Don’t Put All Of Your Alums In One Basket: College Admissions Decisions As A Portfolio Choice Problem
Logan Dahl
Colorado College – Department of Economics and Business
Daniel K. N. Johnson
Colorado College – Department of Economics and Business
July 9, 2016
Colorado College Working Paper 2016-02
Abstract:
We consider philanthropy by college alums from an innovative and provocative perspective: what if prospective college students were considered members of assets classes with different risk-return combinations? Using forty years of merged admissions-philanthropy records on students at a highly selective liberal arts college, we estimate the simple financial model that this allegory implies. We find benefits to diversification, identify the slope of the market risk-return line, and point out the most (and least) attractive potential students in terms of their projected future donations.
Don’t Put All Of Your Alums In One Basket: College Admissions Decisions As A Portfolio Choice Problem – Introduction
Alumni giving has become increasingly important for institutions of higher education, accounting for roughly fifteen percent of all private funding for higher education, or roughly $4 billion (Council for Aid to Education, 2012). Even as alumni giving has been rising (Kaplan, 2007), the participation rate of alumni giving back to their alma mater has been falling, while those who donate choose to contribute larger amounts (Engagement Strategies Group, 2010). Given this dynamic, there is enormous value in finding the right potential donors; it is unsurprising that academic models and consulting companies have tackled the question with fervor.
This paper models alumni giving from a unique perspective, treating college admissions decisions as a portfolio choice problem, where prospective students are members of asset classes with rates of risk and return measured a priori by the propensity of each asset class to subsequently donate to their institution. While we do not suggest that admissions decisions are (or should be) made in this manner, we reflect on the implications of a simple Capital Asset Pricing Model (CAPM) framework using data provided by a selective liberal arts college.
Academic research clearly describes patterns in alumni giving (e.g. Bruggink and Siddiqui,1995; Okunade et al., 1994; Wunnava and Lauze, 2001), identifying descriptive variables that predict philanthropy (Lara and Johnson, 2014; Meer, 2011; Meer and Rosen, 2007; Clotfelter, 2003; Monks, 2003; Cunningham and Cochi?Ficano, 2002; Forbes and Zampelli, 1997; Lindahl and Winship, 1992). Obvious demographic variables such as age, gender, ethnicity, and marital status have been shown to have predictive power, as have activities while in school (major, involvement in college sports, GPA, affiliation with a fraternity or sorority, certain kinds of financial aid) and post?graduation factors (time since graduation, number of relatives at one’s alma mater, reunion years, willingness to share contact information with the college, response to college surveys, highest degree attained, participation in student government, induction into honorary societies, participation in alumni activities).
In contrast, no study has proposed a predictive model based purely on factors known before the student enters higher education. Unlike the literature, our intention is not to explain or predict alumni giving, but to create asset classes of potential students based on characteristics observable among prospective students at least 5 years before they have the ability to donate as an alum.
Method
We use only five variables to categorize individuals, all self?identified on 17,000 admissions applications to Colorado College between 1963 and 2011: gender, race, athletic participation, SAT scores, and age. These were merged with total donations by each individual made to date, as summarized in Table 1. Notice that the entire population is fairly homogeneous in race and age, but has some variation in gender, athletics and SAT scores. Also notice that donations, or expected returns, represent an extremely skewed distribution with a median donation below three dollars and an average above four hundred dollars.
There are several limitations in the data, including missing values for a small subset which we assume to be randomly distributed. Frustratingly, the records do not record the amount of each donation, but simply the total over time, so do not permit detailed analysis of time paths or even time?discounted values of total donations.
Treating each prospective student as a stock, we built asset classes to plot on a risk?return graph; the slope of the computed “line of best fit” will describe the relationship between risk and return for different asset classes. That fitted line will not be a true Security Market Line or Capital Allocation Line, due to a lack of overall market knowledge to inform the value of beta (Sharpe, 1964). While we are fully aware of the limitations of the CAPM model for predicting investor behavior (e.g. Fama and French, 1995; Fama and French, 2006; Campbell and Vuolteenaho, 2004), our goal here is not to predict or even to recommend investment?type decisions but merely to explore the parallel between financial assets and alums as potential investments using the traditional CAPM risk?return relationship.
To create mutually exclusive and exhaustive asset classes, we divided continuous variables into categories: SAT scores (0?800; 801?1000; 1001?1200; 1201?1400; 1401?1600) and age (0?16; 17?22; 23?99; not reported). For groups that had too few members, we aggregated SAT scores into two categories (0?800; 801?1600) to create larger groups. We ultimately evaluate 300 separate asset classes, each representing twenty or more individuals.
In preliminary data exploration, we discovered that eight individuals in our dataset were major donors, and their presence determined all subsequent tests and results. We elected to omit them from consideration as they spanned many asset categories but clearly masked the underlying pattern in the remaining 16, 992 observations.
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