twofold, one, if the college were to choose students to admit based solely on inherent characteristics, what would that class look like, and two, what are admissions departments doing? Are they taking too much risk without an increased expected return?

To understand some of the choices made in the methodology of this paper, it is important to understand where the assumptions I make come from, and how they are justified. There should be two main sections to this literature review; one focusing on past research done into the financial value of students, and one focusing on the capital asset pricing model. Interestingly, upon researching the first topic, it appears as if no one has conducted a study like this before, to evaluate a student’s future expected donation value to a college or university. The explanation I find most likely is that these studies are carried out, but at an internal level within the college. Instead, published academic studies of the issue rest of models of philanthropy as reviewed in this section.

Academia

While there has not been much said on treating students as investments for the college, there has been a fair amount of research done on why people donate to various institutions. Advancement offices around the country would love to know where to best focus their efforts to maximize donations received, not only for the monetary benefit, but also the associated prestige; annual donation levels are often used in college rankings. 1 Because there is a breadth of research spanning many non-profits and organizations, we will be specifically focusing on the research done regarding donations to universities and colleges as this is the closest analog to treating students as an investment.

In order to model donative behavior, this branch of economics literature often use assumptions based on broader charitable giving theory. For instance, Rose-

Ackerman suspects that people spend money (“donate”) on public goods for the long- run benefit they personally will receive at a later time. 2 There is also the more commonly held idea in economics that people give charitably because it makes them feel good about themselves, and therefore donative behavior can be explained in the same terms as many other rational investments.3 To these people, there is no such thing as pure altruism, just very well hidden self-interest. Using these lines of reasoning present in the base literature, that there is no such thing as irrationality in giving, several

1 "Best Colleges," US News and World Report, http://colleges.usnews.rankingsandreviews.com/best- colleges/harvard-university-2155 (accessed 03/30, 2012).

2 Susan Rose-Ackerman, "Altruism, Nonprofits, and Economic Theory," Journal of Economic Literature 34, no. 2 (Jun., 1996)

3 James Andreoni, "Giving with Impure Altruism: Applications to Charity and Ricardian Equivalence," Journal of Political Economy 97, no. 6 (Dec., 1989) 7 authors look more closely at donations to colleges based on characteristics developed during a student’s tenure. We will take this line a further step and conjecture that perhaps there are ever baser reasons for an individual’s giving behavior.

Lara and Johnson explore what factors lead to alumni donations. 4 They found these variables to be statistically significant determinants of whether a person gives an annual gift or a major donation: alum’s distance from campus, income, age, marital status, number of relatives who have attended the college, participation in varsity sports, attainment of a doctoral degree, and participation in alumni events. In order to find this information, they used a model based on a modified demand function. They postulate that philanthropic giving is a function of an individual’s income, the cost of giving as defined by that individuals marginal tax rate at the federal level, and the variables mentioned earlier (among others). They then run these latter variables through

Heckman’s two-step estimation process to create a logistic probability function.

Heckman’s two-step estimation improves upon previous work in that it better incorporates data from individuals who have not given any amount of money to the college. This new function can then produce an estimated probability of an alumnus making either an annual donation or a large gift.

These results are intriguing for the purposes of this paper. As Lara and

Johnson’s paper may have been since used to more effectively target alumni for donation solicitations, it is unclear whether or not the admissions department has been

4 Christen Lara and Daniel K. N. Johnson, "The Anatomy of a Likely Donor: Econometric Evidence on Philanthropy to Higher Education" (Colorado College, 2008) 8 tacitly aware and/or concerned with this information all along. And in fact, I will be using a few of their variables in my own model: gender, age, and their sports affiliation.

Predating the work of Lara and Johnson, this paper has a similar purpose, evaluating what factors contribute to alumni donation at a particular liberal arts college

(Lafayette College). 5 Their data spans from 1986 to 1992 and was gathered using surveys at alumni reunions (which may skew the responses since it will likely under represent those who do not give back to the college and do not stay in contact with it).

They plug income, marital status, parental status, years since graduation, Greek affiliation, major, amount of involvement after graduation, higher educational attainment, sex, and the year of graduation into an ordinary least squares regression.

They found that most variables were statistically significant at the 95% confidence level, but the variables with the greatest magnitude were high income, years since graduating

(likely correlated with income), how involved students are with the college after graduation, and the unemployment rate of the general economy.

Cunningham and Carlena frame the issue in terms of the importance of donations in the prestige of the college. 6 When a college has higher donation rates, it can usually afford to offer more financial aid to qualified students that might otherwise have been priced out of attending the university. With that in mind, much like the other papers here, they are looking for what makes a person donate to a college. Their data set includes observations from around 400 public and private, two- and four-year

5 Thomas H. Bruggink and Kamran Siddiqui, "An Econometric Model of Alumni Giving: A Case Study for a Liberal Arts College," The American Economist 39, no. 2 (Fall, 1995)

6 Brendan M. Cunningham and Carlena K. Cochi-Ficano, "The Determinants of Donative Revenue Flows from Alumni of Higher Education: An Empirical Inquiry," The Journal of Human Resources 37, no. 3 (Summer, 2002) 9 universities and colleges over the span of several years. All of the explanatory variables use the values present in the year 1984. They run ordinary least squares regression on the data, including a 13 year time lag between the mean return of an individual student and the factors that contribute to their giving. Their model is:

(2.1)

The first term is a measure of high school achievement (using SAT scores as a proxy). The second term is a measure of how much value the school adds to a student

(based on student-faculty ratios, percentage of faculty with doctorates, etc.). The gamma term represents a measure of the alumni’s taste for giving, using the type of school (two year, four year, part of a larger university system, etc.) The sigma term represents the wage earning potential of alumni, if they on average have low paying jobs post-graduation, they are unlikely to give back in large numbers. The “endwps” term is a proxy measure for prestige of the college as seen by the endowment size divided by the number of students. The last term is merely the error term.

Using this model, they found that average high school achievement predicted strongly how much that individual would give to the college later in life. Their best explanation is that high school achievement correlates with collegiate achievement which then correlates to workplace success and therefore income. They also found that schools that only offer a four year program (like most liberal arts colleges) tend to receive statistically higher donations. One of the most interesting findings was the lack of evidence that solicitation efforts mattered in alumni donation levels. This refutes the assumptions present in other literature. Given how unintuitive and countervailing this 10 finding is it is unfortunate that the authors spend almost no time discussing it. If this is true, colleges could save much time and money by focusing on improving the experience of their students rather than soliciting them for donations after graduation.

For the purposes of Colorado College in particular, this paper is largely good news.

Schools with high-achieving student bodies, low student-faculty ratios, and a liberal arts bent tend to receive higher donations on average.

Lindahl and Winship also try to understand what factors can predict future giving. 7 Similar to Lara and Johnson, they make a distinction between small periodic donations and large one-time donations. Their data comes from Northwestern

University’s alumni database starting in 1970s to the early 1990s. They couple this data with geographic analysis of where likely donors should reside, the logic being that certain neighborhoods have higher wealth and are therefore more likely to donate. As for methodology, instead of the ordinary least square regression that several other papers used, here they use a logit analysis for both the large gift and annual giving models. This offers the benefit of being better able to predict rare events (a major gift to the college).

Inherent characteristics

While donation literature has thus far focused solely on giving behavior based on observed characteristics developed during or after college, there are other areas of academia that are not so squeamish as to focus on inherent characteristics. One of the more popular areas today is micro-finance. In micro-finance literature and practice, it is

7 Wesley E. Lindahl and Christopher Winship, "Predictive Models for Annual Fundraising and Major Gift Fundraising," Nonprofit Management and Leadership 3, no. 1 (1992) 11 a widely known fact that certain in-born factors make an individual a good or poor investment. For instance, women are seen as a much safer investment than men.8 They are statistically more likely to pay back their loans (have a better credit score), and are more likely to invest their loan in activities that pay dividends to their respective societies. All this based purely on their gender. Of course other considerations contribute to whether or not an individual receives a loan, but this one inherent characteristic is so correlated to credit rating that women are the vast majority of microloan recipients.

The insurance industry also judges individuals based on macro-level patterns in behavior. One does not get an individualized car insurance quote based on an interview about what kind of roads one has driven on in the past number of years. A quote is assigned to an individual based on certain inescapable and unalterable factors: age, sex,

(for young drivers) test scores, etc. And this is true not just for car insurance, but any kind. Lest unfairness be brought up as an argument against this scheme, there has been research done showing that categorization improves efficiency in the actuarial realm. 9

So while the practice of looking at base characteristics of a person to assign a value to them might be a new idea to charitable giving literature, the core principle has been in use for decades in other areas. The key is applying these financial and actuarial principles to students.

8 James C. Brau and Gary M. Woller, "Microfinance: A Comprehensive Review of the Existing Literature," Journal of Entrepreneurial Finance and Business Ventures 9, no. 1 (04, 2004)

9 Keith J. Crocker and Arthur Snow, "The Efficiency Effects of Categorical Discrimination in the Insurance Industry," Journal of Political Economy 94, no. 2 (Apr., 1986) 12

Capital Asset Pricing Model (CAPM)

Traditional CAPM

The capital asset pricing model was created in the mid 1960’s independently by both John Litner10 and William Sharpe11. Sharpe was slightly earlier in publishing and therefore is more widely credited with its invention. As described in the Theory section of this paper, the CAPM essentially provides a proof for investors that their required return on an investment increases as the non-diversifiable risk (Beta) of that stock increases, as well as a more general proof of the relationship between risk taken and reward received. Since its inception, the CAPM has become extremely popular in the financial world, by financial managers using it to calculate a hurdle rate of IRR and by amateur day-traders trying to maximize their portfolio’s return. However this popularity should not be taken as a sign of the CAPM’s accuracy.

In retrospect, it is almost astonishing how little attention the world of finance paid to risk before Sharpe came out with the CAPM in 1964. 12 Most models had been operating under conditions of perfect certainty.13 Sharpe was one of the first to really propose the concrete link between systematic risk and expected return. However this is not to say investors did not already behave this way. As is common in economic papers,

Sharpe was simply describing the mathematical relationship behind somewhat

10 John Lintner, "The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets," The Review of Economics and Statistics 47, no. 1 (Feb., 1965)

11 William F. Sharpe, "Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk," The Journal of Finance 19, no. 3 (Sep., 1964)

12 Ibid.

13 Ibid., 1. 13 commonsense behaviors. Sharpe uses systematic risk as the sole measurement of an individual stock's riskiness (called Beta). His real insight though was applying this idea to the concept of the broader market as a whole instead of at an individual level (which had been done recently before this paper). He builds on the work of Markowitz, Tobin, and Hicks to create a comprehensive model of how a rational investor would choose a basket of stocks to mean-variance optimize his return on his particular portfolio.

Almost from the beginning, the theoretical underpinnings of the CAPM were attacked by behavioral economists. They point out that the expected utility base from which the CAPM stems is largely false because people do not behave rationally in real life. Tverksy and Kaneman proposed in 1992 a different framework that would supplant expected utility, “cumulative prospect theory”. 14 If this is indeed a better way of explain individual’s behavior, then the CAPM is wrong by definition. There was also an argument made based on empirical grounds. Behavioral economists also noted that individuals tend to over and under value certain aspects of a company, such as its book-to-market ratio15. This indicates that investors are not rational, and therefore the

CAPM cannot predict their behavior. These theoretical criticisms had come about around the mid 1960s, but were largely ignored by CAPM proponents until the 1980s16.

14 Amos Tversky and Daniel Kahneman, "Advances in Prospect Theory: Cumulative Representation of Uncertainty," in Preference, Belief, Similarity: Selected Writings, ed. Amos Tversky: Edited by Eldar Shafir; A Bradford Book; Cambridge and London:; MIT Press, 2004) Levy, Haim. "The CAPM is Alive and Well: A Review and Synthesis." European Financial Management 16, no. 1 (01, 2010): 43-71.

15 Josef Lakonishok, Andrei Shleifer, and Robert W. Vishny, "Contrarian Investment, Extrapolation, and Risk," The Journal of Finance 49, no. 5 (Dec., 1994)

16 It is important to note that most of the criticism of the CAPM revolves around the measure Beta, which will not be used directly in this study. 14

Multi-factor CAPM

After several years of CAPM domination in theory and practice, empiricists began chipping away at this cool new model. Perhaps not surprisingly, such a simple model was found to be lacking in several ways beyond that of behavioral criticisms.

Empirical data analysis starting in the 1980s found a few large holes in the CAPM’s predictive power. Consistently, value stocks (stocks with high dividends, low price-to- book ratios, and low price/earnings ratios)17 and small market capitalization were performing above what they should (though this wasn’t obvious at the time, all that was known was that the CAPM had failed to predict observable behavior in the market).

This prompted the rise of the multi-factor Capital Asset Pricing Models. The idea was to find the key explanatory variables and their weights in order to adjust towards the empirical observations.

Fama and French describe why the original CAPM, proposed by Sharpe and others does not function correctly. 18 They come into the literature on a wave of evidence that the CAPM does not accurately predict market outcomes, especially in regards to the previous criticisms about small and value stocks. Their now famous argument is for a three-factor model that looks at not only Beta or market risk, but also a firm’s book-to-market equity and its market capitalization (shares outstanding x share price). This can be written as:

17 "Value Stock Definition," Investopedia.com, http://www.investopedia.com/terms/v/valuestock.asp#axzz1orlXIMAj2012).

18 Eugene F. Fama and Kenneth R. French, "Common Risk Factors in the Returns on Stocks and Bonds," Journal of Financial Economics 33, no. 1 (2, 1993)

(2.2)

This can be expressed as the expected excess return of a stock as a factor of the excess return on a broad market portfolio, the difference between the return on a portfolio of small stocks and the return on a portfolio of large stocks (SMB = small minus big), and the difference between the return on a portfolio of high-book-to-market stocks and the return on a portfolio of low-book-to-market stocks (HML = high minus low). While this new model is empirically more accurate than the traditional model, the authors admit there are still unexplained patterns outside this model’s predictive power.

Fama and French come back to the question unanswered in their 3-factor model.

19 Firm size and book-to-market equity are largely arbitrary indicators of some hidden economic reality. At that time, it was unclear what that factor (or factors) was. In this paper they propose that perhaps these two factors are two different ways of looking at the behavior of a firm’s earnings. At the end of the study, they uncover mixed results.

On the one hand, they find that these two factors seem to be pointing to profitability (or earnings for the company) as the main explanation of price variability. Because firm size and book-to-market equity ratios are correlated, predicted instability by an investor based on these factors will lower the firm’s stock price. Where they hit a stumbling block however, is connecting the price of the stock based on these factors to the earnings of the firm.

Another Fama and French paper in 2006 describing how the empirical evidence against the traditional, single-factor CAPM is even more damning than previously

19 Eugene F. Fama and Kenneth R. French, "Size and Book-to-Market Factors in Earnings and Returns," The Journal of Finance 50, no. 1 (Mar., 1995) 16 thought. 20 They review the “value premium problem” that has been identified in other empirical studies in the past. The value premium problem is the idea that stocks with high ratios of the book value of equity to the market value of equity (known as value stocks) have higher average returns (as measured in stock price) than stocks with low book-to-market ratios (known as growth stocks). (The value premium problem is well known to Warren Buffett21, as value stocks are largely how he made his fortune, according to him). They found that the CAPM relationship works nearly perfectly for the time period 1928-1963, explaining most of the variance seen, but then flips to being exactly wrong from then on. However even when it got it right, it got it wrong.

According to one of the main principles of the CAPM, all variance in Beta is compensated by expected return. However they find this to be empirically untrue for all time periods. This means that using the traditional CAPM, you would take too much risk for insufficient return.

Campell and Vuolteenaho argue that there are in fact different types of Beta, news about the market’s future cash flows, and news about the market’s future discount rate. 22 This study was prompted by the anomaly in empirical tests of the CAPM: value stocks and small market cap stocks have higher than average returns. Under the original CAPM, this is not explainable. The authors find that value stocks and small stocks have higher cash-flow Betas, what they call the “good” Beta. This means their

20 Eugene F. Fama and Kenneth R. French, "The Value Premium and the CAPM," The Journal of Finance 61, no. 5 (Oct., 2006)

21 “Warren Buffet: How He Does It.” Investopedia.com http://www.investopedia.com/articles/01/071801.asp#axzz1rC5OEVR

22 John Y. Campbell and Tuomo Vuolteenaho, "Bad Beta, Good Beta," The American Economic Review 94, no. 5 (Dec., 2004) 17 risk in a traditional CAPM is over-priced which would explain the anomalous results from previous studies. They also found that the “bad” Beta was tied to future discount rates. Other authors looked at the cross-sectional differences in returns for Japanese stocks. 23 They proposed four variables to explain this performance: earnings yield, size, book to market ratio, and cash flow yield. In further support of the “Good Beta, Bad

Beta” findings, they also found that cash flow yield was, along with book to market ratio, the most important explanatory variable (though all were statistically significant).

The literature from this point on seems to be a search for a more accurate measure of

Beta(s). As noted earlier, most of the discussion about the CAPM revolves around Beta, even though there are several other related aspects that are just as interesting and important. This paper will be using these related concepts and relationships instead of true Beta for reasons that will be explained later.

23 Louis K. C. Chan, Yasushi Hamao, and Josef Lakonishok, "Fundamentals and Stock Returns in Japan," The Journal of Finance 46, no. 5 (Dec., 1991)

CHAPTER 3

THEORY

The central aim of this paper is to determine whether admissions officers of colleges behave as though they are mean-variance optimizers, or if they behave in some other quantifiable pattern. In a sense, we are looking to see if students of a college are being treated as an investment in a financial portfolio, and the admissions officers as the portfolio manager. To see that, we must look at how students behave in a financial sense, but before that, a firm grounding in “true” portfolio management theory is a necessary first step.

As described in the literature review chapter, the charitable giving literature uses various kinds of probability functions to identify likely donors based on behaviors observed during an alumnus’ time at the college. Different authors use different specific models, but they are derived from a demand function based on consumer theory. While this kind of modeling would potentially work with the data set used in this paper, one of the goals of this study is to see whether students can be modeled as if they were assets in an investment portfolio. Therefore we will use a different model, described later, to produce numbers similar to probabilities of an individual giving back to their college.

Mean-variance Optimization

Mean-variance optimization of a portfolio of stocks and/or assets is the concept of holding stocks, assets, or investments in order to have the highest mean return with the lowest

variance. 1 Variance here is in the statistical sense, often measured in standard deviations away from a mean. Intuitively this makes sense, as no one would choose an investment that yielded 15% per year with a standard deviation of 10% over an investment yielding 15% per year with a standard deviation of 1%. This is the heart of the CAPM. There are two types of mean-variance optimization: single-period optimization and multi-period optimization.

Single-period optimization requires the expected return for each asset, the standard deviation of the asset, which is a measure of risk, and the correlation matrix between these assets.

2 With this information a single-period mean-variance optimization produces an efficient frontier which is the set of portfolios with expected-return greater than any other with the same or lesser risk, and lesser risk than any other with the same or greater return. There are several important assumptions we must make to use a single-period optimization. First, returns in different periods must be independent from one another. This means that the data gathered from time period has no effect on the data gathered from period . The second is that the returns of different periods are from a similar, if not the same, distribution. The final assumption is that the data used is representative of the true statistical population. The most obvious threat to this methodology is called mean reversion. Mean reversion occurs when a pattern noticed in the past might actually mean that future predictions are inaccurate. It is also true that for the statistical reasons the single-period algorithm will always overestimate the true long-term return of a portfolio.

The alternative to the single-period mean-variance optimization algorithm is the multi- period mean-variance optimization algorithm. While this would be more accurate in certain or

1 Harry Markowitz, "Portfolio Selection," The Journal of Finance 7, no. 1 (Mar., 1952)

2 "Mean-Variance Optimization," Efficient Solutions Inc., http://www.effisols.com/basics/MVO.htm2012). 20 even most instances, in this case it is impossible and would not yield much greater accuracy.

The impossibility comes from limitations in the data which will be discussed later, and the lack of increased accuracy comes from the stated goals of this study. If it were possible to carry out a multi-period optimization, it would produce an efficient frontier of assets that have the highest geometric mean return for the lowest amount of variance. While interesting, the goal of this paper is to determine whether students show the same risk-return relationship as normal stocks, not to create maximized portfolios of students. Not only is that unethical, it also assumes admissions officers are both willing and able to perform complex statistical analyses of incoming students and all prior students every year. This seems unlikely.

Efficient Market Hypothesis

Another important concept when talking about the capital asset pricing model is the efficient market hypothesis. The efficient market hypothesis states that there is no way for one particular investor to beat the system consistently. It states that stock prices are random and unpredictable and that current prices reflect all available information. This is a key point for the functioning of the capital asset pricing model and in fact a few of the big names in CAPM literature are also heavyweights in EMH literature.

There are several flavors of EMH, weak, semi-strong, and strong. 3 Weak-form posits that stock prices already reflect all information that can be derived by examining market trading data such as the history of past prices, trading volume, or changes in interest rates (this is also known as technical analysis). This information is widely available and extremely cheap, and

3 Zvi Bodie, Alex Kane, and Alan J. Marcus, Essentials of Investments, 8th ed.: McGraw-Hill Irwin, 2010); Stanley B. Block, Geoffrey A. Hirt, and Bartley R. Danielsen, Foundations of Financial Management, 13th ed.: McGraw- Hill Irwin, 2009)

21 therefore if any imbalance were to be discovered individual investors would immediately peck at the arbitrage until there is none left.4 Semi-strong form says that all publicly available information about the firm is accurately reflected in the price of the stock. This would include information about management or upcoming legal threats, not just price trends. Strong form says that all information, both public and private, is incorporated into an accurate price for the stock.

This means even insider information is worthless. In other words, any errors end up in the “error term” and are not persistent or predictable.

In the past 10 to 15 years EMH has come under attack by behavioral economists. While these criticisms are somewhat fair, they seem to miss the point. They use empirical studies looking at very specific instances in which EMH breaks down. While it is certainly true that few things fully support any flavor of the EMH, that does not mean it is an unreasonable assumption for a theoretical model. Many scholars still use it in their models with the idea that the details are wrong but the main point is correct. Some explanatory power is better than none, and as we shall see, for the purposes of this paper the holes found are not relevant.

Traditional Single Factor CAPM

The capital asset pricing model is largely an application of mean variance optimization. It plots different stocks or assets on a graph with the y-axis being return and the x-axis being non- diversifiable risk. The end result of this model is that as an investor takes on more risk, they

4 Burton G. Malkiel, "The Efficient Market Hypothesis and its Critics," The Journal of Economic Perspectives 17, no. 1 (Winter, 2003)

22 should demand a higher level of return in compensation. There are several assumptions (some grander than others) that we must make in order for the model to function correctly5:

1) No individual investor trading can affect prices by trading. i.e., there is perfect

competition.

2) All people have an identical holding period for the asset.

3) All investors have access to the same investments.

4) There are no taxes in this world.

5) Investors are rational, mean-variance optimizers

6) There are homogenous expectations among investors, meaning they all calculate the same

standard deviations, correlations, and expected returns.6

Mathematically, the CAPM relationship can be described as:

(3.1)

Where:

is the expected return of asset i.

is the “risk-free” rate. The rate of return an investor can gain risk free, generally a government bond rate.

is the Beta of the asset. This is the sensitivity of the asset in relation to the market as a whole.

5 Bodie, Kane, and Marcus, Essentials of Investments, 716; Block, Hirt, and Danielsen, Foundations of Financial Management

6 Bodie, Kane, and Marcus, Essentials of Investments 23

is the expected return of the market. This is the geometric mean of the returns of the historical market.

FIGURE 3.1

SECURITIES MARKET LINE OF THE CAPM

SOURCE: "Capital Asset Pricing Model." International Financial Risk Institute. http://riskinstitute.ch/00010673.htm2012).

The quantity is often called the risk premium, as this is simply the second term of equation one multiplied by the Beta of the asset.

This relationship is often called the Security Market Line (SML). Essentially the SML equation says that the expected return of asset i is equal to the rate at which you can invest risk free plus the sensitivity of asset i multiplied by how lucrative the market is. This equation is derived from an ordinary least squares regression which creates a (theoretically) upward sloping straight line starting from the risk-free rate. A linear regression is used because (at least in 24 theory) there should be a stock for any given level of risk. The SML is trying to get at the average risk taken by increasing an investor’s risk tolerance n%.

There are two types of risk proposed by the CAPM, systematic and non-systematic. Non- systematic is described as risk that can be diversified away. It is the risk inherent in holding an individual asset. Systematic risk (Beta) is the risk of being in the market at all. For instance, if an investor only owned stock in Johnson & Johnson, they would be subject not only to the risk of the market tanking, but also the risk of Johnson & Johnson failing for some reason particular to that company. On the other hand, if the same investor instead held stock in many unrelated companies, the investor would really only be subject to the risk of the market as a whole moving downward. Any one company in that portfolio failing now has a negligible impact on the performance of the portfolio. A rational investor, assuming they have the funds, would increase the number of individual assets they hold until non-systematic risk has approached zero for their portfolio as there is no benefit to diversifiable risk. Beta is systematic risk. This is the risk of being in the market at all, it cannot be diversified away. A rational investor will accept some level of Beta based on their own risk preferences and desired rate of return. Beta is what an investor has control over when managing a portfolio. They cannot control the market return; they cannot control the risk-free rate. All they can do is choose investments with different risk.

Beta

Beta is one of the key risk-return concepts proposed in the CAPM. It is defined mathematically as:

(3.2)

Where:

is the covariance between a stock and the market return

is the variance in the market return

This essentially means that Beta is a measure of sensitivity to market conditions. An asset or stock with a Beta equaling one moves with the market return. A stock with Beta < 1 moves less than the market return. And a stock with Beta > 1 moves more than the market return.

For instance, assume the risk-free rate is 0 and the market return is 10%. A stock with Beta = 1 would return 10%. A stock with Beta = .5 would return 5%, and a stock with Beta = 2 would return 20%. This example makes it seem like one should always invest in high Beta stocks, but substitute a negative number in for the market return and you will quickly see why becoming a millionaire is not quite that easy.

There are two other major lines proposed by modern portfolio theory and the CAPM.

The Capital Allocation Line (CAL) and the Capital Market Line (CML) seen in figures 3.2 and

3.3 (notice that all graphs plot risk on the x-axis and return on the y). The CAL’s slope is called the reward to variability ratio which means for any level of risk (in this case measured by variability), an investor can expect a certain level of return.7 The CAL plots this relationship for any portfolio mixture that includes a risk-free asset in the investing universe. The CML is a

7 "Capital Allocation Line," Investopedia.com, http://www.investopedia.com/terms/c/cal.asp2012).

26 special case of the CAL in which the portfolio being modeled is the market itself.8 The risk- return relationship is essentially the same.

FIGURE 3.2

THE CAPITAL ALLOCATION LINE OF THE CAPM

SOURCE: "Capital Allocation between a Risk-Free Asset and a Risky Asset." thismatter.com. http://thismatter.com/money/investments/capital-allocation.htm2012).

8 "Capital Market Line," Investopedia.com, http://www.investopedia.com/terms/c/cml.asp#axzz1qpPmLDoe2012). 27

FIGURE 3.3

THE CAPITAL MARKET LINE OF THE CAPM

SOURCE: "CML Plot." Wikipedia. http://en.wikipedia.org/wiki/File:CML-plot.PNG2012).

Multifactor Model CAPM

In response to the empirical faults found in the traditional CAPM9, several adjustments have been proposed in an effort to have the model fit empirical reality (which is reasonably does, explaining an additional 20% of the results from testing)10. The most famous is the Fama and

French three-factor model which was mentioned earlier in the literature review. The model

9 For instance, there have been a few papers that have found downward sloping SMLs, which would disprove the relationship proposed by the CAPM

10 Eugene F. Fama and Kenneth R. French, "Common Risk Factors in the Returns on Stocks and Bonds," Journal of Financial Economics 33, no. 1 (2, 1993). 28 proposed adds, along with the traditional model, book-to-market ratio and company size values.

Mathematically it is expressed as:

(3.3)

Where:

SMB is the value of the excess return that companies with small market capitalizations get over large companies historically

is a value based on a linear regression run on the SMB data

HML is the value of the excess return that value stocks get over growth stocks historically

is a value based on a linear regression run on the HML data

All of these equations are defining certain instances of a risk-return relationship. For any of these, as an investor takes more risk, they should expect more return. For the purposes of this paper, the general relationship between risk and return set out by all three ideas (SML, CAL, and

CML) is what is important, rather than the exact definition of individual coefficients.

CHAPTER 4

DATA

Colorado College keeps track of several metrics for each student that is enrolled. The data was provided by both the Advancement Office of Colorado College, as well as the

Registrar’s Office. The data used in this analysis includes ~17,000 alumni’s sex, race, athletic status, composite SAT scores, year of birth and year of graduation. The data also includes the number of donations an individual has made since graduation, along with the total amount donated. Dividing this total amount by the number of times given creates a new variable which is the mean expected return of a person to the college per year after graduation. Each person’s data is tied to an indentifying number so that there is no way to determine who any individual data point is or was. The data cover individuals from the class of 1963 on, though most data fall within the range of 1973-2011. Summary statistics of the data have been provided on the next page in figure 4.1.

There are several limitations to do the data. Some portion of the metrics are unreported.

For instance there is a significant segment of the data that does not have a year of graduation listed, or no race assigned, or no composite SAT scores. While not completely damning, in an optimal world all alumni would have full data available. For the purposes of analysis, blank entries are treated as their own dummy variable and therefore do not throw off the analysis of reported metrics. For instance, an unreported SAT score is not treated as “0”, it is treated as unreported. Another issue is that the data does not record the specific year a donation was made

30 for each individual, just the totals. Therefore the amounts given cannot be discounted to present value. This means that temporal comparisons become less accurate, though not meaningless.

TABLE 4.1

DATA SUMMARY

By Variable Gender Male 47% Female 53%

Race White 85% African-American 2% Hispanic 5% Asian-American 3% Native American 1% Other/Not Reported 4%

Athletics Athletes 26%

SAT Scores Mean SAT Score 1178 Min SAT 500 Max SAT 1600 SD of SAT 149

Age Young 2% Normal 81% Old 4% Unreported 13%

Expected Return

Mean ER $ 420.12

Median ER $ 2.58 SD of ER $ 3,953.79 CHAPTER 5

METHODOLOGY

To see what the investing universe of an admissions officer looks like, there need to be assets defined by a mean expected return and a variance on that return. Then those classes will be plotted on a graph with variance (risk) as the independent variable and expected return as the dependent variable. After they are plotted, an ordinary least squares regression will be run on the plotted classes. The slope of the computed line will describe the relationship between risk and return for different types of students. The final product will be a plot of all the asset classes and a bastardized security market line. Because a true SML requires Beta, and Beta requires knowledge of the market at large (which is not available in this case), we will instead be using an equation that presents the same risk-return relationship, but in a slightly different form. It will more closely resemble a Capital Market Line or Capital Allocation Line, though again, there will be subtle differences because of the lack of general market knowledge.

The data gathered is completely on an individual level, each person has a certain observed SAT score, race, age, etc. To provide any predictive power, we must group students into certain asset classes based on certain characteristics. Previous studies mentioned in the literature review look at what the students did during their time at college. This is interesting, but from an admissions officer’s perspective, that information will be available too late to have an impact. They have already either accepted or rejected the student’s application. Therefore

32 this study intentionally only categorizes assets based on inherent characteristics that cannot be changed.

TABLE 5.1

ASSET CLASS DEFINITIONS

Gender Male Female African- Asian- Native Other/Not Race White American Hispanic American American Reported Athletics Athlete Non-athlete SAT 800- Scores 0-799 800-1600 1000* 1001-1200* 1201-1400* 1401-1600* Age 0-16 17-22 23+ Not Reported

*For four asset classes, because of the disproportionately large number of students that fell into them, composite SAT scores were further broken down from 800 and above into 800-1000,

1001-1200, 1201-1400, and 1401-1600.

The five variables listed in Figure 5.1 and their associated “buckets” (e.g. male/female, old, etc.) were put into a table where each unique combination was defined. For example, this table defines Class 1 as any students who are white, male, non-athletes, with SAT scores below

800, who were admitted before they were 17 years old. Class 2 is white, female, non-athletes, with SAT scores below 800, who were admitted before they were 17 years old. In the end there were 300 classes defined in such a way.

After the classes were defined, a count was taken as to how many students in the data actually fell into each asset class. The ultimate goal is to plot these assets on the CAPM graph

(risk vs. return), therefore we should recall the discussion earlier about systematic and unsystematic risk. Because of the concept of unsystematic risk (defined in the Theory chapter), 33 if an asset class with just one observed individual were plotted, risk associated with that individual would corrupt the analysis, as there is too much noise in any one stock. Current research on what number of stocks is required before unsystematic risk is neutralized says that around 10-20 stocks are an adequate number. 1 For the sake of carefulness, the cutoff chosen for this analysis was only groups with 22 observations or more would be included. At this point there are several asset classes, all with 22 or more individuals present in them. Using the associated expected return variable tied to each person, an average expected return was created along with a standard deviation, for each asset class. Once we have several asset classes, each with their own associated expected return and stand deviation, we can plot them like we would a stock on a risk-return graph.

1 "What is the Ideal Number of Stocks to have in a Portfolio?," Investopedia.com, http://www.investopedia.com/ask/answers/05/optimalportfoliosize.asp#axzz1pg1KGr2m2012). 34

FIGURE 5.1

DIMINISHING MARGINAL DIVERSIFIABLE RISK

SOURCE: Sutton, Andy. "Portfolio Diversification and Risk: The Basics of Beta." Seeking Alpha. http://seekingalpha.com/article/151352-portfolio-diversification-and-risk-the-basics- of-beta2012).

After the data were plotted, an ordinary least squares regression was run on them. In the first few trials of this plotting, it became clear that there were a few outliers in the data pulling their respective asset classes extremely off-trend. There was severe skewness and kurtosis on the predicted residuals, indicating non-normality of the underlying data. Upon further review, it became apparent that eight individuals from various asset classes who had given exceptionally 35 large donations were skewing the average expected return and standard deviation measurements.

Because these eight outliers had not fallen into one particular asset class, it was deemed acceptable to cut them out of the analysis. Once that was done, normality tests on the residuals from the regression line approached normality in terms of skewness. Though skewness was fixed, kurtosis was still present in the residuals. Despite our best efforts, that persisted.

However, when plotting the frequency of the residuals in a histogram, they tend to be clustered in the middle (see Figure 5.2, below). This is less damning than fat-tailed kurtosis because this essentially means there are numerous small errors rather than several large ones. This is still not ideal, but without a different data set it does not appear to be fixable.

TABLE 5.2

SKEWNESS/KURTOSIS TESTS FOR NORMALITY

Joint Variable Obs Pr(Skewness) Pr(Kurtosis) adj chi2(2) Prob>chi2 res 66 0.1185 0.0064 8.57 0.0137

FIGURE 5.2

HISTOGRAM OF RESIDUALS

Histogram of Residuals

60 40 20 0 Frequency <-326 [-325, - [-237, - [-150, -63] [-62, 24] [25, 112] [113, 199] [200, 287] >287 238] 151] Bin

CHAPTER 6

RESULTS

The goal of understanding whether students can be grouped into asset classes was answered in the methodology chapter (they can), the other goal, understanding what the investing universe an admissions officer at Colorado College faces can be seen by regressing the expected return of the asset classes against their standard deviation. The results of a linear regression on the data are included in figure 6.1. Both the F- and t-statistics for the regression indicate that it is indeed highly statistically significant at the 95% confidence level. Those values can be interpreted as the probability that the data would occur like this if there was no relationship between risk and return (in this case, zero). The R-squared value indicates what percentage of observed behavior in the data can be explained by the variables plotted. Here it is roughly 86%. Be careful to note however, that this does not mean 86% of a return to the college is based on the age, sex, athletic status, race, and SAT scores variables. It simply means that risk alone can explain 86% of the observed behavior of expected return. This is still a very interesting conclusion, but it is important to understand what was proved in this analysis.

FIGURE 6.1

. collapse (mean) er (LINEARsd) sd (REGRESSIONcount) count, RESU by (wLTShat _TABLEclass) . regress er sd if count>21, robust

Linear regression Number of obs = 66 F( 1, 64) = 106.61 Prob > F = 0.0000 R-squared = 0.8657 Root MSE = 123.02

Robust er Coef. Std. Err. t P>|t| [95% Conf. Interval]

sd .1363571 .0132063 10.33 0.000 .1099745 .1627396 _cons 56.55979 14.39531 3.93 0.000 27.80185 85.31773

. predict res if count>21, stdp (139 missing values generated) FIGURE 6.2 . sktest res GRAPH OF REGRESSION LINE ON ASSET CLASSES Skewness/Kurtosis tests for Normality joint Variable Obs Pr(Skewness) Pr(Kurtosis) adj chi2(2) Prob>chi2 Expected Return vs. Standard Deviation res 66 0.0000 0.0000 38.60 0.0000 1600 . plot er sd if count>21 y = 0.1364x + 56.56

1400 1507 + 1200 | * 1000 | | 800 | | * ( 600 | * m 400 |

$ in Return Expected e | a 200 | * n | * ) 0 | * * * |0 2 4 6 * 8 10 12 e | ** * Thousands r | * | * * * | * * Standard Deviation of Each Class | ** * * | ** * ** * | *** .0001Figure53 + * 6.2* is the regression line plotted with all of the asset classes with over 21 students +------+ incorporated. . 0 This0052 confirms2 the CAPM relationship (sd) s thatd is present in the stock market; 10217. the2 more risk. p roneedi takes,ct re thes2 imoref co expectedunt>21, returnr one can expect. While at first this may not seem very (139 missing values generated) exciting,. sktes tit isre nots2 at all obvious that students treated as assets should behave this way. There is a Skewness/Kurtosis tests for Normality joint Variable Obs Pr(Skewness) Pr(Kurtosis) adj chi2(2) Prob>chi2

res2 66 0.1185 0.0064 8.57 0.0137 38 conceivable universe where the SML, CAL, and/or CML would have negative slopes and therefore the college, as a mean-variance optimizer, should charge a high fee during attendance and expect no donations after the student has graduated. Despite what we might like to think about how colleges and universities are different from the more brutish world of business, it seems college officials face similar tradeoffs to hedge fund managers.

The regression line y= 0.1364x + 56.56 is the close approximation of the CAL, CML, and

SML. Based on the equations present in the CAPM, $56.56 can be interpreted as the risk-free rate of investment. For a college which is deciding who to admit or not, it is not immediately obvious what this risk-free rate would be. In this scenario, it would be a return for the college of

$56.56 where the risk of not getting that amount is zero. That means it is a fee. To get the risk- free rate, Colorado College could simply charge students a $56.56 “graduation fee” or something akin to that. The coefficient of the x term is a measure of return per unit of risk (here it is standard deviation). For each dollar of standard deviation one accepts, they can expect a return of $0.16 as well as the $56.56.

This line, while slightly different from that in the literature, accomplishes a similar goal to the CAL or CML. Any asset class that is above the line should be invested in, as it has above average returns for its level of risk. Conversely any asset class that falls below the line should be divested, or in this case, not admitted to the college. Below, in Figure 6.3, each asset class has been plotted with a graduated sphere representing the amount of students in each class. Below figure 6.3 is a graph of the eight asset classes with the furthest distance from the line (positive and negative). The top four highest classes indicate the “best” investment in terms of risk- reward ratios, and the bottom four represent the four worst classes. The numbers above the bars are the asset class identifying number. 39

FIGURE 6.3

GRAPH OF INVESTMENT WEIGHTS

FIGURE 6.4

ASSET CLASSES WITH HIGHEST ABSOLUTE VALUES OF RESIDUALS

Best and Worst Investments 500 293 400 294 184 300 13 200 100 0

Residual Value Residual -100 -200 171 -300 80 -400 298 286 Asset Class

The top four “over-performing” classes are: Class 293 which are white male athletes with

SAT scores between 800 and 999 who were admitted at a “normal” age as defined earlier. Class

294 are the same except they had SAT scores between 1000 and 1199. Class 184 are African-

American female non-athletes with unreported SAT scores admitted at a normal age. Class 13 are white female athletes with SAT scores above 800 who were admitted when they were younger than 18. By virtue of these being the most over-performing classes, these are the people that give a disproportionate amount compared to other types of people. The one trend that seems to be present is that athletes appear to donate with high variance. It is also interesting given what was seen in the literature review, that high SAT scores don’t seem to correlate considering the highest performing asset class had pretty mediocre scores. Class 13, the African-American females without reported SAT scores raises many questions. By not reporting test scores, we can assume they did not take the test, or did poorly enough that they chose not to submit it (assuming 41 anyone who did what they considered well would submit their scores). It is unclear what can be gleaned from this, but it provides good opportunity for further study.

Conversely, the bottom four “under-performing” classes are: Class 286 which are white female non-athletes with SAT scores between 1000 and 1199 admitted at a normal age. Class

298 which are white female athletes with SAT scores between 1000 and 1199 admitted at a normal age. Class 80 which are unreported ethnicity male non-athletes with SAT scores above

800 admitted at a normal age. And Class 171 which are white female athletes with unreported

SAT scores admitted at a normal age. The prevalence of white females in this group perhaps can be explained by the idea that women historically have made less income than men. As seen in the literature review, income has been found to have a large effect on donative behavior. Further research will be needed to decide whether this is purely an historical aberration, a product of odd data, or if there is some deeper cause. For the purposes of this paper, they are merely mentioned as interesting points, and perhaps more data for the Advancement office’s hunt for more donations. CHAPTER 7

CONCLUSION

Coupling admissions data and advancement data from Colorado College, we grouped former students into pseudo-asset classes based on their inherent characteristics. Each asset has its own expected return and standard deviation. After removing a few outliers from the data, a linear regression of the asset classes respective expected returns versus their stand deviations produced a graph showing a similar risk-return relationship to what an investor faces when choosing to invest in normal stocks and bonds.

If a Colorado College admissions officer wished to maximize the endowment return based solely on whom they admit, given information widely available to them, they would face a similar choice to a mutual fund manager. The no free lunch policy of economics holds true even for non-profits and academics. Prospective students, based solely on inherent characteristics, have an average expected return to the college in terms of donations after they graduate, and this value goes up as the variance of the amount donated increases. In the introduction, we asked two questions, can students be grouped into meaningful categories that act like marketable securities, and if so, what does that “stock market” look like? We have found that yes, students can and do behave like stocks, not only in their definition, but in their behavior. The relationship found between risk and return for defined student asset classes was extremely analogous to the relationship posited for stocks in the Capital Asset Pricing Model. This is a very positive result in a normative sense. It means, assuming rationality on the part of admissions officers, that there

43 are hard returns to diversity at Colorado College. With a positive relationship between risk and return, there is no reason to completely drop most asset classes. As for the classes that were discussed as under-performing, they should perhaps be the targets for further advancement office initiatives, using the work of studies like Lara and Johnson and others to help bring up the return of those individuals.

There are several areas in this study that have the potential to introduce error. There could be problems with the underlying data, mainly from input error or people misrepresenting themselves to the college (lying about their race, age, etc.) If this occurred, it could mean certain individuals are mis-categorized and therefore the associated expected return and standard deviations are off. There is also the problem mention in the literature review that the CAPM has been somewhat discredited, at least simplistic, single term model which we are approximating.

However, because we only approximate a CAL or CML, most of the criticism of the CAPM is not relevant as it mainly focuses on how the CAPM does not empirically fit the data. Whereas here we have created the CAPM relationship from the data. So while there may be valid charges of the coefficients being wrong when further research on this topic is done, it does not contradict the main point of this study, namely that there is a positive relationship between risk and return when treating students as assets.

This study has opened the door for many more subsequent inquiries. Now that we know there is a positive relationship between risk and return for Colorado College alumni, does that hold true for other private colleges? What about public universities? Why is this relationship true? Is one characteristic of a person more important than another? Knowing that would allow an approximation of the multi-factor model CAL or CML. With more studies from individual colleges, we could eventually create a market return factor and actually use the security market 44 line as written, as well as calculate the true Beta for any one asset class of students. If we could somehow model the risk preferences of admissions officers or colleges, we could then create truly optimal student portfolios. There also appears to be a pattern in the regression results. In

Figure 6.2, there seem to be three somewhat distinct clumps of points. There is no obvious reason for this, but perhaps a more in-depth mathematical analysis of the results would shed light on this pattern if there indeed is one.

This paper has barely scratched the surface of what could be a very useful set of work.

With more data or creative thinking, there are many further studies that could be carried out. For now we can content ourselves that even using a dehumanizing framework, we find that Colorado

College does not have to make a tradeoff between diversity and endowment performance, at least when it comes to admitting students.

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