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Variable Risk Preference Bias

David Blanchett, CFA, CFP® Head of Retirement Research Morningstar Investment Management [email protected]

Michael Finke, Ph.D., CFP® Professor and Ph.D CoordinatorDepartment of Personal Financial Planning Texas Tech University [email protected]

Michael Guillemette, Ph.D. Assistant ProfessorDepartment of Personal Financial Planning University of Missouri [email protected]

22 W Washington, Chicago, ILWorking Draft, July 7, 2014

of 25©2014 Morningstar. All rights reserved. This document includes proprietary material of Morningstar. Reproduction, transcription or other use, by any means, in whole or in part, without the prior written consent of Morningstar is prohibited. The Morningstar Investment Management group of Morningstar, Inc. includes Morningstar Associates, Ibbotson Associates, and Morningstar Investment Services, which are registered investment advisors and wholly owned subsidiaries of Morningstar, Inc. The Morningstar name and logo are registered marks of Morningstar.

Abstract

There is a growing body of literature that finds evidence of time varying risk aversion. Using a unique dataset with daily responses to a risk tolerance questionnaire from participants in a defined contribution plan, we find significant evidence that risk aversion is time-varying and that changes in risk aversion are primarily related to changes in investor expectations instead of historical market returns. Time-varying risk aversion has important implications for the demand for risky assets if investors reduce demand for stocks when valuations are most attractive.

We note a statistically significant relation between time-varying risk aversion and net equity mutual fund flows, or a variable risk preference bias. We find that net equity flows for more sophisticated investors, such as those who use index (versus active) mutual funds and purchase institutional share classes, exhibit lower time-varying risk aversion. We also find a statistically significant negative relation between time-varying risk aversion and net equity mutual fund flows when sorted by 12b-1 fees. Financial advisor compensation models focused on trail commissions may provide a valuable de-biasing incentive that makes investors less susceptible to the variable risk preference bias.


Variable Risk Preference Bias

Past research on risk aversion has focused primarily on determining which investor characteristics such as age, gender, or income are related to risk aversion (Gibson, Michayluk and Van de Venter, 2013). A growing body of research investigates whether investor risk aversion varies over time. Determining risk aversion is becoming increasingly important both in the United States and internationally for compliance and suitability purposes among financial advisors who are building portfolios for clients.

We use a unique dataset with daily responses to a risk tolerance questionnaire from participants in a defined contribution plan to explore time-varying risk aversion. We estimate whether this change in risk aversion is affected by prior return experience or from expectations of future equity performance. Our results suggest that changes in risk aversion appear to be largely a function of expectations.

Next, we explore the implications of time-varying risk aversion on demand for equity mutual funds. Individual investors suffer wealth losses by making poor market-timing decisions (e.g., from chasing past returns). We note a statistically significant relation between time-varying risk aversion and net equity mutual fund flows, or variable risk preference bias. Net equity flows for more sophisticated fund investors, such as those who use index (versus active) mutual funds and purchase institutional share classes, exhibit a lower relation to time-varying risk aversion and are therefore less likely to suffer underperformance over time.

We also find a statistically significant negative relation between time-varying risk aversion and net equity mutual fund flows when sorted by 12b-1 fees. Financial advisor compensation models focused on trail commissions may provide a valuable de-biasing incentive that makes investors less susceptible to the variable-risk preference bias.


Literature Review

The majority of existing research on risk aversion has focused on determining the investor character-istics that are related to risk aversion. While the findings have varied (Gibson, Michayluk, and Van de Venter, 2013), more risk-averse individuals are likely to be older, lower income, in poor health, not self-employed, female, married, to not use a financial advisor, and to have less investment knowledge and wealth than less risk-averse individuals.

Risk aversion can be estimated in a variety of ways. One of the most popular methods is through some type of a risk tolerance survey instrument such as a risk tolerance questionnaire (RTQ). Risk aversion also can potentially be estimated through portfolio holdings if portfolio selection is assumed to reveal preferences. However, portfolio holdings may be an imprecise measure of risk aversion if allocations are largely the result of random returns and inertia (Brunnermeier and Nagel, 2008). For example, Samuelson and Zeckhauser (1988) and Ameriks and Zeldes (2004), among others, find that most investors rarely trade or rebalance their portfolio.

Traditional finance theory assumes that risk aversion is not time-varying. Fama (1984), however, finds that the pattern of exchange rate movements can only be explained using existing asset pricing models if aggregate risk aversion is time-varying. The large short-run variation in U.S. stock prices may also be explained through variation in risk preferences (Campbell and Cochrane, 1999). An event like the 2008 financial crisis could have a strong impact on individual risk aversion because of its salience (Kahneman and Tversky, 1973). Malmendier and Nagel (2011) found that dramatic market experiences such as the Great Depression can have a permanent impact on investor risk perceptions.

Guiso, Sapienza, and Zingales (2013) found that both a qualitative and a quantitative measure of risk aversion among Italian bank customers increased substantially following the 2008 Global Financial Crisis (GFC). They note risk aversion changes are correlated with portfolio choices, but are uncorre-lated with standard factors that affect risk aversion such as wealth, consumption habits, and background risks. Combining monthly survey data with matching trading records from clients of a large discount broker in the Netherlands, Hoffman, Post, and Pennings (2013) found that investor market perceptions fluctuated significantly between April 2008 and March 2009, but risk tolerance and risk perception were less volatile than return expectations.

Using survey responses from clients at a UK online brokerage between September 2008 and June 2009, Weber, Weber, and Nosic (2013) find that risk attitude is relatively stable, while subjective risk and return expectations change with external market events (though not necessarily in a rational way). Bateman, Islam, Louviere, Satchell, and Thorp (2011) implement a discrete choice experiment


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in Australia to investigate changes in individual risk preferences from two surveys conducted in March 2007 and October 2008 and find a modest decline in risk tolerance and preference for riskier investment options.

Gibson, Michayluk, and Van de Venter (2013) analyze risk tolerance scores of 2,327 individuals immediately following the GFC and find lower risk tolerance among respondents who perceived the stock market to be riskier than it was two years ago. Those who are more risk tolerant have more positive stock market expectations. This relation between market experience and expected returns is consistent with De Bondt and Thaler (1985), who suggest investors overweight the recent past when forming future return expectations. However, investor perceptions appear to provide additional information beyond past return experience alone.

Experiences have the potential to affect risk aversion in different ways. For example, Staw (1976) notes the existence of escalation of commitment in which individuals responsible for a negative consequence are likely to take on more risk following a loss versus a gain. This is consistent with the disposition effect identified by Odean (1998), where investors are more reluctant to sell losing stocks than winning stocks. In contrast, Thaler and Johnson (1990) as well as Barberis (2011) find that experiencing a number of consecutive losses reduces investors’ subsequent willingness to take risks. These differences can potentially be based on how the decision or outcomes are framed.

Brunnermeier and Nagel (2008) find a significant positive relation between changes in liquid wealth and the probability of stock market entry which is inconsistent with a with constant relative risk aversion (CRRA) model. Sahm (2012) also shows that an improvement in macroeconomic conditions is associated with an increase in risk tolerance, an effect also noted by Yao and Curl (2011) using a longer dataset. One problem with these findings is that each is based on some type of holdings data that may be subject to inertia.

An individual’s risk-taking depends on risk preferences as well as subjective estimates of expected return and volatility (Markowitz, 1952). Changes in expectations of the riskiness of stocks can affect their demand, particularly if investors are sensitive to market losses (Tversky and Kahneman, 1992). Possible measures of expectations include the closed-end fund discount, turnover, and demand for IPOs. Expectations can also be estimated through survey data such as the AAII Bullish metric. Baker and Wurgler (2006) note that sentiment has been negatively related to future stock prices. Changes in perception could affect the demand for risky assets in portfolios, especially if investors are loss averse (Tversky and Kahneman, 1992).

A variety of factors are likely to shape investor expectations. During the GFC, investors were ex- posed to an unusually high volume of dramatic and unexpected news. Dzielinski (2012) notes that news can affect both short- and long-term stock market returns by creating uncertainty about the future. Sicherman, Loewenstein, Seppi, and Utkus (2013) find that 401(k) account-level daily


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logins increase with more frequent news media reporting about the stock market and decrease with increases in the VIX Index. These findings suggest that investor risk preferences may arise from behavioral adaptations (when and what to pay attention to) as well as from innate psychological predispositions.

Barberis (2011) argues that the representativeness heuristic is largely responsible for the overly optimistic pre-GFC risk and return expectation formation. The manner in which publicly available information is processed may explain heterogeneity in stock market expectations (Hurd, 2009, Dominitz and Manski, 2011). Investor expectations are developed probabilistically (Doukas, Kim, and Pantzalis, 2004), likely by messages conveyed in the media. Media messages may or may not come to the attention of investors, contributing to differences in return expectations (Carroll, 2003). After the stock market crash of 2008-2009, there was a larger disagreement for future one-year return expectations among stockholders compared to non-stockholders (Hudomiet, Kézdi, and Willis, 2011). Greater variation in return expectations among stockholders during the GFC is likely due to experienced returns.

Prior gains and losses have been found to alter the willingness to take risk. Investors derive utility not only from consumption but also from changes in their final wealth value (Barberis, Huang and Santos, 2001). Prospect theory would predict that investors are much more sensitive to reductions in their final wealth values than to increases (Kahneman and Tversky 1979). After stock prices rise, individuals should become more willing to take risk because prior gains will provide a cushion from subsequent losses,like a gambler who feels that she can take greater risks after hitting the jackpot since she is playing with “house money” (Thaler and Johnson, 1990). After prior losses, investors become less willing to take risk as they are more sensitive to additional setbacks in their final wealth values below their reference point (Barberis, Huang and Santos, 2001). The perception of the risk-return tradeoff has been found to depend on changes in prior stock performance (De Bondt, 1993). Dutch stock prices and expectations of future stock prices increased from 2004 to 2006, sug- gesting that expectations are influenced by prior equity returns (Hurd, Van Rooij, and Winter, 2011).

Changes in risk and return expectations may affect the demand for risky assets. Stock allocations tend to be higher for investors who anticipate higher future returns (Vissing-Jorgensen, 2004; Amromin and Sharpe, 2012). Stock mutual funds have historically had higher net inflows relative to bond funds during bull markets (ICI Factbook). Investor dollars should flow away from stock funds after significant gains if investors maintain constant portfolio weights. Friesen and Sapp (2007), however, find that mutual fund investors lose 1.6% annually, primarily because equity fund flows are negative during bear markets. This effect can also be seen in the gap between dollar-weighted fund performance and the total return for mutual funds which exceeds 1.0% (Kinnel, 2014).

The research on the differences in the relative ability of individual and institutional investors is mixed. Barber and Odean (2013) provide a relatively exhaustive review of the existing empirical and theo-


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retical literature and note that individuals are prone to a number of behaviors that are likely to lead (and have led) to underperformance over time. For example, individual investors trade frequently, tend to hold undiversified portfolios, and are unduly influenced by media and past experience. While the long-term outperformance of institutional investors is questionable (e.g., when viewing the relative performance of actively managed mutual funds), institutional investors, in theory, should suffer less from these biases and outperform individuals.

Given the relatively poor level of financial literacy noted by the general public (Lusardi and Mitchell, 2007), financial advisors can help reduce investor underperformance by counseling individuals to maintain a constant portfolio allocation despite periodic market price fluctuations. The method of advisor compensation, however, may discourage financial service professionals from de-biasing a client (Anagol, Cole, and Sarkar, 2013). The two primary methods of advisor compensation through mutual funds are an immediate front-end load or some type of trailing 12b-1 fee that continues for the duration of ownership. Higher front-end fees give the advisor an incentive not to de-bias clients because a front-end load is only paid if the client actually buys a new fund. A self-serving advisor will encourage a client to reallocate into new funds as their risk tolerance changes over time. An advisor compensated based on a percentage of existing funds will be more likely to de-bias an investor whose risk aversion changes, because the advisor does not receive additional compensation if an investor switches into a new fund.


Data

We collect the responses of participants in a risk tolerance questionnaire (RTQ) that is part of a managed account solution offered by Morningstar Associates, LLC. The RTQ, included in Appendix 1, consists of three questions, each with three possible responses. The same three risk tolerance questions are asked over the entire period, from January 2006 to October 2013. The RTQ taken by the individual when first entering the site is used for the analysis. While a few individuals take the RTQ more than once, the analysis is limited to the first RTQ completed due to questions surrounding the reliability of the repeat responses.1

The level of risk aversion for each investor is based on the total score across all three questions. While each question focuses on slightly different aspects of risk aversion, a composite score is used for robustness purposes. In addition to the RTQ responses, data is also available on participant date of birth, account balance, salary, savings rate, and holdings immediately before taking the RTQ. The account balance and savings rate relate solely to the advisable account, which is generally going to be part of a defined contribution plan such as a 401(k). Salary and account balance are converted into October 2013 values based on CPI-U data obtained from the Bureau of Labor Statistics.

There are 9,449 different investments held by participants. Not all of these investments are identi-fiable through the ticker or SecId (which is the unique Morningstar, Inc. ticker). For all investments without an identifiable ticker or SecId with a total balance of at least $100,000 across all partici-pants, a proxy was identified based on the name of the investment (i.e., whether it was equity, fixed, or allocation). The actual investment or an available proxy was identified for 99.05% of total assets.

The relative risk of each investment is based on its equity allocation. The equity allocation is the historical monthly log rescaled equity allocation for that fund using data obtained from Morningstar, Inc. In addition to determining the equity allocation, the percentage of total assets invested in an asset allocation fund (such as a target date fund) is also determined. All funds with the Morningstar Global Broad Category Group are considered to be asset allocation funds, and these are investments like target-date funds or balanced allocations that are generally a combination of stocks and bonds. These are identified separately, because a participant who chooses to use an allocation fund is effectively deferring the management of his or her account to a professional investment manager and is not trying to build a portfolio from the available investment menu.

1 After receiving the portfolio recommendation through the Morningstar Associates managed account solution, many individuals completing the RTQ will immediately re-take the RTQ or change other pertinent information, likely as an attempt to adjust the recommended portfolio allocation.


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There are a variety of methods that can be used to estimate risk aversion. One approach introduced by Merton (1969), suggests an investor’s risk aversion can be determined based on the share of wealth invested in equities, the equity risk premium, and the risk of equities. A problem with this model is that it requires a number of assumptions that are each likely to be time-varying. The equity allocation is therefore used for simplicity as a proxy for the riskiness of the investor’s portfolio.

A number of constraints are imposed on the data. First, data for each variable must be available for each participant. Second, the inflation-adjusted salary for the investor must be at least $5,000. To participate in a 401(k), an individual must have a salary and must generally be a full-time employee. Third, at least 95% of the participant’s holdings must have an identifiable ticker. The application of these screens results in a dataset of 28,867 individuals.

The proxy for historical market performance is the annual historical return of the S&P 500 Index. We use the S&P 500 because of its salience because it is followed by investors of varying levels of sophistication (Sicherman, Loewenstein, Seppi, and Utkus, 2013). Rerunning the analysis using other total return indexes such as the Wilshire 5000 has no significant impact on our findings.

Future stock market expectations are based on data from the Thomson Reuters/University of Michigan Survey of Consumers, which collects the estimated probability of an expected increase in the stock market in the next year. The question specifically asks: “What do you think the percent chance that this one thousand dollar investment will increase in value in the year ahead, so that it is worth more than one thousand dollars one year from now?” The mean response is used as a proxy for the general public’s expectation of stock market performance in the next year.

Table 1 shows descriptive statistics for the variables included in the analysis.

Table 1: Descriptive Statistics for All Variables

Mean Median Std Dev Min Max

Risk Aversion 4.92 5.00 1.67 3.00 9.00

Age 41.92 41.56 10.84 16.79 89.04

Balance ($) 203,623 74,838 358,196 0 10,117,057

Income ($) 86,461 74,006 54,583 5,074 1,138,549

Savings (%) 7.60 6.00 6.86 0.00 100.00

Equity (%) 75.44 80.31 20.41 0.00 100.00

Alloc (%) 24.83 6.06 34.39 0.00 100.00

Past Return (%) 5.07 9.73 19.23 –44.76 50.25

S&P 500 Level 1,264.69 1,310.33 189.53 735.09 1,549.38

Expectations 50.27 50.50 6.51 34.00 62.20


The proxy for expectations for this analysis is based on the average beliefs of average non-institu-tional investors. This belief indicator of small investors is used because the RTQ responses are from individuals enrolled in a defined contribution retirement plan who are unlikely to be expert investors. The correlation between institutional and individual investors has been modest (.43 historically). In contrast, the correlation between the Yale International Center for Finance Individual One-Year Confidence Index and the Probability of Stock Increase has been much higher (.708).

We convert the raw risk aversion scores to z-values (z) by subtracting the mean value for the series (μ) from the observed value (x), where that number is then divided by the standard deviation of the series (), as noted by equation 1.

Equation 1:


Time Varying Risk Aversion

Recent research provides some evidence that risk aversion varies among individual investors over time (Guiso, Sapienza, and Zingales, 2013). The average monthly risk aversion scores from our dataset are shown in Figure 1 along with the S&P 500 Index to illustrate the relation between stock returns and risk aversion over time.

Average investor risk aversion is not constant over time. The maximum average monthly risk aversion score over the data series was 5.405, while the minimum average score was 4.525. The overall monthly average risk aversion score was 4.949. These changes represent a significant magnitude of variation because the potential scores are bounded by 3.000 and 9.000 where a score of 3.000 indicates a low level of risk aversion and a score of 9.000 indicates a high level of risk aversion.

4.00

4.25

4.50

4.75

5.00

5.25

5.50 5.50

5.25

5.00

4.75

4.50

4.25

1500

1300

1000

900

700

1700

Jan 2006 May 2007 Sep 2008 Feb 2010 Jun 2011 Sep 2011

Average Risk Aversion S&P 500 Index Level

Figure 1: Monthly Average Risk Aversion Values and S&P 500 Index Level


What Drives Time Varying Risk Aversion

While average investor risk tolerance changes over time, there are a number of other investor and market characteristics that affect risk aversion (Gibson, Michayluk, and Van de Venter, 2013). Two potential drivers of risk aversion are historical experiences (i.e., past returns) and future expectations of stock market performance (Malmendier and Nagel (2011), Baker and Wurgler (2006).

To determine whether recent market return experiences or expectations about future market perfor-mance can better explain time-varying risk aversion, we model average monthly risk-tolerance scores as a function of investor characteristics, past returns, current market values, and future expectations.

Age, balance, income, and savings rates are values provided either by the participant or the defined contribution recordkeeper before the RTQ is completed. The balance does not include any assets outside the defined contribution plan (such as an IRA) and the savings rate is based entirely on the percentage of reported income being saved by the participant within that defined contribution plan and ignores any outside savings. Allocation fund usage is based on the percentage of total assets the individual has in an asset allocation fund prior to taking the RTQ, which includes target-date funds.

Past return experience is calculated as the change in the level of the S&P 500 Index during the rolling year prior to taking the RTQ. Current market values are defined as the level of the S&P 500 the date the RTQ is taken. Investor expectation is based on the Thomson Reuters/University of Michigan Survey of Consumers dataset, which provides the mean estimated probability of an expected increase in the stock market by an average investor in the next year the month the RTQ is taken.

Table 2 shows average risk aversion by age, retirement account balance, income, savings rate, equity allocation, percentage invested in asset allocation funds, historical returns, S&P 500 Index level, and investor expectations. For each variable there are five groups.


Table 2: Average Risk Aversion Score, Standard Deviation, and Group Size by Variable

Variable Group # Minimum Maximum Mean RA Std Dev n

Age 1 0 25 4.51 1.54 1,286

2 25 35 4.55 1.51 7,459

3 35 45 4.63 1.55 8,192

4 45 55 5.15 1.66 7,885

5 55 100 5.94 1.81 3,805

Balance 1 $0 $5,000 5.07 1.72 2,970

2 $5,000 $25,000 4.95 1.69 5,269

3 $25,000 $100,000 4.86 1.67 7,920

4 $100,000 $250,000 4.88 1.67 5,765

5 $250,000 $20,000,000 4.94 1.63 6,703

Income 1 $0 $30,000 5.65 1.85 1,134

2 $30,000 $50,000 5.23 1.77 5,431

3 $50,000 $75,000 4.96 1.68 8,062

4 $75,000 $125,000 4.75 1.61 9,404

5 $125,000 $1,000,000 4.66 1.51 4,606

Savings (%) 1 0% 4% 5.03 1.73 9,043

2 4% 7% 4.98 1.67 7,622

3 7% 10% 4.80 1.61 5,386

4 10% 13% 4.68 1.57 2,078

5 13% 100% 4.87 1.66 4,498

Equity (%) 1 0% 40% 5.84 1.93 1,718

2 40% 60% 5.63 1.79 3,680

3 60% 80% 5.05 1.61 8,714

4 80% 95% 4.58 1.53 11,124

5 95% 100% 4.47 1.51 3,391

Alloc (%) 1 0% 1% 4.86 1.72 12,622

2 1% 20% 4.85 1.60 5,478

3 20% 40% 4.90 1.60 3,741

4 40% 70% 4.98 1.63 2,296

5 70% 100% 5.17 1.69 4,490

Past Return 1 –100.00% –15.00% 5.06 1.81 3,808

2 –15.00% 0.00% 4.86 1.64 4,063

3 0.00% 10.00% 4.97 1.67 7,397

4 10.00% 20.00% 4.85 1.63 9,309

5 20.00% 100.00% 4.94 1.66 4,050

S&P 500 Level 1 0 950 5.09 1.83 2,407

2 950 1,100 5.04 1.72 3,315

3 1,100 1,250 5.07 1.70 4,364

4 1,250 1,400 4.95 1.65 9,867

5 1,400 10,000 4.72 1.60 8,674

Expectations 1 30 45 5.11 1.77 5,900

2 45 50 4.99 1.67 7,644

3 50 55 4.94 1.66 7,156

4 55 60 4.71 1.61 5,898

5 60 65 4.67 1.55 2,029


We estimate a multivariate regression that models an individual's risk tolerance score as a function of age, balance, salary, savings rate, equity allocation, and asset allocation fund share. Variables are converted to z-values in order to compare their relative importance.

Individual participant risk tolerance models (Table 3) show that expectations (future) have a larger absolute impact on aggregate mean risk tolerance score than experiences (past) or the current market environment (present). Investor characteristics are also important predictors of individual risk aversion. Our research suggests that risk aversion increases with investor age and with the share of the portfolio invested in asset allocation funds, and declines with income, account balance, savings percentage, and portfolio equity allocation.

We also investigate whether investor risk tolerance is affected by past returns or future expectations similarly among investor groups. For example, older individuals may respond more to past returns (experiences) while younger investors may be influenced more heavily by expectations. We model the relative importance of past returns and future expectations among various groups of investors in Table 4. Control variables are included in each analysis and only the coefficients of past returns and expectations are reported in the table. A slope coefficient is included that is estimated by running a simple univariate regression of the group values (1 through 5) against the respective past and future values. The slope estimate captures whether past returns or future expectations increase or decrease monotonically with age, account size, income, savings rate, portfolio equity share, and current equity allocation.

Table 3: Regressions on Risk Aversion and All Individual z-adjusted Variables

Model Number 1 2 3 4 5 6

Intercept 4.922*** 4.922 *** 4.922*** 4.922*** 4.922*** 4.922***

past –0.030*** 0.028*** 0.036***

present –0.082*** –0.042***

future –0.092*** –0.108*** –0.080***

age 0.462*** 0.462*** 0.458*** 0.458*** 0.457*** 0.457***

balance –0.062*** –0.061*** –0.062*** –0.062*** –0.063*** –0.063***

income –0.281*** –0.281*** –0.276*** –0.270*** –0.268*** –0.269***

savings (%) –0.057*** –0.056*** –0.050*** –0.046*** –0.045*** –0.044***

equity (%) –0.300*** –0.299*** –0.296*** –0.296*** –0.296*** –0.295***

alloc (%) 0.084*** 0.084*** 0.087*** 0.085*** 0.086*** 0.087***

Adjusted R2 (%) 14.83 14.86 15.06 15.12 15.14 15.16

n 28,627 28,627 28,627 28,627 28,627 28,627

* denotes significance at p < 0.1, ** denotes significance at p < 0.05, *** denotes significance at p < 0.01


Consistent with the results in Table 3, the absolute value of each of the expectation’s regression coefficients (future) is greater than the experience’s regression coefficient (past) for all but one of the regressions (the low age group). Also, similar to the model 4 regression in Table 3, the sign of past is generally opposite the expected value because the correlation between historical returns and risk aversion is negative (the coefficient should be negative, not positive). Very few past coefficients are statistically significant, while the majority future values are. This further suggests that expectations are a more important driver of time-varying risk aversion than historical returns. When looking at the slope values by groups, it appears that the relation between expectations (future) and time-varying risk aversion is strongest for investors who are generally more conservative—those who are older and have lower salaries, lower savings rates, and lower equity allocations.

Table 4: Regressions on Risk Aversion and All Individual z-adjusted Groups Variables

By Group, Low to High

Age 1 2 3 4 5 Slope

past 0.115** 0.003 0.028 0.030 0.048 –0.011

future –0.042 –0.055*** –0.106*** –0.125*** –0.214*** –0.041**

R² (%) 6.79 7.06 7.06 8.86 11.45 —

Balance 1 2 3 4 5 Slope

past 0.127*** –0.023 0.048** 0.036 0.011 –0.017

future –0.165*** –0.073*** –0.157*** –0.109*** –0.082*** 0.013

R² (%) 10.48 12.77 14.26 17.91 19.62 —

Salary 1 2 3 4 5 Slope

past 0.092 0.014 0.042** 0.003 0.047* –0.010

future –0.216*** –0.085*** –0.156*** –0.060*** –0.109*** 0.024

R² (%) 12.86 12.13 14.58 14.05 14.16 —

Savings Rate 1 2 3 4 5 Slope

past 0.052*** 0.035* 0.010 0.067 0.011 –0.005

future –0.174*** –0.103*** –0.084*** –0.082** –0.080*** 0.021*

R² (%) 11.57 14.59 16.09 15.53 19.10 —

Equity Allocation 1 2 3 4 5 Slope

past 0.076 0.108*** 0.025 0.023 0.007 –0.022*

future –0.259*** –0.196*** –0.103*** –0.094*** –0.088*** 0.044**

R² (%) 11.00 12.35 7.42 7.73 10.89 —

Allocation Fund Usage 1 2 3 4 5 Slope

past 0.073*** 0.021 –0.008 0.052 –0.042 –0.020

future –0.165*** –0.125*** 0.019 –0.090** –0.094*** 0.018

R² (%) 16.02 13.48 13.04 16.28 10.63 —



Risk Aversion and Mutual Fund Demand

The results of the analysis in the previous sections suggest risk aversion is time varying, and that a key driver in the change over time is likely driven by changes in future market expectations of investors. If changes in risk aversion affect investing behaviors, time-varying risk aversion could affect the demand for risky assets over time. For example, if investors have positive (negative) expectations about the future return of stocks, the demand for risk assets may increase (decrease).

We estimate demand for equity mutual funds through net cash flows, defined as the total cash flows to equity mutual funds minus the total cash flows to bond mutual funds. Equity mutual funds are considered those mutual funds within the “Equity” broad asset class group as defined by Morningstar, Inc. while bond funds are those within Morningstar, Inc.'s broad asset class of “Fixed Income.” Table 5 includes information about the net equity mutual fund flows, the CAPE Ratio (data obtained from Robert Shiller’s website2), and the future one-year return of the S&P 500 for given risk aversion score deciles.

There is a significant relation between risk aversion score decile and net equity mutual fund flows, CAPE Ratio, and future one-year returns. The negative relation between risk aversion and net equity flows suggests that investors tend to favor equities when risk aversion is the lowest, which is also when markets have the least attractive valuations based on the CAPE Ratio and lowest future return one-year returns. Investors appear to be less attracted to stock funds when valuations are most

Table 5: Risk aversion Score Deciles, Net Mutual Fund Flows, CAPE Ratio, and Future One-Year Returns

Risk Aversion Score Decile

Net Equity Mutual Fund Flows ($) CAPE Ratio Future One Year

Return (%)

1 (8,559) 26.13 –21.17

2 2,976 25.25 –8.06

3 (3,427) 24.45 –11.80

4 (18,991) 19.73 19.94

5 (6,221) 22.79 12.44

6 (16,232) 21.35 6.27

7 (6,102) 20.62 13.57

8 (21,211) 20.98 18.18

9 (26,999) 19.23 25.51

10 (24,250) 19.95 17.85

Correlation to Risk Aversion –0.756 –0.848 0.834

2 http://www.econ.yale.edu/~shiller/data.htm


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attractive. The relation between future one-year returns and risk aversion is notable because the relation with historical returns was so poor (note the weak and relatively insignificant past coef-ficient in Tables 3 and 4).

Because risk aversion is time-varying, it is possible that Risk Tolerance Questionnaires (RTQs) may contribute to individual investor underperformance if the scores influence asset allocation selected by the plan providers. The more sophisticated investors may be less susceptible to risk preference bias. One way to determine the relative investor sophistication is to look at the historical relation between net equity mutual fund flows for different types of mutual funds and risk aversion over time. An investor with constant risk preferences would rationally rebalance to equity mutual funds during a bear market. A biased investor may be less attracted to equity funds as valuations fall, increasing the portfolio share of safe assets when valuations of risky assets are most attractive.

We use three different methods to classify investors based on net equity mutual fund flows. First, we sort by whether funds are actively or passively managed. Passive mutual funds are assumed to be those classified as “Index” funds by Morningstar, Inc. while all other mutual funds are considered actively managed funds. Del Guercio and Reuter (2013) find evidence that investors in passive funds are more sophisticated than investors in active funds that are most often sold through the broker channel.

Second, we classify mutual funds into four different fund groups: Broker-Sold, Institutional, Investor, or Retirement. Broker-Sold funds include A, B, and C shares, and Advisor share funds. Investor funds are categorized as either no load or investor. All classifications are constructed by Morningstar Inc. Third, we further decompose the broker-sold category by the form of compensation paid to the financial advisor. 12b-1 fees are technically annual marketing or distribution fees paid by a mutual fund and are generally used as a method to compensate advisors for selling the funds.

Differences in the method of compensation provided through share class structure may influence whether the advisor gains from de-biasing a client who is tempted to shift his or her portfolio to safety during an equity market decline. Class A shares compensate the advisor through the payment of an upfront load. Advisors may have an incentive to encourage a client to buy a safer fund (and pay a front-end load) when they feel more risk averse and then sell them another risky fund when their risk aversion declines after prices rise. This provides a disincentive to de-bias a client. Advisors who receive compensation through higher trail commissions (C shares) have no incentive to encourage a client to shift out of risky funds during a temporary increase in risk aversion. Higher trail compensation may provide a valuable de-biasing incentive since the advisor does not need to sell a new fund to receive compensation. We hypothesize that lower 12b-1 fees lead to an incentive for advisors not to de-bias clients since their compensation is increased by catering to investor variable risk preferences by selling them new funds. For example, if the stock market falls and the client becomes more risk averse, an advisor compensated through front-end commissions has a


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greater incentive to move that client into bonds than an advisor who receives more commissions on a trail basis.

For this analysis, the estimated net flow by share class is obtained from Morningstar DirectSM from January 2006 to October 2013. The dataset is survivorship-bias free and 31,868 unique share classes are included in the analysis. Net flow is determined by subtracting the total flows for equity funds minus the total flows for fixed income (or bond) funds. We assume that the investor chooses to invest in equities or bonds within that fund-type. For example, with the Index (Active) group comparison, the assumption is that an investor would select either an Index (Active) equity or bond fund, and not consider the opposite type.

The regression model used to estimate the relation between net equity mutual fund flows (EqFF) for different types of mutual funds (t) based on the level of risk aversion (RAS) is noted in equation 2. Within this equation the optimal flow would be positive (which would imply a rational rebalancing given constant risk tolerance) or zero (which would imply no rebalancing). A negative flow coefficient would imply a variable risk preference bias in which investors shift money away from equity mutual funds when average levels of risk aversion increase. The results of the univariate regressions are shown in Table 6.

Equation 2:

Table 6: Monthly Regressions of Net Equity Flows on Risk Aversion for Varying Mutual Fund Types

flow R2 (%)

Index 4.803*** –0.971*** 4.16

Active 8.788*** –1.776*** 13.93

Broker-Sold 7.288*** –1.473*** 9.58

Institutional 5.743*** –1.160*** 5.95

Investor 8.208*** –1.658*** 12.15

Retirement 9.116*** –1.842*** 14.98

None 11.862*** –2.397*** 25.37

1-24 bps 11.644*** –2.353*** 24.45

25-50 bps 9.124*** –1.844*** 15.01

51-75 bps 6.595*** –1.332*** 7.84

75 bps+ 5.640*** –1.140*** 5.74



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Results suggest that more sophisticated investors exhibit a lower relation to time-varying risk aversion and therefore are less likely to be impacted by the variable risk preference bias. Investors who purchase index mutual funds (versus active mutual funds) and investors who purchase institu-tional shares do not reduce their demand for equity mutual funds as sharply as active fund investors.

Higher trail compensation (and lower front-end commission compensation) appears to provide an incentive to de-bias clients. Variable risk preferences result in lower flows away from equity mutual funds when trail compensation is higher. If advisors receive the same compensation whether they sell a new fund or not, they are less likely to cater to variable client preferences by selling them a new fund that matches their changing risk aversion. The effect is monotonic with 12b-1 fees. Advisors compensated with front-load commissions (and lower 12b-1 fees) may be more likely to encourage the purchase of new funds to match an investor’s changing risk preferences.


Conclusions

Traditional finance theory assumes that risk aversion is not time-varying; however, there is a growing body of empirical research that suggests that risk preferences change with market conditions. Using a unique dataset with daily responses to a risk tolerance questionnaire from participants in a defined contribution plan, we find significant evidence that risk aversion is time-varying. We also note that investor expectations tend to be a better predictor of time-varying risk aversion than historical performance. So it appears that risk aversion is driven more by the unknown future than the known past. While investor expectations influence risk aversion over time, other investor attributes such as age, equity allocation, and salary appear to play an even greater role in shaping risk aversion.

Time-varying risk aversion has important implications for the demand for risky assets since investors tend to shy away from risky assets when valuations are most attractive and when traditional portfolio theory would predict greater demand for equities to rebalance a portfolio. This effect is especially noteworthy given the increasing use of risk tolerance questionnaires (RTQs) by advisors when recommending an optimal client portfolio allocation. This is noteworthy because the primary reason that individual investors underperform institutional investors is their tendency to sell equity mutual funds during a bear market.

More sophisticated investors, such as those who use index (versus active) mutual funds and purchase institutional share classes (i.e., have more wealth and therefore more implied investing human capital), exhibit lower time-varying risk aversion. We also note a consistent negative relation between time-varying risk aversion and net equity mutual fund flows when sorted by 12b-1 fees. Trail compensation, which provides the same incentive whether the client buys new funds to match their changing risk preferences, is associated with a lower variable risk preference bias. Financial advisor compensation schemes that provide greater compensation for acceding to variable risk preference biases are associated with a failure to de-bias. This finding is consistent with prior studies on perverse incentives from traditional commission models in financial services (Anagol, Cole, and Sarkar, 2013).


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Appendix

Risk Tolerance QuestionnaireAnswer the questions below to help refine the risk level assigned to Your Strategy by Morningstar. Please note that your answers will be added to many other factors considered for the final risk level.

When scoring the questionnaire, all “a” responses are assigned a value of 1, all “b” responses a value 2, and all “c” responses a value of 3. The higher the value assigned (1, 2, or 3) the higher the implied risk aversion from the response. The highest possible “risk score” would be a 9 (an individual who answered “c”) to each question, while the lowest possible “risk score” would be a 3 (an individual who answered “a” to each question).

The information, data, analyses, and opinions presented herein do not constitute investment advice; are provided as of the date written and solely for informational purposes only and therefore are not an offer to buy or sell a security; and are not warranted to be correct, complete or accurate. Past performance is not indicative and not a guarantee of future results.

This white paper contains certain forward-looking statements. We use words such as “expects”, “anticipates”, “believes”, “estimates”, “Forecasts”, and similar expressions to identify forward looking statements. Such forward-looking statements involve known and unknown risks, uncertainties and other factors which may cause the actual results to differ materially and/or substantially from any future results, performance or achievements expressed or implied by those projected in the forward-looking statements for any reason. Past performance does not guarantee future results.

Bear-Market Expectations

Short-term Risk Attitude

Assuming normal market conditions, what would you expect from your retirement investments over time?a. To generally keep pace with the stock marketb. To trail the stock market, but make a moderate gainc. To have a high degree of stability, but make a small gain

Long-term Expectations

Suppose the stock market performs unusually poorly (otherwise called a Bear Market) over the next decade. What would you expect from your retirement investments?a. To lose a lot of moneyb. To lose a little moneyc. To eke out a small gain

Which of these statements would best describe your attitudes regarding the performance of your retirement investments over the next two years?a. I can tolerate a significant loss in 2 years because I have a long term horizonb. I'd better at least break evenc. I'd better end up with at least a little more money than I started with

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