Abstract
The risk of revenue instability is a concern for any nonprofit. Existing research leads to the well-known strategy of equalizing revenues across sources to reduce revenue volatility. This study offers several expansions to this strategy. First, rather than focusing solely on deviations from mean revenue, I incorporate extreme revenue loss, or downside risk, as it threatens organizational survival and occurs more frequently than expected. Second, while revenue equalization is indifferent to the type of revenue source, I incorporate portfolio diversification that seeks a negative correlation between sources to avoid simultaneous losses. Using 2008 to 2012 financial data, results of fixed-effects regression suggest that portfolio diversification can reduce revenue volatility and downside risk. Moreover, the relationships between financial flexibility, growth potential, and revenue risk are more nuanced compared to existing research focused solely on deviation risk. The results can help nonprofits consider incorporating downside risk in revenue portfolio management to enhance financial security.
Keywords
Extreme revenue loss can force any organization to shut down in a very short time period, and nonprofit organizations are no exception. Unexpected events, such as economic recessions, pandemics, or government shutdowns can affect revenue inflow by losing large donations and grants (Qu, 2020). Such catastrophic events can endanger nonprofit sustainability and survival in the short and long term (Irvin & Furneaux, 2022). Proper risk management strategies such as a portfolio revenue strategy can critically minimize the impact of catastrophic revenue risks (Alves & Neves, 2016; Choudhry & Wong, 2013). Classifying revenue risks and investigating whether nonprofit organizations can mitigate revenue risk through different revenue strategies are topics in need of additional research.
This study contributes to our understanding of how nonprofit revenue strategy influences revenue risk in several ways. First, this study adds to the conceptualization of revenue risk by considering both downside and deviation risk in the context of nonprofit finance. Most existing research focuses on deviation risk, which is the extent to which revenue deviates above and below the average. While this type of revenue stability is important, another critical type of risk that has received far less attention in existing research is extreme revenue loss. By adopting extreme value theory (EVT), this study models and measures the likelihood of large, unexpected losses (i.e., downside risk) of nonprofit revenues. Considering both types of revenue risks—deviation and downside—can provide valuable insight for theory and practice in the field of nonprofit finance and risk management.
Second, this study contributes to existing nonprofit portfolio theory by incorporating measures of revenue equalization and portfolio diversification to investigate the potential benefit of using both strategies to mitigate revenue risk. One common measure of revenue equalization is the Herfindahl-Hirschman Index (HHI). The intent of the HHI is to measure diversification across a set of revenue sources in an organization’s portfolio. To focus solely on the HHI suggests revenue diversification—irrespective of any correlation among revenue sources—is sufficient to mitigate risk. As modern portfolio theory indicates, it is important to consider the relationships among revenue sources (Grasse et al., 2016; Kingma, 1993; Qu, 2020). A second strategy referred to as portfolio diversification uses the covariance between revenue sources to strategically distribute revenue inflow shares. These revenue risks and the strategies to manage them are interrelated. By combining both equalization and diversification strategies, this paper provides a more comprehensive approach to revenue risk management in nonprofit finance.
Last, the findings provide valuable practical implications on managing nonprofit finance and revenue risk management. The more commonly studied outcome of revenue deviation concerns an important yet partial picture of revenue volatility. Nonprofit managers may find it easier to address small increases or decreases from the average annual revenue, but managers are often concerned with large, unexpected revenue losses (i.e., downside risk) since these extreme events can happen more frequently than one expects and cause serious damage to the organization. However, implementing portfolio diversification to mitigate downside risk requires knowledge of how an organization’s revenue changes compare with the distribution of revenue changes among a group of organizations. This study provides a nonprofit subsector-level benchmark of revenue downside risk. With this benchmark, nonprofits can better understand whether they face high downside risk relative to comparable organizations and implement strategies to reduce risk, securing better financial security to achieve their social mission.
This study uses fixed-effects to estimate the association of two revenue risk outcomes, deviation and downside, with two risk mitigation strategies, equalization and diversification. The model uses financial data from nonprofit service fields based on the National Taxonomy of Exempt Entities (NTEE) over a period of five years between 2008 and 2012. The results indicate that portfolio revenue diversification reduces revenue deviation and downside risk. Furthermore, when including both revenue equalization and portfolio diversification in the same model for each risk outcome, there is no evidence that equalization via the HHI measure is associated with changes in deviation or downside risk, while portfolio diversification remains significant. Additional financial factors, such as financial flexibility and growth potential impact deviation and downside risk. Overall, the results provide nonprofit organizations in each service field novel strategic guidance for mitigating revenue risks.
Theoretical Background
Extreme Value Theory
EVT examines periods of extreme events that represent the discontinuity of normal periods. During some periods, for example, much larger changes will occur than those predicted by the normal distribution, where the market exhibits relatively modest changes in prices and returns. This theory has been developed and applied in various fields, including insurance, financial markets, natural disasters, weather, and pollution studies, where the analysis of extreme outliers is particularly important (Alves & Neves, 2016; Choudhry & Wong, 2013; Porter, 2007; Reiss & Thomas, 2007). For example, the theory has been used to model extremely high temperatures or to evaluate the impact of earthquakes in different regions (Brown & Katz, 1995; Suzuki & Ozaka, 1994).
In the financial world, EVT has become more critical following the financial collapse of 2007–2008 as well as the 1987 stock market crash, often called Black Monday (Alves & Neves, 2016). Both financial crises significantly impacted enough the market that they are difficult to categorize as normal market behavior. Specifically, the stock market return dropped around 23% in a single day on October 19, 1987, and by 9.5% on October 15, 2008.
Empirically speaking, EVT is associated with “fat-tailed” behavior, which implies the extreme risks inherent in finance. In other words, these extreme events might happen only rarely, but their impact can be larger than under normal, stable conditions, where clustering around the center of the normal probability distribution is more common (Kemp, 2011). For the most part, conservative investors prefer to avoid (or to prepare for) such unexpected outlier events, especially negative values in the left tail.
Revenue Risk: Deviation Risk and Downside Risk
Limitations of the Coefficient of Variation
While the coefficient of variation (CV) is a useful tool for measuring financial volatility, it does have limitations. First, the measure presents deviation risk, which includes both upside and downside risk, and not specifically the latter. In financial risk management, the term “risk” refers to “a loss or an injury created by an activity” (Tarantino & Cernauskas, 2010, p. 2) and typically assumes the negative consequences of risk. CV essentially shows how the large majority of the actual revenue deviates above and below the mean (upside and downside risk). From a practical point of view, nonprofit managers are usually more concerned with excessive losses that occur with less frequency but have dire consequences for their organization.
Second, the use of CV as a volatility measure might be inaccurate in the case of skewed or leptokurtic (thick-tailed) non-normal distributions. The central limit theorem holds that the shape of the tail in a normal distribution is symmetric on both sides of the mean, which implies that the data are equally distributed around the middle. Unfortunately, the distribution of many nonprofits’ revenue is leptokurtic, with tails thicker than a normal probability distribution. This situation means that large fluctuations occur more frequently and with higher and lower values compared with normal distributions. Asymmetry also implies that CV can understate or overstate the downside risk since CV averages deviation risk in both directions. CV thus may be a misleading measure of revenue risk for nonprofits that wish to minimize their downside risk.
Value-at-Risk: Downside Risk Estimation
To measure the downside risk and overcome the limitation of the normal distribution, this study applies the concept of value-at-risk. The value-at-risk framework is widely used to measure and quantify losses that occur in the lower tail of a probability distribution, that is, downside risk (Butler & Schachter, 1996). More specifically, value-at-risk answers the question of how much one expects to lose with a given probability—typically 1% or less. Value-at-risk provides the threshold value of the potential loss that is expected to be greater than the value-at-risk amount for a given probability. For example, if 1% of the value-at-risk on an asset equals a revenue decrease of 40%, then revenue declines of 40% or more are expected to happen in only 1% of all cases.
In mathematical terms, value-at-risk is based on the percentile point function (
where X is the random variable describing the value of the loss of a portfolio, and α*100% (0 < α < 1) is a specific percentage that selects a sample of the worst cases for the portfolio to be analyzed (Acerbi & Tasche, 2002; Cade & Noon, 2003; Davino et al., 2014; Hosking & Wallis, 1987; Jorion, 2001). The quantile α is usually a small probability, such as .05, .01, or .001 (respectively, 5%, 1%, and 0.1%). This study, like many previous studies, will use the probability of 1%, which means that the events happen in the lowest 1% of the distribution (the first percentile).
The qualitative benefits of EVT in the corporate sector are many, and yet, EVT theory and value-at-risk have not yet been actively applied to nonprofit finance. Despite the potential benefits of EVT to the nonprofit sector, the calculation of value-at-risk often requires ample data to generate the probability distribution of the downside tail. Corporate financial data are frequently collected in daily or weekly intervals, making it possible to find a value-at-risk specific to each firm. However, nonprofit finance data are reported on an annual basis, which makes it difficult for researchers or risk managers to generate the probability distribution and calculate the value-at-risk. Alternatively, a portfolio approach may be taken using pooled data from firms that share common attributes or characteristics (such as the healthcare sector). The value-at-risk can be calculated based on the distribution of losses among organizations clustered by subsector for given years. This approach has been often used in the corporate finance literature to compare the individual firm with the industry, so that, the individual firms can compare themselves with their peer organizations or competitors. I employ the cluster sampling method approach to generate the probability distribution and calculate the value-at-risk: I use the nonprofit subsector pre-existing unit as the cluster of this study.
Table 1 illustrates the difference between the concepts of value-at-risk and CV in the context of the nonprofit subsectors. In the subsector of Arts, Culture, and Humanities, the value-at-risk is −0.81 for the average of years 2008 to 2012. This means that the average 5-year revenue decline for the Arts subsector was equal to or less than −0.81 for 1% of the organizations in that subsector. Another way to say this is that revenue growth exceeded −0.81 for 99% of the organizations in the Arts subsector. The Environmental subsector provides an apt comparison. The value-at-risk for the Environmental subsector is larger than that for the Arts subsector, indicating that the Environmental sector has more downside risk. Specifically, 1% of the organizations in the Environmental subsector experienced revenue decline greater than or equal to 90%. What makes this comparison interesting is that by the CV measure, the Arts subsector has more dispersion of risk than the Environmental subsector. How is it that CV and value-at-risk produce seemingly contradictory results? The average and standard deviation are influenced by outliers, and the value-at-risk depends on the thickness of the tail. The Animal-related subsector is an example of relatively low financial risk, as indicated by both measures.
Summary Statistics of Total Revenue by Sector (Total Revenue; $, %Δ; Average 2008–2012).
Note. Value-at-risk equals the percent change in revenue for the first percentile of the distribution. Total observations equal the sum for all years, not the average. NTEE = National Taxonomy of Exempt Entities.
Nonprofit Revenue Strategy: Revenue Equalization and Portfolio Diversification
The Herfindahl–Hirschman Index
The Herfindahl-Hirschman Index (HHI) was originally developed to quantify the competition of different industrial sectors (Herfindahl, 1951). Many scholars from the nonprofit sectors use HHI calculations to measure how concentrated or evenly distributed a nonprofit’s revenue sources are (Carroll & Stater 2009; Frumkin & Keating, 2011). I will refer to this revenue diversification measured by HHI as “revenue equalization.” Previous studies have used normalized HHI to measure diversification as follows:
where
Even though the HHI is a widely used measurement tool in the nonprofit finance sector, it needs to be adopted with care as to how decisions are made to improve nonprofit financial health (Chikoto et al., 2016; Chikoto & Neely, 2014). For instance, due to organizational characteristics or charitable missions, some nonprofits are highly dependent on a single revenue source, such as donations, commercial, or investment income. Such revenue concentration mechanically leads to a low normalized HHI index, which implies that the nonprofit carries a low diversification level and high financial risk even if a particular revenue source is relatively stable. Furthermore, the HHI measure disregards the cross-correlation across revenues when measuring portfolio diversification, in contrast to modern portfolio theory.
Portfolio Strategy and Risk Model
The portfolio, in general, refers to a diversified collection of investments that can reduce the risk of investment return—in common parlance, not putting all your eggs in one basket (Tarantino & Cernauskas, 2010). Portfolio theory has contributed to the development and measurement of portfolio diversification and risk management (Fabozzi, 2012). Prior to the development of portfolio theory, diversification and risks were generally considered independent of each other, thus leading scholars to underestimate the covariance between assets (Fabozzi, 2012). Markowitz (1952), however, formulated the portfolio variance model (popularly referred to as the theory of portfolio selection), which became the foundation of modern portfolio theory (Fabozzi, 2012). Well-diversified portfolios are efficient and can maintain high expected returns while lowering risk through an analysis of the covariance between asset returns (Fabozzi, 2012; Jegers, 1997).
For multiple-asset portfolios, the variance of the portfolio return is the sum of the squared-weighted variances of the individual revenues plus twice the sum of the weighted pairwise covariance of the assets. For example, the equation measuring portfolio diversification with the revenue of three assets—
where
The key determinant of portfolio variance is the covariance of revenues. The Markowitz portfolio variance model emphasizes the importance of cross-correlation among revenue sources. For instance, the variance of a portfolio can increase if the revenue covariances are large and positive, which implies that the revenues move in the same direction: as asset A increases (decreases), asset B also increases (decreases). Ideally, negative correlations are best, but rare, since the negative value can reduce the portfolio variance. Perhaps, nonprofits might be able to at least acquire nearly independent sources, where the correlation is close to zero.
Table 2 helps to illustrate the difference between the HHI and portfolio variance in the context of nonprofit subsectors. For instance, the Philanthropy, Voluntarism, and Grant-Making Foundations subsector has relatively high values on both HHI, 0.62, and portfolio standard deviation, 0.69. These values tell us that this sector, on average, earns from diverse revenue sources yet has high risk in regard to portfolios. In contrast, the Arts, Culture, and Humanities subsector has relatively low values on both HHI, 0.12, and portfolio standard deviation, 0.16, meaning that this sector earns income from few sources but still has stable portfolios. This comparison tells us that diversifying revenue by adding more sources may not be equivalent to portfolio stability.
Summary Statistics of Revenue Diversification by Sector (Average 2008–2011).
Note. Standard deviation of portfolio is the square root of portfolio variance. Total observations for each National Taxonomy of Exempt Entities (NTEE) Code are the same as reported in Table 1. NTEE = National Taxonomy of Exempt Entities; HHI = Herfindahl–Hirschman Index.
Variable Specification and Hypotheses
The previous section discussed revenue risk measurement (the limitations of CV and the potential benefits of value-at-risk) as well as revenue diversification measurement (the limitations of HHI and the potential benefits of portfolio variance). This section discusses in more detail key variables and related research that motivates three hypotheses.
Downside risk is calculated as value-at-risk at the 1% level (α = .01) of the percentage change of total revenue (Part VIII, Line 12, on IRS form 990, p. 8, 2008). The interpretation is the expected threshold percentage change of total revenue that occurs in the lowest 1% of the organizations in the subsector. Deviation risk is measured as the coefficient of variation for percent change in revenue. That is, the standard deviation of percent change revenue divided by the average percent change of total revenue (Carroll & Stater, 2009; Chang & Tuckman, 1994; Chikoto & Neely, 2014; Mayer et al., 2014). A higher CV value represents a larger standard deviation relative to the expected mean, which implies a greater level of revenue deviation risk. Percentage change in total revenue to calculate both CV and value-at-risk. This normalizes the impact of different-sized revenues and includes the zero value, unlike the logarithmic form (Chikoto & Neely, 2014; Yan et al., 2009).
Research includes different explanatory variables depending on the hypothesis. For nonprofit revenues, several scholars have confirmed that greater revenue equalization can reduce revenue deviation risk (Carroll & Stater, 2009; Chikoto & Neely, 2014; Froelich, 1999; Frumkin & Keating, 2011; Mayer et al., 2014; Yan et al., 2009). It is also well known in portfolio theory that revenue diversification can lower volatility. This is because greater diversification decreases the chances that all revenue sources will be exhausted at the same time. For example, if a nonprofit depends on only one source of revenue, then it may have high revenue risk since no alternative source exists. Taken together, the research shows that revenue equalization and portfolio diversification will decrease revenue risk. However, revenue risk in existing research refers to deviation risk, not downside risk. Therefore, I incorporate downside risk into hypothesis tests similar to but distinct from existing research:
Testing these hypotheses can show whether portfolio variance and value-at-risk are applicable to nonprofit finance.
In addition to revenue diversification, several factors can influence revenue risk, such as financial flexibility and growth potential. Financial flexibility can connote financial leverage or the use of debt. According to Carroll and Stater (2009) and Mayer et al. (2014), greater financial leverage can intensify or mitigate the impact of revenue risk. For instance, greater financial leverage becomes less vulnerable to economic shocks by enhancing the liquidity of the funds. Consequently, organizations with greater financial leverage can better plan their budgets for the future (thus minimizing risks), which is critical for stable revenue streams. Previous studies have measured financial leverage with the debt margin (the total liability divided by total assets). A smaller debt margin means more financial leverage (Chang & Tuckman, 1994). Mayer et al. (2014) found that a greater debt margin (i.e., less financial leverage) increases revenue risk.
Another view of debt margin exists even though most of the literature in the nonprofit finance sector views the debt margin as a sign of limited financial capacity. In the risk management literature, Acharya et al. (2007) found that financially constrained firms tend to keep their debt level low, so that, they can increase future debt capacity. Keeping a low debt margin allows the firm to borrow more in the future when a profitable investment opportunity arises. Therefore, a higher debt margin can be a sign of a healthy level of investment since nonprofits have invested profitable assets that they do not need to save the debt capacity for future opportunities. I examine the following hypothesis that builds on previous studies:
Growth potential signals that a nonprofit’s financial health makes it a viable business. I measure growth potential by the fund balance (total asset minus total liability), retained earnings (total revenue minus total expenses), and total asset value of land, buildings, and equipment. Higher fund balances, retained earnings, and asset values represent higher growth potential. Specifically, the fund balance refers to the accumulation of assets, such as savings or idle cash. Retained earnings refer to the accumulated surplus balances of the organization’s programs. Tangible assets, such as land, buildings, and equipment can involve maintenance expenses, and also earn revenue. The appropriate level of surplus assets can provide nonprofits with the opportunity to respond to unexpected events and seize opportunities when they come, which translates into less risk and more stable and sustainable growth. Mayer et al. (2014) and Carroll and Stater (2009) confirmed that greater growth potential decreases deviation risk. As a counter hypothesis, the risk management literature, generally, has found that higher profitability or growth potential is strongly associated with high risk (Probst & Raisch, 2005). I examine the following hypothesis that builds on previous studies:
Several organizational factors were also included as control variables in this study since funding capacity or stability may differ by organizational factors and size. Specifically, the following variables were included for organizational factors: years of operation, the log of lagged employee salaries and benefits, the ratio of administration and fundraising expenses, the size of the governing board, the number of volunteers, and the share of unrelated business income (UBI). These variables represent the longevity of the nonprofit, its reputation, the involvement of communities, and the expanse of the organization. A greater value of these factors could decrease risk indirectly by changing the larger environment of the nonprofit.
Particularly high functional expenses and overhead costs (i.e., administration and fundraising costs related to total expenses) can be considered indicators of organizational inefficiency. Mayer et al. (2014) and Chikoto and Neely (2014) found that greater fundraising or administration expenses decrease deviation risk. This situation may result when an organization’s management utilizes its limited resources to the best of its capabilities, which potentially increases revenue stability (Tuckman & Chang, 1991). Chikoto and Neely (2014) measured financial capacity growth using the percentage growth in total revenue, total fund balance, and unrestricted fund balance. Carroll and Stater (2009), however, did not find statistically significant results on the relationship between organizational efficiency and deviation risk. On the other hand, revenue can grow as the organizational efficiency increases until a certain point but can then decrease due to excessive spending on administration and fundraising activities (Weisbrod & Dominguez, 1986). The detailed data sources are summarized in Appendix 1.
Model Specification and Data
This study includes a primary model that investigates the impact of revenue diversification, financial flexibility, and growth potential on revenue risk within a given subsector (service field) classified by the National Taxonomy of Exempt Entities (NTEE) code. In this model, nonprofit revenue volatility is estimated as follows:
where RR, RD, FF, GP, and C for i category of ΝΤΕΕ in year t represent the following categories of variables, respectively: revenue risk, revenue diversification, financial flexibility, growth potential, and control variables. This econometric model was adapted from Carroll and Stater’s study (2009); the major difference is that I have applied an alternative measure of revenue volatility and diversification—value-at-risk and portfolio variance—in addition to the CV and HHI measures. Other differences are that Carroll and Stater’s unit of observation is individual organizations from 1991 to 2003, and they control for subfields; in contrast, the unit of observation comprises 25 NTEE subfield types from 2008 to 2012. The specific NTEE codes are shown in Appendix 2.
The unit of analysis is the group of nonprofits stratified by subsectors. This approach increases the validity of the probability distribution and value-at-risk calculation. Before the data were aggregated by subsectors, this study’s panel data included 85,286 total observations over 5 years (Appendix 3). In terms of using Form 990 data, I followed the data-clearing filters suggested by Bowman et al. (2012), although the data still included different types of small organizations in the sample. The original data had 100,344 total observations, I excluded nonprofits if they (a) reported group returns (575; 0.57%), (b) used non-accrual accounting (10,872; 10.83%), and (c) used non-positive assets or revenue (respectively, 62 and 3,549; 0.06% and 3.54%) (Bowman et al., 2012). Among the remaining 85,286 observations, each subfield included 750 observations on average. Subfields related to social science, civil rights, social action, and advocacy were the smallest group with fewer than 100 observations for each year.
The number of observations is 125 aggregated observations, with 25 NTEE fields over a 5-year period between 2008 and 2012, retrieved from Form 990 (Internal Revenue Service [IRS], 2015). As this study intends to explore revenue risk management strategies with respect to extreme negative events, this time period was chosen to approximately cover the full length of the Great Recession (Lin & Wang, 2016; Park & Mosley, 2017). The financial crisis of 2008 to 2009 is considered the worst recession in history, putting many nonprofit organizations in financial danger. While this study is not limited to the impact of economic recessions, studying the worst-case scenario can provide generalizable implications. The time period is also partially dictated by changes in data reporting. The IRS redesigned the Form 990 and 990-EZ reporting requirements for the 2008 tax year (returns filed in 2009 and later) and the 2012 tax year. Limiting to this period helps to enhance the data reliability and validity that align with the purpose of this study.
The variables were calculated from individual nonprofits, which were then averaged by NTEE subfields. For example, for the value-at-risk of total revenue in percentage change, the percentage change in total revenue was calculated at the organizational level and the value at 1 percentile (lowest) was chosen within NTEE subfields. For dependent and control variables, values were calculated at the organizational level and then averaged by subsectors and year. For certain control variables, a few observations were excluded before I created the average value by subsector in cases where certain variables had a logarithmic form or negative or zero denominators. After dropping these observations, more than 99% of the total observations remained.
Descriptive Findings
Table 3 provides the descriptive statistics for each variable in the analysis. Referring to the mean values of 12.17 deviation risk, nonprofits, on average, had a high standard deviation of the percentage change in total revenue. This value is very high as a standard deviation value above or equal to 2 is considered high in a normal distribution. The high standard deviation means that nonprofits had a high revenue deviation risk, indicating that the nonprofit revenues are widely spread out to the mean. Their revenues seem to be concentrated on one revenue source between donations, earned income, and investment revenue (they had an HHI of 0.33). Their average portfolio across all subsectors was .84, or 84% of the standard deviation of the portfolio. Excluding the exceptionally high standard deviation in the portfolio in certain subfields, such as Youth Development, Human Services, and Mutual and Membership, the average standard deviation of the portfolio was approximately .37, or 37%. Note that a negative value-at-risk should be interpreted with an absolute value. For example, a value-at-risk of –.75 for the percentage change of total revenue means that the nonprofits, on average, will have 75% or greater percentage change in 1% of the organizations.
Descriptive Statistics.
For financial flexibility, the average debt margin was roughly U.S. $.53 per $1 in assets or half their assets. On average, organizations had positive growth potential, such as a $53 increase in fund balance, $2.38 of revenue per total expenses, and $17 million of asset value.
Organizations in the sample have operated for approximately 47 years on average and have expenses of approximately $38.5 million. The average nonprofit spent around 6% and 3% on administration and fundraising, respectively. They have around 25 voting members on each organization’s governing body. On average, they have approximately 1% of UBI and have expenses of $40 million. The correlations among the explanatory and control variables were low. The variance inflation factor (VIF) also indicated that the model was controlled for potential multicollinearity.
Estimation Results
The models used fixed effects with Driscoll–Kraay (D–K) standard errors, which correct for correlations between sectors and correlations within sectors. Prior to running the fixed-effects regression model, several tests were conducted to estimate the method. To select between the fixed and random effects models, I ran a Hausman test, which rejected the null hypothesis that the preferred model was random; thus, I selected the fixed-effects model (Greene, 2010; Wooldridge, 2010). The average absolute correlation suggested that all four models exhibited cross-sectional dependence (i.e., high average absolute correlation values) even though the Pesaran test for cross-sectional independence failed to reject the null hypothesis of no cross-sectional dependence (De Hoyos & Sarafidis, 2006). The modified Wald test for group-wise heteroscedasticity in fixed-effects models indicated that all four models had heteroscedasticity. After considering these tests, I employed the fixed-effects model using D–K standard errors. Hoechle (2007) suggested robust standard estimates for panel models (or fixed effects within regression models with D–K standard errors). This method helps to control for heteroscedasticity, autocorrelation, and cross-sectional dependency. In addition, some variables, such as debt margin, retained earnings, and employee salaries and benefits used 1-year lag values to control the potential endogeneity of variables.
One potential problem is reverse causality between revenue diversification and volatility (Carroll & Stater, 2009). To correct for this potential endogeneity, I also estimated a fixed-effects model with instrumental variables as lagged dependent and explanatory variables. The fixed-effects model with lagged explanatory variables, however, did not show any substantive differences in the statistical results. This situation shows that no apparent evidence was found that diversification is endogenously determined.
Combining the two different measures of diversification and volatility produced three models (Table 4). The first model used deviation risk measured by CV and portfolio diversification measured by the portfolio standard deviation, which is the square root of the portfolio variance. This model showed statistically significant results in hypotheses 1(b) and 3. For H1(b), the existence of a more diversified portfolio decreased the deviation, as expected and as portfolio theory generally assumes. Specifically, as portfolio standard deviation increases (less diversification), the standard deviation of the percentage change of total revenue is increased by 0.52, or 52%.
Fixed-Effect Regression With Driscoll–Kraay (D–K) Standard Errors.
Note. Standard errors in parentheses. +p < 0.1. *p < 0.05. **p < 0.01. ***p < 0.001. Some variables are applied in the logarithmic form (ln). CV = coefficient of variation; HHI = Herfindahl–Hirschman Index; NTEE = National Taxonomy of Exempt Entities.
For H3, results show mixed directions for the impact of growth potential on deviation risk. The existence of a higher fund balance and retained earnings was found to increase the deviation risk, but higher asset value decreases the risk. Specifically, with a 1% increase in current-year assets compared to the previous year, the standard deviation of the percentage change of total revenue is increased by 0.21, or 21%. As the retained earnings from the previous year increase by $1 million, the standard deviation of the percentage change of total revenue increases by 0.463, or 46.3%. On the other hand, as asset value increases by 1%, the standard deviation of the percentage change of total revenue decreases by 0.095, or 9.5%, as previous research confirmed (Mayer et al., 2014). These results imply that nonprofits with larger fund balance and retained earnings might pursue riskier revenue sources with high return (high deviation risk); one with higher value in assets might be more inclined to maintain more stable revenue.
Model 2 in Table 4 tests the impact of revenue equalization (using HHI) on downside risk (value-at-risk). This model showed statistically significant results for hypotheses 1(a), 2, and 3. For H1(a), organizations or groups of nonprofits with equally distributed revenue among donations, earned revenue, and investment income were found to encounter lower downside risk. For example, the average value-at-risk was –.75 across subsectors (Table 4), meaning that 1% of nonprofits can lose 75% or more. With a one unit increase in HHI (more revenue sources or equally distributed sources), the percentage change of revenue is increased by 17.4%, which leads to a positive impact on the negative value-at-risk. Therefore, the average value-at-risk becomes approximately -.62 across subsectors, meaning that 1% of nonprofits can lose 62% or more after perfect revenue equalization. This means that revenue equalization by adding more revenue sources or distributing equally among revenue sources reduces the downside risk.
An increase in debt margin (i.e., less financial flexibility) decreases downside risk, contrary to the expectation in H2. In other words, an increase in debt margin has a positive impact on downside risk, which reduces downside risk. For instance, the average value-at-risk of -.75 moves toward zero due to the positive coefficient of .027 or 2.7%. Results also indicate that higher fund balances and asset value (i.e., greater growth potential) are associated with greater downside risk, contrary to H3. In addition, nonprofits with more years of operation and that spend less on employee salaries seem to have less downside risk. On the other hand, nonprofits that rely more on volunteers seem to have higher downside risk.
Compared with model 2, model 3 in Table 4 uses portfolio diversification as an explanatory variable. As assumed in H1(b), portfolio diversification decreases downside risk. The negative coefficient of -.007 implies that a less diversified portfolio (higher variance) negatively influences the negative value-at-risk, meaning that more a diversified portfolio considering inter-correlations among different revenue sources decreases the impact of extreme revenue loss.
Table 5 shows results of two models with both revenue equalization and portfolio diversification included as explanatory variables. The first uses deviation risk as the dependent variable, and the second uses downside risk. A diversified portfolio (lower portfolio standard deviation) decreases both deviation risk and downside risk while revenue equalization measured by HHI becomes statistically insignificant. This direct comparison suggests that portfolio variance has a stronger influence on explaining revenue risks than revenue equalization. In other words, controlling for portfolio diversification seems to make HHI an insignificant measure for revenue diversification. The results pertaining to financial flexibility and growth potential are similar to the results reported in Table 4.
Fixed-Effect Regression With Driscoll–Kraay (D–K) Standard Errors With Both Revenue Equalization and Portfolio Diversification.
Note. Standard errors in parentheses. CV = coefficient of variation; HHI = Herfindahl–Hirschman Index; NTEE = National Taxonomy of Exempt Entities.
p < 0.05. **p < 0.01. ***p < 0.001. Some variables are applied in the logarithmic form (ln).
Discussion
In practice, portfolio diversification is easier said than done for nonprofit organizations, especially in times of financial crisis. Given the challenges these organizations face, an important step in assisting nonprofits with portfolio diversification is demonstrating its potential to reduce revenue risk, especially extreme revenue loss. Due to limited resources or capacity, organizations may lack the motivation to explore the feasibility of portfolio diversification. The results of the study suggest that the time and resource investment to consider and implement portfolio diversification could be net positive.
In addition to providing motivation to consider implementing portfolio diversification, this study provides nonprofits or nonprofit associations a possible blueprint for assessing downside risk. Downside risk is a major concern among nonprofit managers. The results suggest portfolio diversification is an effective strategy to reduce downside risk as well as deviation risk. Therefore, a group of nonprofits or an organizing entity for nonprofits with similar missions or resources, identified by NTEE service field or a more granular group level, may find it beneficial to regularly assess downside risk by sharing or collecting percent changes in revenue annually or some other frequency. Then, each nonprofit can gauge their downside risk to the distribution and evaluate whether greater portfolio diversification may be warranted. For nonprofits that decide to improve portfolio diversification, they need to calculate the portfolio variance among revenue sources. Though this calculation may be unfamiliar to nonprofit staff, the study provides the portfolio variance equation and explains each term. Once an organization has calculated its baseline portfolio variance, it can compare it with future values. Nonprofits with high downside risk should seek a lower portfolio variance value. This can be achieved in two ways: (a) establish a new revenue source that has negative or relatively low covariance compared with the covariances between existing revenue sources or (b) adjust the weighting (or shares) of existing revenue sources so that sources with the lowest or relatively lower covariances represent a higher weight of total revenue.
Another important question is what should nonprofit managers prioritize most when attempting to implement portfolio diversification? Based on portfolio variance, the covariance of revenue sources is the key factor when deciding on portfolio diversification. By nature of the calculation of portfolio variance, portfolio variance will inevitably increase by adding more revenue sources unless the revenue sources are negatively correlated. If options with zero correlation or inverse relationships exist among revenues, then the covariances will have no impact or will decrease the portfolio variance, respectively. In this case, more revenue sources will decrease or increase portfolio variance by a lower amount than sources with a positive correlation. In reality, however, negative correlations among assets are rare. If the only revenue sources available are positively correlated, portfolio variance becomes larger. It would therefore be better for organizations to pursue fewer revenue sources than adding more if minimizing portfolio variance is a priority.
Regarding financial flexibility, as measured by debt margin, and growth potential, as measured by fund balance and asset value, the results are slightly more nuanced compared with existing research that has focused solely on deviation risk. Higher debt margins are associated with improved deviation and downside risks. In other words, organizations with lower debt margins may be more vulnerable to extreme revenue loss. A plausible explanation for this is that nonprofits with high debt margins already have stable financial conditions.
Fund balance and asset value were used to operationalize growth potential. As discussed in the previous section, research is mixed as to whether growth potential is positively or negatively related to deviation risk. The analysis finds higher fund balances are associated with worse deviation and downside risks. This may be due to organizations with high surplus assets having the opportunity to seek high-risk, high-yield investments, while organizations with low fund balances place assets into more secure investments. Conversely, higher asset value is associated with improved deviation risk but worse downside risk. This result potentially highlights the important difference between deviation and downside risks. High asset values likely involve fixed assets, such as property and buildings. Rents or realized gains from appreciated property (i.e., revenue) are relatively stable, resulting in lower deviation risk, but are vulnerable to extreme revenue loss, resulting in higher downside risk.
There are several opportunities for future research. First, researchers could explore how results are sensitive to different calculations of value-at-risk. Modern portfolio theory has developed multiple methods to calculate value-at-risk. This study incorporates one of the least technical methods to maximize the chance of practical application. While it is not expected that more sophisticated methods would lead to antithetical conclusions, they may reveal additional insights, such as how much revenue an organization with high downside risk could expect to lose in an extreme event. Also, future research could test the generalizability of the results to time periods that exclude the Great Recession. As previously mentioned, the 2008 to 2012 time period provides a worst-case scenario that is ideal for testing the potential of using portfolio diversification to mitigate revenue risk. However, it could be the case that this assumption does not hold and results differ when the macroeconomic environment is significantly different. Another opportunity for future concerns dependent variables. This study models downside risk as the outcome in the empirical model, but this is unlikely to be an outcome for a nonprofit organization with a social mission. Future research could examine how downside risk impacts organizational performance in areas outside of finance, such as service provision and mission achievement.
Ultimately, portfolio diversification requires cooperation between multiple nonprofit organizations so that any single organization can better protect itself from catastrophic revenue loss. This, in turn, increases the likelihood of survival for all nonprofit organizations within the cooperating group as they pursue critical social missions.
Conclusion
This study addressed three central questions. First, how might revenue risk with respect to both deviation and downside be conceptualized within the context of nonprofit finance? I model and measure the likelihood of large, unexpected downside risk by incorporating EVT and value-at-risk into the fields of nonprofit finance and risk management. Second, is there evidence that revenue portfolio diversification reduces downside or deviation risk when combined with the more common strategy of naïve revenue equalization? The results indicate a well-diversified portfolio, as measured by portfolio standard deviation, stabilizes revenue inflows and also makes an organization less vulnerable to major losses (i.e., downside risk). Third, how can nonprofit organizations assess their downside risk and implement a portfolio diversification strategy? This study demonstrates how organizations can use a downside risk threshold at the service field level to assess their own downside risk and adopt the portfolio variance measure to improve revenue diversification. Furthermore, this study applied alternative measures in combination with those traditionally used in nonprofit finance literature. Specifically, portfolio variance combined with HHI for revenue diversification measures and value-at-risk combined with CV for the risk measure. These alternative measures compensate for the weakness of traditional measures and will help nonprofit managers and scholars to better consider the impact of portfolio diversification and downside risk.
Footnotes
Appendix
Number of Nonprofit Organizations by Year and National Taxonomy of Exempt Entities (NTEE) Codes.
| NTEE code | Description | 2008 | 2009 | 2010 | 2011 | 2012 | Total |
|---|---|---|---|---|---|---|---|
| A | Arts, culture, and humanities | 767 | 829 | 721 | 731 | 767 | 3,815 |
| B | Education | 2,712 | 2,852 | 2,733 | 2,833 | 2,967 | 14,097 |
| C | Environment | 228 | 231 | 208 | 219 | 225 | 1,111 |
| D | Animal-related | 129 | 146 | 120 | 124 | 130 | 649 |
| E | Health care | 3,467 | 4,133 | 3,904 | 4,026 | 4,088 | 19,618 |
| F | Mental health and crisis intervention | 280 | 377 | 277 | 286 | 294 | 1,514 |
| G | Disease, disorders, and medical disciplines | 136 | 156 | 159 | 158 | 159 | 768 |
| H | Medical research | 136 | 144 | 144 | 136 | 145 | 705 |
| I | Crime and legal-related | 96 | 112 | 97 | 99 | 99 | 503 |
| J | Employment | 411 | 447 | 424 | 443 | 467 | 2,192 |
| K | Food, agriculture, and nutrition | 128 | 156 | 147 | 151 | 172 | 754 |
| L | Housing and shelter | 836 | 932 | 728 | 753 | 792 | 4,041 |
| M | Public safety, disaster preparedness, and relief | 61 | 76 | 69 | 70 | 74 | 350 |
| N | Recreation and sports | 986 | 1,006 | 995 | 1,013 | 1,060 | 5,060 |
| O | Youth development | 149 | 166 | 118 | 125 | 135 | 693 |
| P | Human service | 2,004 | 2,130 | 1,710 | 1,782 | 1,805 | 9,431 |
| Q | International, foreign affairs, and national security | 181 | 202 | 182 | 200 | 200 | 965 |
| R | Civil rights, social action, and advocacy | 29 | 23 | 24 | 28 | 34 | 138 |
| S | Community improvement and capacity building | 832 | 893 | 858 | 882 | 956 | 4,421 |
| T | Philanthropy, voluntarism, and grant-making foundations | 494 | 518 | 527 | 575 | 623 | 2,737 |
| U | Science and technology | 116 | 130 | 132 | 134 | 136 | 648 |
| V | Social science | 23 | 25 | 24 | 31 | 32 | 135 |
| W | Public and societal benefit | 242 | 267 | 239 | 259 | 262 | 1,269 |
| X | Religion-related | 166 | 177 | 155 | 154 | 170 | 822 |
| Y | Mutual and membership benefit | 1,669 | 1,710 | 1,823 | 1,806 | 1,842 | 8,850 |
| Total | 16,278 | 17,838 | 16,518 | 17,018 | 17,634 | 85,286 |
Source. From the National Center for Charitable Statistics (2019).
Data Availability
Declaration of Conflicting Interests
The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Funding
The author(s) received no financial support for the research, authorship, and/or publication of this article.
