Optimization routines for endowment

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THE JOURNALOF PORTFOLIO MANAGEMENT 109 FALL 2014

Donation Risk and Optimal

Endowment Portfolio Allocations

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LANCHETT DAVID BLANCHETT is head of retirement research at Morningstar Investment Management in Chicago, IL. david.blanchett@morningstar. com

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ptimization routines for endow-ment portfolios commonly focus on the risk characteristics of the opportunity set of investable financial assets and ignore the risks of the other assets owned by the charity, such as real estate, donation revenue, and program service fees. The value of these other assets signifi-cantly exceeds the value of the endowment for most charities; therefore, ignoring these other assets cannot result in a truly efficient portfolio for the endowment. This article takes a total wealth perspective on port-folio optimization, where the endowment is used as a completion portfolio to minimize the funding volatility for the charity.

For the analysis, the revenue for the char-itable organization is assumed to be composed entirely of endowment income and charitable donations. Including the volatility of donation revenue for charitable organizations, referred to as donation risk, in the optimization rou-tine results in a more efficient allocation for the endowment because there are statistically significant relationships between donation risk and different asset classes and risk fac-tors. For example, 54% of the variation in the historical change in charitable donations made by individuals can be explained using a seven-factor model that includes the original five Fama–French factors plus momentum and liquidity. This relation is especially note-worthy because individuals have historically

made approximately 80% of all charitable donations in the United States.

Through a series of portfolio optimi-zations, it is demonstrated that the optimal allocation for an endowment varies materially depending on different types of donation risk, varying levels of risk aversion, and the per-centage of total income of the charitable orga-nization funded by the endowment. Charities with riskier donation revenue should likely have less aggressive portfolios, and vice versa. Even after holding the equity allocation con-stant for the optimization routine, the average absolute difference in optimal asset class weights varied by more than 25% on average when compared to either a portfolio that did not incorporate donation risk or the average portfolio that did. These findings suggest that narrowly focused endowment optimization routines that ignore donation risk are insuf-ficient, and that a holistic definition of wealth is necessary to build a truly efficient endow-ment portfolio for a charitable organization.

A TOTAL WEALTH PERSPECTIVE

When determining the optimal weight for different asset classes in a portfolio, most investment professionals focus entirely on the risk and return characteristics of the opportu-nity set of investable financial assets, such as cash, bonds, stocks, and so forth. This per-spective ignores the other assets owned by that

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110 DONATION RISKAND OPTIMAL ENDOWMENT PORTFOLIO ALLOCATIONS FALL 2014 investor and the unique risk factors associated with each.

These other risks are commonly referred to as background risks and include things like human capital and real estate for an individual investor (or household) and donations and program service revenue for a charity.

Ignoring background risks when building a portfolio effectively assumes that background risks are irrelevant; that is, that the covariances between the background risks and the investable opportunity set are zero. However, if the covariances are not zero, the resulting portfolio allocation may not be truly efficient from a total wealth (that is, holistic) perspective. Cochrane [2007] specifi-cally notes that an investor with nontradeable assets should deviate from the market portfolio to the extent that he or she is different from everyone else. For the purposes of this analysis, those differences would be the varying levels of risk associated with different types of donation revenue.

Research on total wealth optimization is primarily focused on households, where the goal is to incorporate nontradeable assets like human capital into the portfolio decision. The relative importance of human capital has been well documented; for example, Becker [1993] esti-mates the value of human capital to be at least four times as large as the value of stocks, bonds, housing and all other assets combined. Heaton and Lucas [2000] report that approximately 48% of household wealth is due to human capital, whereas only 7% is invested in finan-cial assets. Notable works exploring optimal lifecycle investing include Heaton and Lucas [2000]; Ibbotson et al. [2007]; and Cochrane [2014].

An alternative approach used to determine optimal allocations for portfolios that exist to fund specific lia-bilities is a process known as surplus optimization. Surplus optimization is an extension of the traditional Markowitz [1952] asset-only approach, where the optimizer is con-strained to hold a short position in a particular asset class (or combination of asset classes) representing the future liability. Important works on liability-relative investing include Siegel and Waring [2004] and Waring [2004]. Surplus optimization represents a definite improvement over traditional asset-only optimization approaches, yet it is also incomplete from a total wealth perspective because it focuses entirely on explicit funding risks and ignores the other background risks that may be present for an investor.

Dimmock [2012] performs an analysis—similar to the underlying goals of this article—in which he seeks

to determine the effects of background risk, defined as the volatility of universities’ nonfinancial income, on university endowment portfolios. Dimmock finds that universities with higher background risk should invest significantly more in fixed income and less in alterna-tives, even after controlling for many university charac-teristics. This is consistent with economic theory, which suggests investors endowed with exogenous nontradable risks should reduce their exposure to other sources of risk (for example, the equity weight in the endowment). To this point, Black [1976] has stated, “It is important to see the endowment fund as just one of the university’s sources of income … the relevant risk is the risk of all these sources of income taken together, not just the risk of the endowment fund itself.”

The total wealth optimization approach in this article is most similar to research by Blanchett and Straehl [2014], who incorporate assets such as industry-specific human capital, region-specific housing, and pension wealth into the portfolio decision process for an indi-vidual. Two key differences between this work and Blanchett and Straehl are that this article uses a different optimization routine, focusing on minimizing funding volatility versus total wealth volatility, and that this piece is geared toward charities, whereas Blanchett and Straehl focus on individuals.

DIFFERENT DIMENSIONS OF CHARITABLE WEALTH

An endowment is a pool of money or other financial assets that has been donated to an institution or charity. In many cases, restrictions or stipulations may exist on how the funds may be invested or spent. For the purposes of this analysis, the term endowment is used to describe a liquid pool of assets (for example, stocks and bonds) that can be used to fund the operations and activities of a given charitable organization. As of 2010, 186,417 different 501(c)(3) charitable organizations held a total of approximately $1.5 trillion in endowment like assets, according to data obtained from the IRS.1_{Although this} pool of assets is significant, it represents only a fraction of the other assets owned by charities, such as real estate, donation revenue, program service fees, and so forth.

Investable assets, that is, those assets designated as endowment assets for the purposes of this article, are approximately equal to the total value of all other nonfi-nancial assets owned by 501(c)(3) charitable organizations.

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Land, buildings, and equipment are the predominant nonfinancial asset type, representing approximately 60% of the total, with the remaining primarily being some type of receivable (for example, account receivable, note receivable, or loan receivable).

The amount and type of assets differ considerably by the type of charitable organization. For example, Sherlock and Gravelle [2009] note that when combined, health and education charities hold 69% of charitable assets (36% and 33%, respectively), whereas they repre-sent only 24% of charitable organizations filing a Form 990 (6% and 18%, respectively).

Charitable revenues consist primarily of donations, contributions, dues, and fees. Similar to the differences in assets, the form and type of revenue varies materially across charitable organizations. Larger charities tend to receive a greater portion of their funding from program service revenue,2_{whereas smaller charities tend to generate more} revenue from donations. For example, charities with less than $10 million in total assets receive approximately half of their revenue from donations and approximately half from program service revenue, whereas charities with assets greater than $10 million receive approximately 25% of their revenue from donations and approximately 75% from program service revenue.

Although the amount of revenue received by chari-ties is approximately equal to the endowment assets, this does not mean they have the same value. If this revenue is assumed to be the observable dividend of the revenue capital of the charity, a dividend growth model, such as the Gordon growth model, could be used to estimate the present value of the revenue capital. Using this approach, the total value of the revenue capital (RC) at a given time (t) can be estimated using Equation (1), where (r) is the amount of revenue, (d) is an appropriate discount rate, and (g) is the expected growth rate. Although the assumed discount rate and expected revenue grow rate would vary materially by charity, the revenue capital would likely be at least 10 times the revenue (r) generated by charity, which would imply that d_t – g_t is at most 10%.

RC r d g t t rr t gt = (1)

An alternative perspective that can be used to estimate the relative importance of charitable revenue would be to view it as income. Private foundations are required to pay out a portion of their assets, subject to

a minimum rate of 5%; however, the average payout is 7% according to Gravelle [2007]. Assuming a payout rate of 7% would imply that if the charitable revenues and endowment assets are equal (which they are in the aggre-gate), charitable revenues generate 14.28 times (1/7% = 14.28) more income by leveraging their assets (facilities, branding, and so forth.) than does the endowment by investing its financial assets.

In summary, the total wealth of a charity includes assets beyond just the endowment. Regardless of how charitable revenues are accounted for (either from an asset or income perspective), the effective value of the revenues is likely to be a materially larger asset than the endowment for most charitable organizations. In the following sections, the relations between changes in donations to charitable organizations (that is, dona-tion risk) and various asset classes are reviewed, as well as the potential impact of considering donation risk when determining the optimal asset allocation for endowment.

DONATION DATA

For the analysis, historical data on 11 types of char-itable donations is obtained from the Giving USA 2013 Annual Report on Philanthropy. The donations are grouped by source (that is, the entity making the dona-tion) or recipient (that is, the type of charity receiving it). The four charitable sources include: corporations (Corp), foundations (Fou), bequests (Beq), and indi-viduals (Ind). The six charitable recipients include: reli-gious charities (Reli); education charities (Edu); human services charities (Hum); health charities (Heal); public-society benefit charities (Public); and arts, culture, and humanities charities (Arts). The 11th donation amount is the total contributions, which is the sum of all dona-tions across all sources or recipients.

Exhibit 1 provides some perspective on the relative weights, as percentages of total donations, for the dif-ferent sources and recipients of charitable donations con-sidered for this analysis. In terms of sources, individuals have made, and continue to make, the vast majority of charitable contributions, constituting roughly 80% of all charitable donations over the entire historical period, although this figure dropped to 72.4% as of 2012. In terms of recipients, although religious organizations are, and have been, the largest recipients of donations, the percentage of donations received by religious charities

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112 DONATION RISKAND OPTIMAL ENDOWMENT PORTFOLIO ALLOCATIONS FALL 2014 has been declining. At their peak, donations to religious

charities were more than half of all donations (52.9% in 1987) yet were less than a third as of 2012 (32.11%).

Although donation data is available for additional charitable recipients, such as international affairs, the environment, and so forth, these other recipients do not have historical data going back to 1972, and are therefore excluded from the analysis. The excluded sources are noted as “Other” in the recipients Panel of Exhibit 1. The percentage of donations going to other recipients has been increasing over the historical period reviewed, with an average of 18.1% over the entire period and a value of 21.7% as of 2012.

Charitable donations have historically increased at a pace that is significantly faster than inf lation, although there has also been signif icantly higher volatility. Exhibit 2 includes historical attributes for the average change in donation behavior for the 11 donation types included in the analysis, along with general inf lation, as well as the correlation for each change in donation amount to inf lation over the historical test period.

Total charitable donations have increased by 11.5% per year, on average, versus 4.35% for inf lation from 1972 to 2012. The donor type with the highest average annual increase has been foundations (13.21%) whereas the smallest has been individuals (11.27%). The recipient with the greatest change in donations has been public-society charities (15.46%) whereas arts, culture, and humanities charities have seen the smallest increase, at 7.93%.

The correlation between annual changes in dona-tions and general inf lation has been relatively low (aver-aging 0.30), although it varies significantly by donation

type. Religious charities had a change in donations that had the highest correlation to inf lation (0.71) whereas arts, culture, and humanities had the lowest (−0.01).

INVESTABLE OPPORTUNITY SET

Fourteen different individual asset classes are included in the investable opportunity set for the anal-ysis: one cash asset class (cash), five bond asset classes (U.S. Intermediate-term bond, U.S. long-term bond, U.S. TIPS, U.S. high-yield bond, and non-U.S. bond), six equity asset classes (U.S. large growth, U.S. large value, U.S. small growth, U.S. small value, non-U.S. equity, and emerging markets), and two alternative asset classes (REITs and commodities). The opportunity set

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Percentage of Total Donations by Source and Recipient

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Historical Attributes for Average Annual Change in Donation Amounts

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is intentionally selected to ref lect the asset classes com-monly used by investment professionals when building portfolios for all clients, not necessarily endowments or foundations.

The index proxies, returns, and standard deviations of the assets classes included in the analysis are displayed in Exhibit 3. The historical return period for the analysis is from 1973 to 2012, for a total of 40 years, which is based on calendar year returns. Although inf lation is listed in Exhibit 3, it is not considered an investable asset for the analysis and is therefore included solely for informational purposes.

The nominal returns for the asset classes were rela-tively high over the historical test period. This is espe-cially true for cash and the fixed-income asset classes when compared to current bond yields and forward-looking return projections. For example, the average annual return on cash over the test period was 5.3%. This historical return is considerably higher than the yield currently available on three-month Treasury bills, which is less than 0.1% (as of January 2014). This histor-ical return of cash over the period (5.3%) is also signifi-cantly higher than the forecasted return of cash, which is 1.2% based on Ibbotson Associates’ 2013 20-year capital market assumptions.

ASSET CLASS CORRELATIONS

There is a potential benefit to a charitable orga-nization from considering background risks, that is,

donation risk, when determining the asset allocation for the endowment. This is in contrast to the vast majority of models used for endowment optimization, which generally ignore background risks and therefore effec-tively imply that all the correlations (or really covari-ances) between the returns of the investable asset classes and background risks are zero. Therefore, it is worth exploring the historical relations between changes in donations and the returns of the investable asset classes included in the analysis. These correlations are included in Exhibit 4.

The correlations between the historical changes in donations and test asset classes are not zero and are in many cases statistically significant. In Exhibit 4, 23.4% of the correlations were statistically significant at least at the 10% level. The correlations for 7 of the fourteen asset classes were significant at at least the 10% level for indi-vidual donors, which is important, given that roughly 80% of all donations are made by individuals.

The positive correlation between changes in dona-tions and the returns for the U.S. stock markets creates an interesting problem for charities because the largest holding in most endowments is generally U.S. equities. Ideally, the relation would be negative, whereby low stock market returns could be offset by higher dona-tion amounts; however, the opposite reladona-tion exists (that is, the correlation is positive). This creates a potential double whammy for charities, where low market returns are likely to be accompanied by lower donation revenue, as they were after the global financial crisis.

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Asset Classes, Proxies, and Historical Returns

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114 DONATION RISKAND OPTIMAL ENDOWMENT PORTFOLIO ALLOCATIONS FALL 2014

THE MAGNITUDE OF DONATION RISK

An important concern for charitable organiza-tions with respect to donation risk is its magnitude. The higher the volatility of donation risk, the more conservatively the endowment should be invested, and vice versa. This concept has been verified empirically by Dimmock [2012] and is consistent with theoretical models (for example, Merton [1993]).

In order to determine the magnitude of dona-tion risk, a multifactor model is used. The model is an expanded version of the original five-factor model intro-duced by Fama and French [1993], where momentum and liquidity are included as the sixth and seventh fac-tors, respectively.

The seven-factor model includes a market factor (R_Mkt – R_f), which is the return of the stock market minus the risk-free rate; a size factor (SMB), which is the return of small-cap stocks minus large-cap stocks; and a value factor (HML), which is the return of value stocks minus the return of growth stocks. Historical data for these three factors is obtained from Kenneth French’s data library.3_{The two additional factors introduced by} the original Fama and French [1993] research are TERM

and DEF. TERM is a bond duration factor calculated by subtracting the return on the Ibbotson Long-Term Gov-ernment Bond Index from the Ibbotson 30-Day Trea-sury Bill Index. DEF is a bond default factor calculated by subtracting the return on the Ibbotson Long-Term

Corporate Bond Index from the Ibbotson Long-Term Government Bond Index.

The final two factors included in the regression are momentum (MOM) and liquidity (LIQ). Momentum is an effect reported by Jegadeesh and Titman [1993], where stocks that have performed well (or poorly) his-torically tend to continue to perform well (or poorly) in the future. The data for the momentum factor was also obtained from Kenneth French’s data library. Research by Pastor and Stambaugh [2003], among others, has demonstrated that illiquid securities tend to outperform more liquid stocks, which suggests the existence of a liquidity premium. Data for the liquidity factor (LIQ) is obtained from Lubos Pastor’s website.4_{The seven-factor} model used for the analysis is noted in Equation (2).

= α + + + + + + + + ε ( − ) ( ) ( ) ( ) ( ) ( ) ( ) 2( )+ 3 4 5( )+ 6 7 R −R B( B2(( B3( B4( B ( B₆( B ( HC f α +B11(( MMMkt f (2) The resulting beta coefficients from Equation (2) provide insight into the relation between the change in donations (that is, donation risk) and the respective factor. In particular, the coefficient for B₁ provides insight into the extent a given donation type is more or less stock-like. This would be indicated by a higher, positive coefficient value. The beta coefficients from the

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Correlations between Changes in Donations and Test Asset Classes

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regression using Equation (2) for each of the 11 different types of donation risk are included in Exhibit 5, along with information about the varying levels of statistical significance.

The explanatory power of the regression varied significantly by donation type, although tended to be relatively high with an average R² of 30%. This means that 30% variation in the change of donations, on average, can be explained by the seven factors included in the model. The lowest R² value was 6.92% for health recipient donations, whereas the highest R² was for indi-vidual source donations at 53.41%, with the R² for total donations being 53.73% (which as a reminder is domi-nated by individuals from a source perspective).

The B₁ coefficients in Exhibit 5 are generally posi-tive, with an average value of 0.23. This is not surprising given the correlations noted in Exhibit 4, which tended to be positive for the equity asset classes, especially the U.S. equity asset classes. The positive B₁ coefficient of 0.27 for individuals in Exhibit 5 suggests that individual donation behavior is approximately 25% stock-like.

Although a number of the donation types did not have statistically significant coefficients, the coefficients for the individual donations tended to be statistically significant, which is notable given the fact ∼80% of donations come from individuals. The positive coef-ficient on HML suggests individual donation behavior is more small-cap stock-like versus large-cap stock-like. The negative weights on TERM and DEF suggest that individual donation behavior tends to be more related to shorter duration, higher-quality bonds. The positive weight on MOM suggests that high (low) historical stock performance is likely to be associated with higher (lower)

levels of future charitable giving, this could implicitly be accounting for the lagged effect of multiyear gifts.

The results of the correlation and seven-factor analysis suggest economically and statistically signifi-cant relations exist between the historical changes in charitable donations and returns of different market fac-tors. The implications of these relations with respect to portfolio optimization for endowments will be explored in the following sections.

ENDOWMENT OPTIMIZATION

The endowment is treated as a completion port-folio for the optimization routine, where the optimal weights to the financial assets are determined in order to minimize the volatility in the annual funding for the charitable organization. The premise behind the optimization routine is that charities prefer consistent income to fund their operations, and any changes, espe-cially negative changes, result in a suboptimal use of resources.

For the optimization, the charitable organization is assumed to have two revenue sources: donations and endowment income. Although charities receive revenue from sources other than donations, such as program ser-vice revenue, for this analysis charitable donations are assumed to be the only other revenue source apart from the endowment, due to the lack of data available on other potential sources (for example, program service revenue). Donations vary by the 11 types noted previ-ously, based on historical data obtained from the Giving USA 2013 Annual Report on Philanthropy.

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Coefficients for the Seven-Factor Regression

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116 DONATION RISKAND OPTIMAL ENDOWMENT PORTFOLIO ALLOCATIONS FALL 2014 The amount of income received by the

endow-ment each year varies based on the performance of the endowment, although the distribution is assumed to be some constant percentage of the endowment assets. For example, if the withdrawal from the endowment in year 1 was $100, and the endowment grows by 10%, the withdrawal for the following year would be $110. There-fore, the income is always assumed to be some constant value of the endowment (for example, 5% of corpus). Total income supplied by the endowment is assumed to be 5%, 20%, or 50% of total charity revenue, where donation revenue is assumed to represent the remaining 95%, 80%, and 50% of the income, respectively.

The actual income received by the charity from the endowment is going to vary depending on the return of the endowment, because income used to fund opera-tions is assumed to be withdrawn at the end of the year. The change in the realized income from the endow-ment versus the expected income from the endowendow-ment could create a potential budget surplus or shortfall for the charitable organization. Whether the charitable organi-zation realizes a shortfall, though, will depend on the amount of donations received. The amount spent by the charity during the year is assumed to be the total amount of income received during the previous year (donations and endowment income) increased (or decreased) by inf lation over that year, where inf lation is defined as the change in the Consumer Price Index for Urban Consumers.

Optimal weights to the 14 different asset classes are determined based on the idea of minimizing the volatility in the annual funding of the charitable orga-nization. A constant relative risk aversion (CRRA) utility function is used as the basis of optimization. The actual utility function used for the analysis is included in Equation (3), where the goal is to maximize total utility (U), based on past and expected donations (Don) and endowment income (EndInc), increased by inf la-tion (Inf), between two periods (t and t − 1), over the entire period of available returns (T, which equals 40, or the years 1973 to 2012), subject to a given level of risk aversion (γ). max[ ] ( ) (1 ) 1 1 1 1 U d ) (1 IIInf Don EndInc t 1 t fft t EndInct t T

∑

= ) − γ ⎛ ⎝ ⎜ ⎛⎛ ⎜ ⎜⎜ ⎜ ⎝⎝ ⎜⎜ ⎞ ⎠ ⎟ ⎞⎞ ⎟ ⎟⎟ ⎟ ⎠⎠ ⎟⎟ = −γ (3)

The risk aversion value (γ) would be considered the pain incurred (or felt) by the charitable organiza-tion associated with changes in relative funding levels. For the analysis, four different levels of risk aversion are considered: 2, 4, 8, and 16. The higher the risk aversion value, the more risk-averse the charitable organization is assumed to be with respect to funding its operations (that is, the higher the potential costs associated with a shortfall). The ideal portfolio would perform well when donations fall and not necessarily have to do as well if donations go up, that is, serve as a hedge for changes in donor behavior, thereby minimizing funding volatility.

This model takes a consumption perspective when determining the optimal weights for an endowment. An alternative approach would be to take a total wealth perspective, where the goal would be to minimize the variability of the change in the total wealth of the charity over time. The consumption perspective is used under the assumption that charities are more concerned with being able to meet ongoing commitments than minimizing the volatility of total wealth. Also, the true total wealth of a charity would be difficult to estimate, because it would need to include things like the real estate owned by the charity, program service revenue, and potentially even intangible assets such as branding and volunteer hours. Therefore, while the consumption optimization approach taken in this article is better than focusing entirely on the investable assets (that is, entirely ignoring donation risk), it is far from complete, espe-cially for charitable organizations with more complex income streams and asset types.

Two constraints are placed on the optimization to ref lect common investor considerations. First, there is no shorting (that is, all asset class weights must be positive). Second, the maximum allocation to a single asset class is 20%. This maximum ensures the portfolio must have non-zero weights to at least five classes and therefore cannot be dominated by the one or two asset classes that were the most efficient.

OPTIMIZATION RESULTS

The results of the optimizations based on solving Equation (3) are reviewed in this section. The primary focus is on the varying equity allocations for the different scenarios, where the equity allocation is determined by summing the weights to the six equity asset classes and the

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two alternative asset classes. Exhibit 6 includes the equity allocations for the eleven donation types, four levels of risk aversion, and three different levels of endowment income considered for the analysis. The nondonor equity allocations are the equity weights for those portfolios that entirely exclude donation risk, which implicitly assumes all funding comes from the endowment.

The optimal equity allocations vary significantly by scenario; however, there are a number of obvious trends. First, the equity allocations tend to be lowest for the nondonor optimizations, that is, those simula-tions that do not include donation revenue. The lower allocation is likely due to the fact that donation risk is relatively more bond-like than stock-like, based on the weights to B₁ in Exhibit 5. Second, equity allocations tended to be higher for simulations when donation rev-enue was a greater portion of overall revrev-enue. Third, equity allocations were higher for lower levels of risk aversion. This was expected and suggests that charities that are more willing to take on funding risk can invest more aggressively. This is also consistent with general perspectives on risk aversion and investing.

EQUITY ALLOCATIONS AND B₁ COEFFICIENTS

An additional analysis is performed to determine whether there is any relation between the equity allo-cations noted in Exhibit 6 and the B₁ coefficients esti-mated using Equation (2) (in Exhibit 5). In theory, if the donation risk for a given source or recipient is more bond-like, the equity allocation in the endowment can be greater, and vice versa. The correlations between these equity weights, which include the allocation to the real assets, and the 12 different scenarios are included in Exhibit 7.

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Equity Allocation for Dif

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version

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Correlation Between Equity Allocations and B₁ Coefficients

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118 DONATION RISKAND OPTIMAL ENDOWMENT PORTFOLIO ALLOCATIONS FALL 2014 The average correlation between the equity

allo-cations and the B₁ coefficients is −0.63, whereas the maximum correlation is −0.43 and the minimum cor-relation is −0.83. These negative correlations imply that donation types that had higher B₁ coefficients from the seven-factor regression (that is, were more equity-like, such as educational charities) had lower resulting equity allocations in the portfolio optimizations. This is consis-tent with both with general economic theory as well as empirical research performed by Dimmock [2012].

FIXED EQUITY WEIGHT OPTIMIZATIONS

Given the varied equity allocations from the gen-eral optimizations (Exhibit 6), it would be difficult to isolate the differences in the individual asset classes for a single scenario. For example, assuming the endowment provides 20% of total income and a risk-aversion level (γ) of 8, the equity allocations range from 38% to 100% across the 11 donation types. Therefore, certain asset classes (like small value) may have higher weights solely because the optimal total weight to equities is higher given the relative riskiness of the donation type.

For the following optimizations, an additional con-straint is imposed, where the sum of the weights in the six equity asset classes and two alternative asset classes must equal 60%. The 60% equity target assumption ref lects the historical tendency for endowment portfo-lios to invest 60% in stocks, and is also representative of the average equity weight of the opportunity set of asset classes because 57% (8 out of 14) of the asset classes included in the analysis are equity under the definition

used. Therefore, the equity target of 60% is approxi-mately targeting an equal-weight allocation.

For these additional optimizations, the endowment income is assumed to be 20% and the risk-aversion level is assumed to be 8, which is a relatively high level of risk aversion. These assumptions are selected because the average equity allocation using these assumptions (in Exhibit 6) is 64% equity, which is relatively close to the 60% equity constraint target. The results of the optimizations are included in Exhibit 8, where the non-donor portfolio is the optimized portfolio that does not consider any donation risk.

There are a number of similarities between the portfolio allocations in Exhibit 8, but also some notable differences. The most consistently used asset class is small value, with an average allocation of 18.2%. The only donation type that doesn’t have the maximum 20% allocation to small value is public-society benefit recipient charities, which has no allocation to small value whatsoever. The high average weight to small value is not surprising, because it had the highest risk-adjusted return. Long-term bonds were the second most uti-lized asset class (average allocation of 15.1%), followed by commodities (average of 12.3%), and non-U.S. bonds (average of 12.2%).

The average absolute difference in the portfolio allocations that include donation risk and the one that does not is 38.4%, with a minimum absolute differ-ence of 20.1% for education charities and a maximum absolute difference of 52.5% for health care charities. This suggests the weights to the different asset classes varied by 38.4% on average. The absolute differences

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Optimal Allocations by Donor Type, Assuming a 60% Equity Allocation

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were lower when the donor-optimized portfolios are contrasted against each other, with an average difference of 28%. These differences are still significant, though, because they suggest that the average asset class weights should vary by more than 25%, on average, depending on the charity type, even when holding the equity allo-cation constant.

CONCLUSIONS

This article explores the implications of taking a total wealth perspective when optimizing an endow-ment for a charitable organization. For the analysis, the optimization routine is expanded to include the risks associated with the changes in different types of chari-table donations, where the endowment is treated as a completion portfolio that is optimized to minimize the funding volatility of the charity.

Variability in charitable donations, or donation risk, has statistically significant relations with market factors. For example, 54% of the variation in the his-torical change in individual donations can be explained using a seven-factor model that includes the original five Fama–French factors plus momentum and liquidity. Ignoring donation risk implicitly assumes there is no relation between market returns and donor behavior, which is contrary to historical evidence.

A series of portfolio optimizations demonstrates that the optimal allocation for an endowment varies materially depending on different types of donation risk, varying levels of risk aversion, and the percentage of total income of the charitable organization funded by the endowment. Donations that are more stock-like result in lower equity allocations for the same level of risk aver-sion, and equity weights should decline as the percentage of income derived from the donations decreases. Even after holding the equity allocation constant, the average absolute difference in optimal asset weights varied by more than 25%, on average, when compared to either the average portfolio that incorporates donation risk or an optimized portfolio that did not.

This research has important and practical implica-tions for investment professionals providing advice to endowments. Perhaps most notably, the perspective of an efficient portfolio must be gauged with respect to its risk contribution to the ability of a charity to fund its mission. Ignoring the risk associated with donations

results in incomplete optimizations, since a material asset of the charity is excluded. Additionally, while this article incorporated donation risk into the optimiza-tion, charitable organizations have other assets, such as nonfinancial assets, program service revenue (that is, dues or fees), and so forth that should potentially be considered as well.

ENDNOTES

The author thanks Alexa Auerbach, Drew Carter, Rus-sell James, Hal Ratner, and Philip Straehl for helpful com-ments and edits.

1

http://www.irs.gov/uac/SOI-Tax-Stats-Charities-and-Other-Tax-Exempt-Organizations-Statistics.

2_{The IRS defines program service revenue as fees}

col-lected by organizations in support of their tax-exempt pur-poses, and income such as tuition and fees at educational institutions, hospital patient charges, and admission and activity fees collected by museums and other nonprofit orga-nizations or institutions.

3_{http://mba.tuck.dartmouth.edu/pages/faculty/ken.}

french/data_library.html.

4_{ht t p://facu lt y.ch icagobooth.edu/lubos.pa stor/}

research/liq_data_1962_2012.txt.

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