LITERATURE REVIEW
CAN DIVERSIFICATION BE LEARNED?
CAN DIVERSIFICATION BE LEARNED? Abstract This paper investigates the role of financial education in household portfolio allocation decisions using data from a survey of 1,385 professors at universities across the United States. The results suggest that knowledge of finance increases the likelihood that an investor will efficiently allocate his direct investments across the major asset classes, invest in foreign assets and hold a diversified equity portfolio. However, there is no evidence that investors who are more financially sophisticated make superior allocation decisions in their retirement savings. In particular, we find that irrespective of age and other domestic factors, Finance professors are more likely to allocate more than 70% of their retirement savings to Domestic Equities. We also find that English professors are more likely to practice a naïve diversification strategy of choosing a subset of the available funds and allocating equal proportion of their portfolio to each of the chosen funds.
JEL category: G11, D10, D31 Keywords: portfolio choice, diversification, behavioral finance
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1.
Introduction The benefits of diversification have been recognized and documented in the finance
literature for decades. Many chapters in finance textbooks have been devoted to portfolio theory, which focuses on how an investor should diversify his investments across stocks, bonds and other assets to maximize return and reduce risk. However, Bertaut & Starr-McCluer (2002) note that “the portfolio decisions of households in the United States is not very well understood”. Further, Statman (2004) acknowledges that the level of diversification observed in the equity portfolios of households in the United States presents a “puzzle”. In this paper, by comparing the investment behavior of individuals proficient in finance to those who have little knowledge of finance, we investigate whether knowledge of the benefits of diversification helps investors minimize risk. We survey Finance and English professors at universities across the United States to investigate the extent to which members of these two groups pursue diversification benefits. Since Finance professors have advanced knowledge of the benefits of diversification, if they make superior asset allocation decisions it may be attributed to their education in finance. On the other hand, if the investment patterns of Finance and English professors are found to be similar and they don’t hold diversified portfolios, then this would provide evidence that investment behavior is based more on psychological factors. In other words, rather than using the theories in finance textbooks, investors construct their portfolios based on their sentiments. We investigate if the individuals in our sample diversify across broad asset classes and within their equity portfolios. Since a number of diversification strategies may be justified for asset allocation, we ensure that the model is tractable by examining two indirect tests of active diversification. The first test investigates if individuals allocate greater than 70% of their direct
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investments to mutual funds or a mix of Stocks, Bonds and Cash. We find that after controlling for economic and demographic factors, individuals with knowledge of finance are more likely to efficiently allocate the majority of their direct investments. We also perform a similar study of allocations in retirement savings. For the faculty sample, we ask respondents to provide the breakdown of their retirement savings based on the TIAA-CREF® funds. Specifically, using the investments in five of the major funds and two sub-categories of the equities funds, we find no evidence that knowledge of finance increases the likelihood that an investor will invest the majority of his retirement savings either in Multi-asset investments or a mix of at least three of the available funds. While our asset allocation measure is admittedly crude, most financial professionals use heuristic measures in making recommendations to their clients. One such measure is based only on the age of the investor, whereby he allocates [100 – Age]% of his personal wealth to a diversified equity portfolio (see Malkiel (1996) p. 418). In the second test, we investigate the extent to which knowledge of finance increases the likelihood that an investor will seek the benefits of international diversification. We consider the inclusion of foreign stocks or bonds in an individual’s portfolio to be an indicator of international diversification. Lewis (1999) suggests that a US investor with mean-variance preferences should invest at least 40% of his portfolio in foreign stocks. We find that that after controlling for economic and demographic factors, Finance professors are more likely to invest in foreign stocks/bonds or foreign mutual funds and allocate a larger share of their retirement savings to international equities. To study whether knowledge of finance helps investors diversify their equity portfolio, we investigate three proxy measures of equity diversification. Each measure is conditional on the respondent investing a positive amount directly in individual stocks. The first measure of equity
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diversification is the probability of investing in more than 15 stocks; the second measure is the probability of investing in stocks from four or more sectors and the third measure is a combination of the first two, i.e., the probability of investing in 15 or more stocks from four or more sectors. Friend & Blume (1975), Kelly (1995) and Polkovnichenko (2005) use the Federal Reserve’s Survey of Consumer Finances (SCF) 1 data and find that among households that hold stocks directly, the median number of stocks held was less than three, suggesting a lack of diversification in investors’ equity portfolios. Our analysis shows that knowledge of finance increases the likelihood that an investor will diversify within his equity portfolio. However, after controlling for income and age, the impact is significantly reduced and is more related to the number of sectors chosen than the number of stocks held. We also investigate two diversification strategies that have received attention in the literature recently: A naïve diversification strategy or “framing 1/n heuristic” 2 in which the individual invests an equal proportion of his portfolio in each of the available asset categories; and a “conditional 1/n heuristic” diversification strategy in which the investor chooses a subset of the available asset categories and invests an equal proportion in each of the chosen categories. The framing 1/n heuristic strategy is considered irrational since the number of categories chosen depends on the number of choices available, while the conditional 1/n heuristic may be deemed rational. Agnew (2006) investigates the extent to which participants in a 401(k) plan practice each of these diversification strategies and finds that demographic factors are significant predictors in each of her models. We investigate whether after controlling for demographic factors, investors who have knowledge of finance are less likely to practice these naïve
1
The Survey of Consumer Finances is a triennial survey of US household balance sheet and demographic factors conducted by the Board of Governors of the Federal Reserve System.
2
See Shlomo and Thaler (2001) for a detailed description of these strategies.
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diversification strategies. We find that both Finance and English faculty are equally likely to practice the framing 1/n heuristic but the English professors are more likely to practice the conditional 1/n heuristic. This finding suggests that knowledge of finance does not necessarily lead to a reduction in less than fully rational behavior. 2.
Related Literature and Motivation
2.1. Household Portfolio Asset Allocation Decisions According to King & Leape (1998), the empirical literature on household savings behavior has focused primarily on the total amount of savings rather than relative allocations among different types of assets. Nonetheless, there is ample evidence of hetergeneity in household portfolio allocation decisions (see for example Curcuru et al. (2004)). This heterogeneity may be justified purely on the basis of differential risk tolerance. Canner et al. (1997) examine popular advice on portfolio allocation among cash, bonds, and stocks and find that the advice is not consistent with the mutual-fund separation theorem, which states that all investors should hold the same composition of risky assets. They find that popular advisors recommend that aggressive investors hold a lower ratio of bonds to stocks than conservative investors. However, in addition to the traditional variables such as age, income and wealth, some researchers have found that some seemingly “unlikely” candidates are contributory factors in the household portfolio allocation decision. These include marital status, gender and health status. Sunden & Surette (1998) use SCF data from 1992 and 1995 to investigate how individuals allocate assets in defined contribution plans and find that after controlling for a wide range of demographic, financial and attitudinal characteristics, gender and marital status are still important factors in the household portfolio allocation decision. They find that single women are
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less likely to invest a significant portion of their retirement savings in risky assets. They argue that with the increasing trend toward defined contribution (DC) plans, such sub-optimal portfolio allocation decisions could adversely impact the accumulated retirement wealth. Rosen & Wu (2004) analyze the role of health status in the household portfolio decision and find that the probability of holding different types of assets and the share of wealth allocated in each asset category is affected by the health status of members of the household. Their results suggest that households in poor health are less likely to own retirement accounts, bonds and risky assets. They point out that the health status effect does not seem to operate through the individual’s attitude towards risk. In his presidential address to the American Finance Association, Campbell (2006) acknowledges that even though “many households seek advice from financial planners and other experts, some households make decisions that are hard to reconcile with this advice or with any standard model.” While he hesitates to advocate expansion of financial education to avoid the potential mistakes that households make in their portfolio allocation decision, our basic motivation is to investigate whether this would be a plausible solution. In particular, we use two groups of investors who are similar in all respects except for their knowledge of finance. This allows us to investigate if individuals with superior knowledge of finance are more likely to make efficient portfolio allocation decisions.
2.2. International Diversification Researchers have considered the lack of investment in foreign stocks to be inconsistent with the standard theory of portfolio choice. Baxter & Jermann (1997) argue that the divergence between diversified portfolios and observed portfolios, the “international diversification puzzle” is wider than was thought. They suggest that whereas in the past this phenomenon could be
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explained by the lack of financial integration and national barriers to capital flows, the growth and integration of markets over recent years has not seen similar portfolio reallocations. For example, French & Poterba (1991) report that U.S. investors hold about 94% of their financial assets in the form of U.S. securities, and for Japan, the United Kingdom, and Germany, the portfolio share of domestic assets in each case exceeds 85%. More recently Lewis (1999) suggests that a US investor with mean-variance preferences should invest at least 40% of his portfolio in foreign stocks. However, Kalra et al. (2004) examine the effectiveness of international diversification in the presence of periodic rebalancing and associated transaction costs and find that the benefits of international diversification are much smaller than previously understood; they suggest that only a small allocation (10%) of domestic investor’s portfolio to international securities may be justified. In our empirical investigation, we quantify the differential impact of increased financial knowledge on international diversification ceteris paribus.
2.3. Equity Diversification There has been ample evidence in the finance literature of investors holding undiversified equity portfolios. We discuss a few of the more recent studies here. Goetzmann & Kumar (2008) study more than 40,000 stock accounts at a brokerage firm in the 1991-96 period and find that the mean number of stocks in a portfolio was four and the median number was three. In their sample, more than 25% of investor portfolios contain only one stock, more than 50% contain fewer than three stocks and in any given monthly time-period only 5-10% of the portfolios contain more than 10 stocks. The above investment behavior sheds some light on why investor portfolios have extremely high volatility and exhibit worse risk-return trade-off than randomly constructed portfolios.
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Polkovnichenko (2004) use SCF household data for the years 1983, 1989, 1992, 1995, 1998 and 2001 and find that most households that invest directly in stocks (i.e., not through mutual funds) had portfolios consisting of one to five stocks, with the median being between one and two. They also find that more wealthy investors hold more directly held stocks than the less wealthy. However, they conclude that most direct stockholders invest substantial fractions of their wealth in undiversified portfolios of individual stocks and often combine such investments with well-diversified mutual funds. Polkovnichenko (2004) suggests that while standard expected utility theories cannot reconcile these observations, they can be explained by rankdependent preference models. Statman (2004) argues that the levels of diversification in U.S. investors’ equity portfolio presents a puzzle, since based on the rules of mean-variance portfolio theory, optimal levels of stocks exceeds 300, but the average investor holds only three or four stocks. However, he acknowledges the finding of Campbell et al. (2001), who provide evidence that most of the benefits of equity diversification is obtained with a portfolio of 20 stocks. Statman (2004) suggests that the diversification puzzle can be solved in the context of Shefrin & Statman (2000) behavioral portfolio theory, wherein investors construct their portfolios as layered pyramids in which the bottom layers are designed for downside protection and the top layers are designed for upside potential. In our empirical investigation, we expand the scope of analysis beyond the number of individual stocks held and also include the number of sectors where the stocks are from. Cavaglia et al. (2000) examine five years of data from the twenty-one countries that comprise the current MSCI World Developed Markets and find that diversification across industries provides greater risk reduction benefits than diversification across countries.
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2.4. Naïve Diversification With the proliferation of mutual funds, most investors have been able to achieve the benefits of diversification indirectly. However, there is still empirical evidence of sub-optimal asset allocation and naïve diversification strategies being the norm rather than the exception. Benartzi & Thaler (2001) investigate diversification strategies in defined contribution plans and find that many investors follow a simple naïve strategy of dividing their contributions equally among all available investment alternatives and suggest that the diversification benefits achieved is a function of the available choices. Huberman & Jiang (2006) investigate the records of over half a million participants in more than 600, 401(k) plans and find that participants tend to allocate their contributions evenly across the funds they use with the tendency weakening with the number of funds used. They find that participants typically invest their savings in a small number of funds (between three and four), irrespective of the number of funds offered, (which is typically between four and fiftynine.) They suggest that their results are at odds with the finding that investors have a “propensity to diversify”, in studies such as Simonson (1990) and Read & Lowenstein (1995). In addition, unlike Benartzi & Thaler (2001) who find that participants follow the 1/n rule in defined contribution (DC) plans which would be irrational, Huberman & Jiang (2006) find that participants allocate 1/n to each of the chosen funds, which they consider to be consistent with K-fund separation theories. Agnew (2006) investigates behavioral biases in individual 401(k) investments by using data from an anonymous large benefits provider which includes detailed individual demographic and contribution data. The overall sample includes 73,699 eligible employees and the sub-sample of active participants includes a total of 22,979 employees with contribution allocations, where
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an employee is considered active if a contribution was made to the plan during the first two weeks of August 1998. Agnew (2006) investigates three naïve diversification strategies, the framing 1/n heuristic, the modified 1/n heuristic and the conditional 1/n heuristic. 3 In the framing 1/n heuristic, individuals distribute their contributions equally among the n choices available. In the modified 1/n heuristic, investors treat their company’s stock as a separate asset class and divide the remainder of their investment equally among the other asset classes. In the conditional 1/n heuristic, the individual divides his allocations evenly among the funds chosen, where the funds chosen may be less than the total offered. Agnew (2006) finds that salary and other demographic factors such as gender are significant predictors in each of these choices. She acknowledges that while the data used overcomes the common disadvantage of aggregation inherent in most studies involving plan data, her study still has the drawback of missing information on the participant’s assets outside the plan. In addition, variables that have been shown to impact asset allocation decisions such as marital status, education and financial literacy are missing from the dataset. In our empirical study, we use a broader set of control variables.
2.5. Survey of Finance Academicians A number of previous studies have used surveys of finance academicians to investigate financial economic theories. One of the most widely cited is the study done by Welch (2000) who use a survey of 226 academic financial economists to investigate if they are trend followers like most individual investors or do they instead rely on academic studies in forming their predictions of the market? Welch (2000) identifies a high level of heterogeneity in predictions of the equity premium puzzle among the respondents in his study even though they had similar information. He also finds that on average, there was a downward bias in the prediction versus 3
Agnew (2006) also investigates other allocation biases such as investing in company stock and choosing not to participate in the DC plan.
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historical values. As suggested by Welch (2000), this finding is “striking” since the equity premium is of fundamental importance in both asset pricing and corporate finance. 3.
Data and Empirical Methods
3.1. Survey of professors The data used in this study is from a survey of professors across the United States. During the summer of 2007, we manually collected the names and email addresses of Finance and English faculty at universities in the United States. We use a questionnaire to collect actual portfolio holdings and demographic information from each of the individuals selected. In Appendix A we provide the questionnaire used in our survey. The questionnaire was emailed to 4,381 finance professors and 4,447 English professors. To increase the rate of participation, two follow-up emails were sent to individuals who had not responded after one week and after two weeks respectively. We received responses from 1,430 of the finance professors and 414 of the English professors 4 for a response rate of 33% and 9% respectively. The survey includes information on their total investments in financial and non-financial assets, retirement savings and demographic variables. Since our primary aim is to investigate whether the Finance professors exhibit a greater propensity to diversify, we only include respondents that invest in financial assets either directly or through their retirement savings. The final sample consists of 1,147 finance professors and 238 English professors who own financial assets. The sample of respondents who currently invest in a retirement plan includes 1,074 Finance and 168 English professors. For the direct investments, we include an extensive set of categories that would be as 4
We also received email responses from some of the subjects citing reasons why they are unable or unwilling to participate. The reasons include being ill, being on sabbatical, being too busy to participate and having privacy concerns.
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inclusive as possible and also provide the granularity to identify any inherent sophistication. The first category includes safe assets; Checking Accounts, Savings Accounts, CDs and Government Bills and Bonds (hereafter referred to as Cash). The second category includes Federal Agency Bonds and Municipal Bonds. There are three separate categories for Corporate Bonds, Mutual Funds and Stocks and two categories for REITs and Derivatives. For the retirement savings, we use the funds offered by TIAA-CREF 5 . The TIAA-CREF has six major categories for investments but we give seven options in our question. Five of the options are the same as the five major categories of TIAA-CREF funds, (1) Fixed Income, (2) Guaranteed Income, (3) Money Market Investments, (4) Multi-Asset Investments and (5) Real Estate Funds. We separate the sixth TIAA-CREF category of Equities funds into two sub-categories of (1) EquitiesDomestic and (2) Equities-International 6 . Table 1 provides summary statistics for the overall sample as well as the sub-sample of Finance and English professors respectively. The number of participants who invest in each category and the mean allocation in each category are given for direct investments and retirement savings. Not surprisingly, Panel A shows that Cash is the most widely used category with 88.6% of the Finance faculty holding some Cash and 91.6% of the English faculty holding cash as part of their overall portfolio. For both groups, the largest allocation is to Mutual Funds. On average, the mean allocation to mutual funds is 60% for Finance professors and 51% for English professors. However, whereas Finance professors invest the second largest share of their portfolio in stocks, a mean of 34%, the second largest share of the English professors’ portfolio is held in Cash accounts, a mean of 46%. The mean allocation to Stocks by the English faculty is 5
TIAA-CREF is the largest manager of defined contribution retirement plans for employees of educational organizations.
6
We separate the Equities fund into Domestic Equities and International Equities to investigate international diversification in Section 2.3.3
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the same as that by the Finance faculty but ranks third in order of preference. Panel A also shows that relative to their Finance counterparts, English professors invest a larger share of their portfolio in Federal Agency Bonds and Municipal Bonds while the opposite holds for corporate bonds. In addition, Finance professors are twice as likely to invest in REITs and three times as likely to invest in derivatives as English Professors. The results for the retirement savings in Panel B are more similar between the Finance and English professors. Domestic Equities is the most widely used category for both the Finance and English professors, where on average the largest share is allocated; 55% by the Finance professors and 48% by the English professors. In addition, similar to the domestic equities, Finance professors invest slightly more in international equities than their English counterpart. On the other hand, the English professors invest a larger share in all of the other categories, i.e., in Real Estate, Fixed Income, Money Market, Guaranteed Income and Multi-Asset Investments. In summary, Table 1 provides preliminary evidence that the Finance professors are more likely to invest in “riskier” products and will invest a larger share of their portfolio to these assets than their English counterparts.
3.2. Asset Allocation Decisions We start our empirical investigation by comparing how the respondents allocate their portfolios across the major asset categories. We group Federal Agency Bonds, Municipal Bonds and Corporate Bonds into a new category and name it Bonds. We then investigate the extent to which the respondents allocate a significant share of their portfolio to each of the four major categories, i.e. Cash, Stocks, Bonds and Mutual Funds. Since there is a wide spectrum of allocation strategies employed by the individuals in other similar studies, deciding on a basis for comparison is inherently subjective. First, we define the “majority” of the individual’s portfolio
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as being 70% or more. We then compare the asset categories that account for 70% or more of each of the respondents’ direct investments and their retirement savings 7 . We define two strategies to serve as proxies for active diversification. For direct investments, the two strategies are: i. Invest 70% or more in Mutual Funds ii. Invest 70% or more in a mix of Cash, Bonds and Stocks For retirement savings, we consider the following two strategies to indicate active diversification: i. Invest 70% or more in Multi-Asset Investments ii. Invest 70% or more in a mix of at least three of the seven Categories Table 2 and Figure 1 compare the number of participants in allocations that account for 70% or more of the direct investments and the retirement savings. We also provide the relative participation in each of the diversification strategies defined above. For direct investments, the most significant difference between the sub-samples is among those who invest the majority of their portfolio in Mutual funds, Cash and Stocks. A larger proportion of the Finance professors invest the majority of their portfolio in mutual funds and stocks, 38.9% and 13.9%, compared to the English professors who invest 26.8% in mutual funds and 7.7% in stocks. On the other hand, a significantly larger proportion of the English professors (31.1%) allocate the majority of their direct investments to Cash than the Finance professors (7.3%). While a substantial portion of both sub-samples allocate the majority of their portfolio to a mix of Cash, Stocks and Bonds (38.8% of the Finance professors and 34.0% of the English professors), this difference is statistically insignificant. Only 4% of both groups allocate the majority of their direct
7
Since some categories, e.g., REITs and derivatives do not account for 70% of any of the respondents’ portfolios they are automatically eliminated as subjects for this investigation.
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investments to Bonds. Panel A of Table 2 presents the proportion of individuals in each group that employ either of the diversification strategies defined above, i.e., invest the majority of their portfolio in Mutual Funds or a mix of Cash, Stocks and Bonds. We also report results of the Mantel-Haenszel Chi-Squared test which confirms that Finance professors are 22.6% more likely to employ either of these strategies than English professors. The results in Panel B of Table 2 suggest that both groups of respondents invest the majority of their retirement savings either in a mix of at least three of the seven available choices or in Equities: 61.8% of the Finance professors allocate the majority of their retirement savings to equities and 30.6% allocate the majority to a mixture of at least three of the available choices. Among the English professors, 41.3% allocate the majority of their retirement savings to a mix of at least three of the available choices and 40.1% allocate the majority of their portfolio to Equities. A significantly larger proportion of the English professors invest the majority of their portfolio in Multi-Asset investments (6.6% vs. 2.1%) and Money Market Instruments (4.2% vs. 1.1%). Only a small number of both groups invest most of their retirement savings in the Real Estate fund. We also compare the diversification strategies defined for the retirement savings between the Finance and English professors. We find that the English professors are significantly more likely to invest the majority of their retirement savings in Multi-Asset Investments or a mix of at least three of the available choices. The preliminary findings of Table 2 and Figure 1 suggest that compared to their English counterparts, Finance professors are more likely to diversify in their direct investments but are less likely to diversify in their retirement savings. However, it may be argued that these results are driven by other factors such as income, age or gender (see Cohn et al. (1975); Riley & Chow (1992); Dwyer et al. (2002); Agnew et al. (2003)). To investigate the likelihood that our results
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are driven by other factors, we perform a cross-sectional multivariate regression analysis of the probability of the respondents employing either of the diversification strategies outlined above. Table 3 provides summary statistics for the control variables included in the analysis. The proportion of women in the English sample (42%) is much larger than that in the Finance sample (16%). The age distribution is similar across both groups with each sample split almost perfectly in half at the 50-year old mark. Caucasians dominate both samples but there is more diversity in the finance sample, due primarily to the large proportion of Asians and Pacific Islanders (12%). Most of the respondents in both samples are married or live with a partner. The number of single English professors (26%) is slightly higher than the number of single Finance professors (16%). The majority of the households in both samples have no children under 18 years old but the proportion is significantly higher in the English sub-sample. Most of the finance professors (55%) are in the highest household income category, earning more than $150,000 while most of the English professors (46%) are in the $75,000 - $150,000 household income bracket. Finally, in both samples most of the households have minimal unsecured debt. The proportion of Finance and English professors having less than $100,000 in unsecured debts is 83% and 88% respectively. For our cross-sectional analysis, we estimate the following probit regression model:
Pr ( Diverse = 1) = α + α Faculty + α Gender + α Married + α Age i
0
1
i
2
i
3
i
4
i
(1)
+ α Race + α Children + α Income + α Debt + e 5
i
6
i
7
i
8
i
i
We estimate the model separately for the direct investments and for the retirement savings. For the direct investments, the dependent variable, Diverse is “1” if the respondent invests 70% or more of his portfolio in mutual funds or a mix of Cash, Stocks and Bonds and “0” otherwise. For the retirement savings, Diverse is “1” if the respondent invests 70% or more of his retirement savings in Multi-asset investments or a mix of at least three of the seven funds available. The
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results of the estimation of Equation 1 are given in Table 4. Panel A provides the results for the direct investments and Panel B provides similar results for the retirement savings. We estimate the model separately for the Finance and English sub-sample as well as for the combined sample. The indicator variable Faculty which takes a value “1” if the respondent is in the Finance sample and “0” otherwise is included only in the full-sample regression. The results in Panel A of Table 4 shows that for the full sample, the faculty variable is positive and significant, suggesting that Finance faculty are more likely to actively seek diversification benefits in their direct investments. There is a significantly positive relation between the propensity to diversify and the income level. Older respondents and those who are married are more likely to diversify their direct investments, but as the level of unsecured debt increases the probability of holding a diversified portfolio decreases. Panel A also shows that within the Finance sample, age is the most important predictor and women are more likely to diversify than men. However, in this sub-group, the income level does not have a significant impact on the propensity to diversify by holding mostly mutual funds or a mix of Cash, Stock and Bonds. English professors who are older, Caucasian and earn higher income are significantly more likely to invest most of their portfolio either in mutual funds or a mix of Cash, Stocks and Bonds. The full-sample results in Panel B of Table 4 show that the faculty variable is negative and significant suggesting that Finance professors are less likely to diversify in the retirement savings than English professors. Within the Finance sub-sample, women, older respondents and individuals who are married or live with a partner are significantly more likely to invest the majority of their retirement savings either in Multi-Asset Investments or a mix of at least three of the seven available funds. Finance professors are less likely to diversify as the number of
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children in their household increases. For the English sub-sample, the probability of diversifying within the retirement savings increases with income and men in this group are more likely to diversify than women. To investigate if knowledge of finance helps individuals to manage their retirement savings more efficiently, we extend the model to include four additional variables; Changeplan, PlanAge, YrstoRet and Planratio. ChangePlan is the frequency with which the respondent changes the composition of his retirement plan, PlanAge is the number of years the respondent has been investing in the retirement plan, YrstoRet is the number of years remaining until retirement and PlanRatio is the percentage of the household total assets that the retirement plan represents. The respective values for these variables are: ChangePlan: 0=Never, 1=Every 5 years or more, 2=every 2-5 years, 3=at least once every 2 years. PlanAge: 1=less than 5 years ago, 2=5-20 years ago, 3=more than 20 years ago. YrstoRet: 1=within 10 years, 2=10-25 years, 3=later than 25 years. PlanRatio: 1=less than 20 percent, 2=20 percent to 49 percent, 3=50 percent to 79 percent and 4=80 percent or more. The extended model is given by:
Pr ( Diverse = 1) = α + α Faculty + α Gender + α Married + α Age i
0
1
i
2
i
3
i
4
+ α Race + α Children + α Income + α Debt 5
i
6
i
7
i
8
+ α Changeplan + α PlanAge + α Yrsto Re t 9
i
10
i
11
i
(2) i
i
+ α PlanRatio + e 12
i
i
We expect a positive relation between the frequency with which an investor changes the composition of his plan and the probability that he holds a diversified portfolio. However, the relation between the other variables and the probability of holding a diversified portfolio is not unambiguous. For example, an investor who has most of his assets in his retirement savings (PlanRatio = 4), could conceivably be balancing the need to minimize risk and maximizing the
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return on his major investment. Table 5 provides the results of the estimation of the model given by Equation 2 for the overall sample and each of the sub-samples. Of the three additional variables, the only one that is significant is the YrstoRet variable, which is negative and significant for the Finance sample. However, the age variable (Age) which was positively related to the probability of holding a diversified portfolio is now no longer significant. This suggests that the Age variable was a proxy for the remaining years to retirement and the relation is negative since an older respondent would have a shorter time remaining to retirement, consistent with a lower value for YrstoRet. In other words, Finance professors who have a shorter time remaining until retirement are more likely to diversify across different asset classes within their retirement savings. In summary, our findings on the allocation decisions of the households in this sample suggests that after controlling for economic and demographic factors, individuals who have knowledge of finance are more likely to actively seek the benefits of diversification in their direct investments but are more willing to hold less diversified portfolio in their retirement savings.
3.3. International Diversification In this section, we investigate a specific asset allocation decision, the propensity to invest in foreign assets. We use two measures of international diversification. Our first measure is obtained by asking respondents if they have ever invested in “Foreign stocks/bond or foreign mutual funds”. The top half of Figure 2 shows the respective proportion of Finance and English professors who indicate that they have ever invested in this category of financial asset. Finance professors are almost two times more likely than English professors to have ever invested in foreign stocks/bonds or foreign mutual funds (74.6% vs. 42.9%).
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Our second measure of international diversification is the proportion of the respondent’s retirement savings that is invested in the International Equities funds. We form quintiles based on the percentage allocations to this fund category. The bottom half of Figure 2 compares the relative allocation of the sub-samples into each of the quintiles. Two-thirds of the English professors invest less than 20% of their retirement savings in international equities while more than half of the Finance professors invest less than 20% of their retirement savings in international equities. On the other hand, one-third of the finance professors and one-fourth of the English professors invest between 20% and 40% of their retirement savings in international equities respectively. We perform cross-sectional analysis to investigate which of the other economic and demographic factors affect the probability of seeking the benefits of international diversification. Since our first measure of international diversification is a dichotomous variable, we estimate the following probit regression model:
Pr ( Foreign = 1) = α + α Faculty + α Gender + α Married + α Age i
0
1
i
2
i
3
i
4
i
+ α Race + α Children + α Income + α Debt + e 5
i
6
i
7
i
8
i
(3)
i
The dependent variable, Foreign is “1” if the respondent has ever invested in foreign stocks/bond or foreign mutual funds and “0” otherwise. We estimate the model for the full sample and for the Finance and English sub-samples separately. We exclude the indicator variable, faculty, which is “1” if the respondent is a Finance professor and “0” otherwise from the sub-sample regressions. The results of the estimation are in Table 6. The full sample results of Table 6 shows that the probability that an individual will diversify internationally is positively related to his income and Finance professors are significantly more likely to have ever invested in foreign stocks/bond or foreign mutual funds than their English counterpart. Further inspection of Table 6 also shows that consistent with the 21
overall results, Finance professors who earn more are more likely to hold foreign investments. However, of the variables included in our investigation, the probability that an English professor will diversify internationally is only related to the age of the respondent. In this sample older professors are more likely to hold foreign investments. We investigate if the second measure of international diversification is affected by other economic and demographic factors by performing cross-sectional analysis using the following regression model.
Intl = α + α Faculty + α Gender + α Married + α Age i
0
1
i
2
i
3
i
4
i
+ α Race + α Children + α Income + α Debt + e 5
i
6
i
7
i
8
i
(4)
i
The dependent variable, Intl, is the percentage of the respondent’s retirement savings that is invested in International Equities. Since the dependent variable is bounded at 0 and 1, we estimate a two-limit censored (tobit) regression. The results provided in Table 7 confirm that Finance professors allocate a significantly larger share of their retirement savings to international equities. Among the Finance professors, the amount invested in international equities is positively related to income but decreases with age. We also find that female professors are less likely to invest in international equities. The findings of Tables 2-6 and 2-7 confirm the results in Figure 2, that after controlling for economic and demographic factors, Finance professors are significantly more likely to invest in foreign stock/bonds or foreign mutual funds and allocate a larger share of their retirement savings to international equities.
3.4. Equity Diversification In this section we investigate if respondents who invest directly in individual stocks hold
22
diversified stock portfolios. We use two proxy measures of equity diversification. The measures are based on the responses to the following two questions from the survey: (i) How many stocks do you currently own (excluding mutual funds)? (ii) Which of the following sectors do you own stocks in? (Choose as many as apply) Figure 3 provides the breakdown of the respondents based on the response to these two questions. The top section of Figure 3 shows that while more than half of the English professors (53.8%) do not invest directly in equities, the corresponding proportion of the Finance professors is 31.0%. The proportion of Finance professors in each of the other three buckets, i.e. invest in 15 stocks, invest in 5-15 stocks and invest in greater than 15 stocks, is approximately uniform while the proportion of the English sample decreases monotonically as the number of stocks increases. The lower section of Figure 3 shows that most respondents in both samples invest directly in stocks that are in the same sector but the proportion is much larger for the English sample than the Finance sample (30.0% versus 17.7%.) To investigate the extent to which investors in both samples diversify within their equity portfolio, we define two proxy measures of equity diversification: i. The respondent invests in more than 15 stocks ii. The respondent invests in stocks from at least 4 sectors. Panel A of Table 8 compares the probability that a respondent will practice each of these diversification strategies as well as a combination of the two, i.e., invest in more than 15 stocks from four or more sectors. Results of the Mantel-Haenszel Chi-squared test confirm that the respondents in the finance sample are 10% more likely to invest in more than 15 stocks, 17% more likely to hold stocks in four or more sectors and 11% more likely to practice both strategies.
23
We also investigate if these results hold after controlling for other economic and demographic factors. We estimate the following probit regression model:
Pr (Diverse = 1) = α + α Faculty + α Gender + α Married + α Age i
0
1
i
2
i
3
i
4
+ α Race + α Children + α Income + α Debt + e 5
i
6
i
7
i
8
i
i
(3.5)
i
The model is estimated separately for each strategy and in each model the dependent variable Diverse is “1” for respondents that employ the respective strategy and “0” otherwise. The results for each of the strategies are given in Panels B, C and D of Table 8. In Panel B, Diverse is “1” only for those respondents that invest directly in 15 or more stocks and “0” otherwise. In Panel C, Diverse is “1” for respondents who invest directly in stocks from four or more sectors and in Panel D, Diverse is “1” only for respondents who invest directly in more than 15 stocks from four or more sectors and “0” otherwise. Panel B of Table 8 shows that Finance professors who are older and have higher income are more likely to invest directly in 15 or more stocks. For the English sample, the probability that a respondent will invest in more than 15 stocks is positively related to the income level but unrelated to the other factors included in the model. Further, there is no significant difference between the likelihood that respondents in either of the two sub-samples will undertake this strategy. The results in Panel C of Table 8 indicate that Finance professors are significantly more likely to invest in stocks from four or more sectors. In both samples, respondents who are older and have higher income are more likely to diversify across sectors. Within the Finance group, men are more likely to invest directly in stocks from four or more sectors. Inspection of the results of the combined equity diversification strategy in Panel D of Table 8 shows that respondents in the Finance sample are more likely to hold more than 15 stocks from four or more sectors. The other results in Panel D are similar to the findings in Panels B and C, with income and age having a positive affect on this strategy for the Finance
24
professors and income being the main contributing factor among the English professors. Male English professors are also moderately more likely than their female counterpart to invest in more than 15 stocks from four or more sectors. Together the results in this section suggest that knowledge of finance increases the likelihood that investors will diversify within their equity portfolio. However, after controlling for income and age, the impact is significantly reduced and is more related to the number of sectors chosen than the number of stocks held.
3.5. Naïve Diversification Strategies We now investigate two naïve diversification strategies that have received attention in the literature recently. The first is the “framing 1/n heuristic” in which the individual invests an equal proportion of his portfolio in each of the available asset categories and the second is the “conditional 1/n heuristic” in which the investor chooses a subset of the available asset categories and invests an equal proportion in each of the chosen categories. Specifically, we investigate if investors with more knowledge of finance are less likely to employ either or both of these naïve diversification strategies. We use the individual’s allocations to his retirement savings for our empirical investigation. Since we ask respondents to indicate how they allocate their retirement savings to seven funds, the framing 1/n heuristic is synonymous with an individual investing one-seventh of his retirement savings in each of the seven available funds. The conditional 1/n heuristic is equivalent to the investor choosing between two and six funds and investing equal proportion in each of the funds chosen. For example, if two funds are chosen, 50% would be invested in each, if three funds are chosen, 33.33% would be invested in each fund. Figure 4 shows the distribution of the funds chosen by both the Finance and English
25
professors. The distribution closely approximates a normal distribution, rising from one fund to a maximum at three funds and then falling to a minimum at seven funds. In Table 9, we provide results of t-test that the mean allocation to each of the funds chosen is “1/n”. We provide results for the overall sample as well as for each of the two sub-samples. If the framing 1/n heuristic holds, when seven funds are chosen the mean allocation to each fund should be 14.3%. If the conditional 1/n heuristic holds, when two, three, four, five or six funds are chosen, the allocation to each fund should be 50%, 33.3%, 25%, 20% and 16.67% respectively. The results for the full sample in Panel A shows that for respondents who invest in all seven funds, the allocation to four of the funds is not statistically different from 14.3%. However, for those choosing between two and six funds, only the allocations to the Multi-Asset Investment are consistently indistinguishable from 1/nth of the number of chosen funds. This is a preliminary indicator that overall, investors seem to treat multi-asset investments as a separate asset class, invest 1/n in that category and then subjectively allocate the remainder of their retirement portfolio to the other (n-1) chosen funds. The results for the Finance sub-sample in Panel B are qualitatively similar to the overall results in Panel A. However, the results for the English sub-sample in Panel C suggests that when respondents in this group choose n funds, except for the allocations to Domestic and International equities and Real Estate, the allocations to the other funds are largely indistinguishable from 1/n. 8 Together the results in Table 9 suggest that both Finance and English faculty are equally likely to practice the framing 1/n heuristic but the English professors are more likely to practice the conditional 1/n heuristic. Since the framing 1/n heuristic is considered to be irrational but the 8
In the English sub-sample, it is not possible to make an assessment of the framing 1/n heuristic or the conditional 1/n heuristic when 6 funds are chosen since only 3 respondents chose all 7 funds and 6 funds respectively, in this group.
26
conditional 1/n heuristic may be perceived as being rational, the findings in this section suggest that knowledge of finance does not necessarily lead to a reduction in the likelihood of less than fully rational behavior. 4.
Conclusions In this paper we investigate if the household asset allocation and diversification decision is
influenced by the individual’s knowledge of finance. Using a survey of Finance and English academicians at universities across the United States, we examine the extent to which knowledge of finance results in investors holding more diversified portfolios. We study both the asset allocation decision, (to see how efficiently households in our sample choose among the major asset classes) as well as the extent to which they diversify within their equity portfolios. For the asset allocation decision, we employ two proxy measures of active diversification. The first one tests if individuals allocate the majority of their direct investments to mutual funds or a mix of Stocks, Bonds and Cash. Using cross-sectional probit regression models, we find that after controlling for economic and demographic factors, individuals who have more knowledge of finance are more likely to efficiently allocate the majority of their direct investments. Our second test investigates the extent to which knowledge of finance increases the likelihood that an investor will seek the benefits of international diversification. We find that Finance professors are significantly more likely to invest in foreign stock/bonds or foreign mutual funds and allocate a larger share of their retirement savings to international equities than their English counterparts. Conditional on an investor holding a positive amount directly in individual stocks, we employ three tests of equity diversification. The first test is the probability of investing in more than 15 stocks; the second test is the probability of investing in stocks from four or more sectors and the third test is a combination of the first two, i.e., the probability of investing in 15 or more
27
stocks from four or more sectors. We find evidence that knowledge of finance increases the likelihood that an investor will diversify within his equity portfolio. However, after controlling for income and age, the impact is significantly reduced and is more related to the number of sectors chosen than the number of stocks held. We also investigate asset allocation decision in retirement savings but find no evidence that knowledge of finance increases the likelihood that an investor will invest the majority of his retirement savings either in Multi-asset investments or a mix of at least three of the available funds. Specifically, we find that within the Finance sample, the propensity to diversify in the retirement savings is most related to the age of the respondent. Finally, we investigate two naïve diversification strategies, the “framing 1/n heuristic” in which the individual invests an equal proportion of his portfolio in each of the available asset categories and a “conditional 1/n heuristic” in which the investor chooses a subset of the available asset categories and invest an equal proportion in each of the chosen categories. Our empirical findings suggest that both Finance and English faculty are equally likely to practice the framing 1/n heuristic but the English professors are more likely to practice the conditional 1/n heuristic. We acknowledge that by using a cross-sectional dataset, we have investigated the portfolio allocation decision in a static framework. However when we include dummy variables in our model to capture subjective rebalancing/life-cycle effects, our results are largely unchanged. The main difference is that the respondent’s years to retirement seem to be a more precise factor than age in retirement savings allocation decisions. Notwithstanding this finding, a follow-up survey may provide useful insights.
28
Table 1: Portfolio Allocations of Finance and English faculty This table presents summary statistics of the allocation into each of the asset groups. We provide the number and percentage of respondents who invest in each group and the mean allocation. Finance and English are the results of a survey of Finance and English faculty at universities across the United States. Panel A provides the allocations for the direct investments and Panel B provides allocations for the retirement savings. The number of observations in Panel B is less than Panel A since some respondents do not have a retirement account. The categories in Panel B are based on the TIAA-CREF asset classes.
Panel A – Direct Investments Number of Participants All (1385)
Mean Allocation
Finance (1147)
English (238)
All
Finance
English
Checking, Savings, CDs, Govt. Bills and Bonds
1234
(89.1%)
1016
(88.6%)
218
(91.6%)
26.5%
22.4%
45.9%
Federal Agency Bonds and Municipal Bonds
445
(32.1%)
386
(33.7%)
59
(24.8%)
8.2%
7.6%
12.2%
Corporate Bonds Mutual Funds Stocks REITs Derivatives
481 1099 869 342 223
(34.7%) (79.4%) (62.7%) (24.7%) (16.1%)
446 933 755 313 208
(38.9%) (81.3%) (65.8%) (27.3%) (18.1%)
35 166 114 29 15
(14.7%) (69.7%) (47.9%) (12.2%) (6.3%)
9.9% 58.7% 33.9% 7.4% 2.7%
10.0% 60.0% 33.9% 7.7% 2.9%
8.8% 51.3% 33.6% 4.1% 0.0%
Panel B – Retirement Savings Number of Participants All (1242) Equities – Domestic Equities – International Real Estate Fixed Income Money Market Guaranteed Income Multi Asset Investment
1134 928 494 708 474 302 246
(91.3%) (74.7%) (39.8%) (57.0%) (38.2%) (24.3%) (19.8%)
Mean Allocation
Finance (1074)
English (168)
1001 830 423 645 412 255 196
133 98 71 63 62 47 50
(93.2%) (77.3%) (39.4%) (60.1%) (38.4%) (23.7%) (18.2%)
29
(79.2%) (58.3%) (42.3%) (37.5%) (36.9%) (28.0%) (29.8%)
All 54.3% 22.6% 14.5% 21.5% 16.3% 17.5% 25.1%
Finance
English
55.2% 22.7% 13.5% 21.0% 14.2% 15.7% 21.8%
47.9% 21.9% 20.8% 27.5% 30.0% 26.8% 38.0%
Table 2: Investment Strategies by Discipline In this table we compare how individuals allocate the majority of their financial assets. We provide the breakdown of the strategies that account for 70 percent or more of the respondents’ portfolios. The results for the Finance and English professors and the combined sample are given. Panel A provides the allocations for the direct investments and Panel B provides similar results for the retirement savings. We also perform Mantel-Haenszel Chi-Squared test that the proportion using each allocation is the same for both sub-samples; *, ** and *** denote significance at the 10%, 5% and 1% level respectively.
Panel A – Direct Investments Allocations
All
Finance
English
MantelHaenszel Chi-Squared
N (1) Invest 70% or more in Mutual Funds (2) Invest 70% or more in mix of Cash, Bonds and Stocks (3) Invest 70% or more in Cash (4) Invest 70% or more in Bonds (5) Invest 70% or more in Stocks
1385 36.8% 37.9% 11.3% 0.4% 12.8%
1147 38.9% 38.8% 7.3% 0.4% 13.9%
235 26.8% 34.0% 31.1% 0.4% 7.7%
13.057*** 2.248 106.834*** N/A 7.012***
Diversified Portfolios - (1) and (2) above
89.4%
93.2%
70.6%
32.234***
Panel B – Retirement Savings Allocations
Finance
N (1) Invest 70% or more in Multi-Asset (2) Invest 70% or more in mix of Categories (3) Invest 70% or more in Money Market Investments (4) Invest 70% or more in Fixed Income or Guaranteed Income (5) Invest 70% or more in Equities (6) Invest 70% or more in Real Estate
1241 2.7% 32.1% 1.5%
1074 2.1% 30.6% 1.1%
167 6.6% 41.3% 4.2%
10.584*** 7.263*** 8.960***
3.6%
3.3%
6.0%
3.016**
58.9% 1.1%
61.8% 1.0%
40.1% 1.8%
28.866*** 0.755
Diversified Portfolios - (1) and (2) above
34.8%
32.8%
47.9%
14.101***
30
English
MantelHaenszel Chi-Squared
All
Table 3: Summary Statistics for Control Variables This Table presents summary statistics for the result of our survey of Finance and English professors at universities across the United States. Finance
English
All
1106
279
1385
N Gender Male Female
967 180
84% 16%
139 99
58% 42%
1106 279
80% 20%
Age (Age) 20-29 30-39 40-49 50-59 60 or above
12 232 290 378 235
1% 20% 25% 33% 20%
9 59 51 58 61
4% 25% 21% 24% 26%
21 291 341 436 296
2% 21% 25% 31% 21%
17 142 906 18 6
1% 12% 79% 2% 1%
14 8 202 5 1
6% 3% 85% 2% 0%
31 150 1108 23 7
2% 11% 80% 2% 1%
53
5%
8
3%
61
4%
Marital Status (Married) Single Married or Living with partner
184 963
16% 84%
61 177
26% 74%
245 1140
18% 82%
Number of Children in Household (Children) None 1 2 More than 2
645 190 208 104
56% 17% 18% 9%
179 37 18 4
75% 16% 8% 2%
824 227 226 108
59% 16% 16% 8%
Income (Income) Less than $75,000 $75,000 - $149,999 $150,000 and above
41 467 628
4% 41% 55%
67 110 60
28% 46% 25%
108 577 688
8% 42% 50%
Unsecured Debts (Debt) Less than $25,000 $25,000 - $99,999 $100,000 - $249,999 $250,000 - $499,999 $500,000 or more
817 140 103 52 31
71% 12% 9% 5% 3%
167 44 21 6 0
70% 18% 9% 3% 0%
984 184 124 58 31
71% 13% 9% 4% 2%
Race/Ethnicity (Race) African-American (Non-Hispanic) Asian/Pacific Islanders Caucasian (non Hispanic) Latino or Hispanic Native American, Aleut or Aboriginal Peoples Other
31
Table 4: Analysis of Asset Allocation Decisions This table provides probit regression analysis for the combined faculty sample and the Finance and English sub-samples using the following model:
Pr (Diverse = 1) = α + α Faculty + α Gender + α Married + α Age + α Race + α Children i
0
1
i
2
i
+ α Income + α Debt + e 7
i
8
i
3
i
4
i
5
i
6
i
i
Panel A provides the results for direct investments and Panel B provides similar results for the retirement savings. In Panel A Diverse is “1” for individuals who invest more than 70 percent of their portfolio in either mutual funds or a mixture of at least Cash, Stocks and Bonds. In Panel B Diverse is “1” for individuals who invest more than 70 percent of their retirement savings in either multi-investment assets or a mix of at least three of the other categories. The faculty variable (0=English, 1=Finance) is omitted from the regressions of the sub-samples. The chi-squared values for each of the estimates are in parenthesis below the respective estimates. Significant estimates at the 10%, 5% and 1% level are denoted by *, ** and *** respectively.
Panel A – Direct Investments Faculty
Gender
Married
Age
Race
Children
Income
Debt
Intercept
Log Likelihood
N
0.687*** (15.76)
0.165 (1.00)
0.341** (3.98)
0.272** (18.40)
-0.078* (3.08)
0.066 (1.19)
0.301*** (7.63)
-0.152** (5.74)
-1.623*** (11.22)
-737.721
1371
Finance
0.406** (3.70)
0.384* (3.60)
0.242*** (10.74)
-0.044 (0.84)
0.050 (0.63)
0.199 (2.34)
-0.141** (4.26)
-1.004* (3.01)
-590.641
1134
English
-0.324 (1.23)
0.383 (1.25)
0.299** (4.11)
-0.338** (5.88)
0.138 (0.48)
0.525** (4.65)
-0.207 (1.17)
-1.101 (1.48)
-141.071
237
All
Panel B – Retirement Savings Faculty
Gender
Married
Age
Race
Children
Income
Debt
Intercept
Log Likelihood
N
-0.494*** (7.19)
0.264* (2.64)
0.453*** (6.16)
0.292*** (19.60)
-0.048 (1.06)
-0.138** (5.47)
-0.066 (0.36)
0.028 (0.19)
-2.095*** (15.42)
-764.380
1230
Finance
0.570*** (9.31)
0.676*** (9.89)
0.354*** (22.52)
-0.045 (0.81)
-0.131** (4.43)
-0.184 (2.15)
0.012 (0.03)
-3.277*** (29.06)
-643.268
1063
English
-0.607* (3.35)
-0.301 (0.58)
-0.163 (0.86)
-0.103 (0.48)
-0.180 (0.67)
0.589** (4.70)
0.076 (0.15)
0.754 (0.45)
-110.606
167
All
32
Table 5: Extended Model of Retirement Savings This table provides probit regression analysis for the combined faculty sample and the Finance and English sub-samples using the following model:
Pr ( Diverse = 1) = α + α Faculty + α Gender + α Married + α Age + α Race + α Children i
0
1
i
2
i
3
i
4
i
5
i
6
i
+ α Income + α Debt + α Changeplan + α PlanAge + α Yrsto Re t + α PlanRatio + e 7
i
8
i
9
i
10
i
11
i
12
i
i
The dependent variable, Diverse is “1” for individuals who invest more than 70 percent of their retirement savings in either multi-investment assets or a mix of at least three of the other categories. The faculty variable (0=English, 1=Finance) is omitted from the regressions of the sub-samples. ChangePlan is the frequency with which the respondent changes the composition of his retirement plan, PlanAge is the number of years the respondent has been investing in the retirement plan, YrstoRet is the number of years remaining until retirement and PlanRatio is the percentage of the household total assets that the retirement plan represents. The chi-squared values for each of the estimates are in parenthesis below the respective estimates. Significant estimates at the 10%, 5% and 1% level are denoted by *, ** and *** respectively.
ChangePlan: 0=Never, 1=Every 5 years or more, 2=every 2-5 years, 3=at least once every 2 years. PlanAge: 1=less than 5 years ago, 2=5-20 years ago, 3=more than 20 years ago. YrstoRet: 1=within 10 years, 2=10-25 years, 3=later than 25 years. PlanRatio: 1=less than 20 percent, 2=20 percent to 49 percent, 3=50 percent to 79 percent and 4=80 percent or more.
All
Finance
English
Faculty
Gender
Married
Age
Race
Children
Income
Debt
Change Plan
PlanAge
-0.598***
0.262
0.424**
0.016
-0.053
-0.127**
-0.085
0.035
0.072
(10.02)
(2.57)
(5.30)
(0.02)
(1.08)
(4.59)
(0.58)
(0.32)
(1.63)
0.558***
0.626***
0.099
-0.054
-0.115**
-0.192
0.022
(8.82)
(8.35)
(0.66)
(0.98)
(3.40)
(2.27)
(0.10)
Intercept
Log Likelihood
N
-0.066
-0.260
-757.345
1230
(1.06)
(0.11) -637.548
1063
-109.908
167
YrstoRet
PlanRatio
0.101
-0.428***
(0.59)
(10.14)
0.072
0.071
-0.422***
-0.079
-1.499*
(1.36)
(0.25)
(8.05)
(1.26)
(2.91)
-0.595*
-0.304
-0.366
-0.075
-0.199
0.581**
0.046
0.101
0.011
-0.344
0.040
1.925
(3.01)
(0.56)
(1.43)
(0.20)
(0.78)
(4.25)
(0.05)
(0.43)
(0.00)
(1.03)
(0.06)
(1.05)
33
Table 6: Analysis of Investment in Foreign Assets This table provides probit regression analysis for the combined faculty sample and the Finance and English sub-samples using the following model:
Pr (Foreign = 1) = α + α Faculty + α Gender + α Married + α Age + α Race + α Children i
0
1
i
2
i
+ α Income + α Debt + e 7
i
8
i
3
i
4
i
5
i
6
i
i
Foreign is “1” for individuals who have invested in foreign stocks/bonds or foreign mutual funds and “0” otherwise. The faculty variable (0=English, 1=Finance) is omitted from the regressions of the sub-samples. The chi-squared values for each of the estimates are in parenthesis below the respective estimates. Significant estimates at the 10%, 5% and 1% level are denoted by *, ** and *** respectively.
Log Likelihood
N
-1.150** (4.61)
-706.991
1230
-0.070 (1.01)
0.420 (0.50)
-596.948
1063
-0.094 (0.21)
-3.508*** (7.69)
-101.938
167
Faculty
Gender
Married
Age
Race
Children
Income
Debt
Intercept
1.136*** (37.51)
-0.136 (0.66)
0.003 (0.00)
0.080 (1.42)
-0.067 (2.17)
0.066 (1.17)
0.452*** (15.70)
-0.080 (1.53)
Finance
-0.181 (0.86)
-0.112 (0.28)
-0.002 (0.00)
-0.052 (1.12)
0.039 (0.39)
0.491*** (14.20)
English
-0.027 (0.01)
0.690 (2.56)
0.654*** (11.70)
-0.224 (1.57)
0.292 (1.75)
-0.008 (0.00)
All
34
Table 7: Proportion of Portfolio invested in International Equities This table provides results of two-limit censored (tobit) regression analysis for the combined faculty sample and the Finance and English sub-samples using the following model:
Intl = α + α Faculty + α Gender + α Married + α Age + α Race + α Children i
0
1
i
2
i
+ α Income + α Debt + e 7
i
8
i
3
i
4
i
5
i
6
i
i
Intl is the percentage of the individual’s retirement savings invested in International Equities. The faculty variable (0=English, 1=Finance) is omitted from the sub-sample regressions. The Qualitative Limited Independent Model procedure which uses a non-linear optimization is used for the estimation. The t-values for each of the estimates are in parenthesis below the respective estimates. Significant estimates at the 10%, 5% and 1% level are denoted by *, ** and *** respectively.
Faculty
Gender
Married
Age
Race
Children
Income
Debt
Intercept
Log Likelihood
N
0.057** (2.83)
-0.030 (-1.79)
-0.014 (-0.78)
-0.052*** (-7.92)
0.000 (-0.06)
0.003 (0.48)
0.028** (2.40)
0.005 (0.81)
0.252*** (4.66)
-192.206
1230
Finance
-0.047*** (-2.53)
-0.025 (-1.24)
-0.057*** (-8.11)
0.002 (0.33)
0.002 (0.34)
0.032*** (2.54)
0.004 (0.63)
0.353*** (6.27)
-130.917
1063
English
0.041 (1.01)
0.050 (0.98)
-0.011 (-0.49)
-0.025 (-1.29)
0.006 (0.24)
-0.017 (-0.49)
0.026 (1.06)
-0.028 (-0.19)
-53.255
167
All
35
Table 8: Analysis of Equity Diversification This table compares direct investment in equities. Panel A compares three diversification strategies: (i) Invest in greater than 15 stocks, (ii) Invest in stocks from at least 4 different sectors and (iii) a combination of (i) and (ii). Results of Mantel-Haenszel Chi-Squared tests that the proportion of respondents using each strategy is the same for both the Finance and English sub-sample are also given. We also perform probit regression analysis of each strategy using the following model;
Pr ( Diverse = 1) = α + α Faculty + α Gender + α Married + α Age + α Race + α Children i
0
1
i
2
i
+ α Income + α Debt + e 7
i
8
i
3
i
4
i
5
i
6
i
i
The results for each strategy are given in Panels B, C and D respectively. In each Panel Diverse is “1” for individuals who employ the respective strategy and “0” otherwise. For example, in Panel B Diverse is “1” for respondents who invest in greater than 15 stocks. We provide results for the overall sample and for the Finance and English sub-samples. The faculty variable (0=English, 1=Finance) is omitted from the regressions of the sub-samples. The chi-squared values for each of the estimates are in parenthesis below the respective estimates. In all panels, *, ** and *** denote significance at the 10%, 5% and 1% level respectively.
Panel A – Measures of Equity Diversification Mantel-Haenszel Chi-Squared
All
Finance
English
N Invest in greater than 15 stocks Invest in stocks from 4 or more sectors
1377 20.2% 35.8%
1137 21.5% 38.8%
240 13.8% 21.7%
7.473*** 25.251***
Invest in greater than 15 stocks from 4 or more sectors
18.2%
20.1%
8.8%
17.291***
Panel B – Invest in more than 15 stocks Faculty
Gender
Married
Age
Race
Children
Income
Debt
Intercept
Log Likelihood
N
0.133 (0.37)
-0.293 (2.13)
-0.131 (0.39)
0.256*** (12.05)
0.023 (0.22)
0.026 (0.16)
0.706*** (28.09)
0.087 (1.68)
-3.795*** (36.69)
-652.299
1363
Finance
-0.239 (1.11)
-0.044 (0.04)
0.247*** (9.58)
0.025 (0.23)
0.022 (0.11)
0.597*** (16.67)
0.071 (1.01)
-3.538*** (27.89)
-567.291
1125
English
-0.474 (1.19)
-0.437 (0.78)
0.170 (0.59)
-0.038 (0.04)
0.037 (0.01)
1.213*** (12.13)
0.221 (0.98)
-3.994*** (7.49)
-83.113
238
All
36
Table 8 contd. Panel C – Invest in stocks from 4 or more Sectors Faculty
Gender
Married
Age
Race
Children
Income
Debt
Intercept
Log Likelihood
N
0.551*** (8.95)
-0.394** (5.78)
-0.066 (0.15)
0.251*** (17.05)
-0.024 (0.30)
-0.028 (0.28)
0.434*** (16.89)
0.033 (0.32)
-2.432*** (23.55)
-843.922
1363
Finance
-0.456** (5.92)
-0.138 (0.54)
0.240*** (13.15)
-0.014 (0.09)
-0.041 (0.55)
0.410*** (12.17)
0.030 (0.24)
-1.574*** (8.68)
-727.690
1125
English
-0.212 (0.37)
0.278 (0.41)
0.296* (2.77)
-0.180 (0.88)
0.183 (0.74)
0.548** (4.02)
0.135 (0.45)
-3.739*** (9.27)
-114.063
238
All
Panel D – Invest in more than 15 stocks from 4 or more Sectors Faculty
Gender
Married
Age
Race
Children
Income
Debt
Intercept
Log Likelihood
N
0.558** (4.76)
-0.458** (4.22)
-0.146 (0.43)
0.277*** (12.56)
-0.036 (0.44)
0.029 (0.19)
0.751*** (27.80)
0.024 (0.11)
-4.100*** (36.02)
-604.761
1363
Finance
-0.293 (1.54)
-0.114 (0.23)
0.257*** (9.79)
-0.033 (0.36)
0.023 (0.12)
0.658*** (18.76)
0.028 (0.15)
-3.472*** (25.40)
-544.330
1125
English
-1.450** (4.73)
-0.198 (0.09)
0.399 (1.89)
-0.074 (0.07)
0.155 (0.17)
1.304*** (8.60)
-0.073 (0.06)
-4.477** (4.81)
-57.220
238
All
37
Table 9: Naïve Diversification Strategies This table compares two “naïve” diversification strategies. The first strategy is the “framing 1/n heuristic”, where individuals invest 1/n in each of the n funds available for their retirement savings. The second strategy is the “conditional 1/n heuristic” where the individual chooses a subset, n of the available funds and invests 1/n in each of the n chosen funds. We use 5 of the 6 major funds available via TIAA-CREF and 2 sub-categories of the 6th fund. Since the maximum number of funds is 7, the “framing 1/n heuristic” is analogous to individuals investing 1/7th in each of the 7 funds. Results are provided for the combined faculty in Panel A and for the Finance and English sub-samples in Panels B and C respectively. We test if the mean proportional allocation in each of the n funds chosen differs significantly from 1/n. For example, for respondents who invest in 2 funds, we perform t-test that the mean allocation in each of the 2 funds is 50% etc. *, ** and *** denote significance at the 10%, 5% and 1% level respectively.
Panel A – All Faculty Investment in each of the Funds Chosen Number of Funds Chosen
1
2
3
4
5
6
7
Equities Domestic
100
63.6***
56.0***
48.4***
41.5***
33.4***
26.5***
Equities International
100
35.5***
22.6***
19.0***
16.2***
16.3
11.8**
Real Estate
100
45.7
17.4
13.4***
12.6***
10.3***
11.8
Fixed Income
100
40.5***
22.9***
19.0***
15.5***
15.3
13.9
Money Market
100
44.4
22.5
13.1***
12.0***
8.7***
8.0***
Guaranteed Income
100
39.1**
26.4**
18.7***
14.5***
13.7
17.8
Multi Asset Investment
100
52.0
34.8
23.2
20.3
16.6
14.8
N
119
265
357
298
149
36
17
38
Table 9 contd. Panel B – Finance Faculty Investment in each of the Funds Chosen 3 4 5 6
Number of Funds Chosen
1
2
Equities Domestic
100
64.5***
56.2***
49.0***
44.1***
34.5***
30.0***
Equities International
100
35.4***
22.6***
18.8***
16.4***
15.8
12.1
Real Estate
100
44.7
18.0***
13.2***
10.9***
10.6***
11.9
Fixed Income
100
39.1***
22.1***
18.7***
15.3***
15.6
14.4
Money Market
100
41.0
21.4***
12.7***
11.4***
7.9***
7.9***
Guaranteed Income
100
36.7**
27.4*
18.4***
13.0***
13.9
9.9***
Multi Asset Investment
100
49.0
33.8
25.1
20.4
16.3
13.9
93
229
308
271
126
33
14
Number of Funds Chosen
1
2
3
4
5
6
7
Equities Domestic
100
55.7
54.1***
41.5***
27.7***
21.3
10.0
Equities International
-
36.4***
22.1***
21.2
15.4***
21.3
10.0
Real Estate
100
47.2
15.3***
15.4***
21.3
5.5**
11.7
Fixed Income
100
51.1
30.4
26.0
17.4
12.0
11.7
Money Market
100
55.8
27.3
17.4**
16.2
20.5
8.3
Guaranteed Income
100
46.4
21.4*
20.1
20.8
12.5
54.7
Multi Asset Investment
100
58.0
36.5
17.2**
20.0
18.3
19.0
26
36
49
23
3
N
7
Panel C – English Faculty Investment in each of the Funds Chosen
N
39
27
3
Figure 1: Relative Allocations by Discipline
Direct Investments
Invest 70% or more in Mutual Funds Invest 70% or more in mix of Cash, Bonds and Stocks Invest 70% or more in Cash
Invest 70% or more in Bonds
Invest 70% or more in Stocks 0.0%
5.0%
10.0%
15.0%
Finance
20.0%
25.0%
30.0%
35.0%
40.0%
English
Retirement Savings
Invest 70% or more in Multi-Asset Invest 70% or more in mix of Categories Invest 70% or more in Money Market Investments Invest 70% or more in Fixed Income or Guaranteed Income Invest 70% or more in Equities Invest 70% or more in Real Estate 0.00%
10.00%
20.00%
30.00%
Finance
40
English
40.00%
50.00%
60.00%
70.00%
Figure 2: Investment in International Equities
80.0%
Finance
English
70.0% 60.0% 50.0% 40.0% 30.0% 20.0% 10.0% 0.0% Has Invested in Foreign Stocks
70.0%
Finance
English
60.0% 50.0% 40.0% 30.0% 20.0% 10.0% 0.0%
≤20%
20 - 40%
40 - 60%
60 - 80%
Proportion in International Equities
41
≥80%
Figure 3: Direct Investment in Equities (a) Number of Stocks
Finance
60.0%
English
50.0% 40.0% 30.0% 20.0% 10.0% 0.0%
None
Less than 5
Between 5 and 15
Greater than 15
(B) Number of Sectors 30.0%
Finance
English
25.0% 20.0% 15.0% 10.0% 5.0% 0.0%
1
2
3
4
5
6
Number of Sectors
42
7
8
9
10
Figure 4: Number of Retirement Funds Chosen
30.0% Finance
English
25.0%
20.0% 15.0% 10.0%
5.0% 0.0% 1
2
3
4
5
Number of Funds Chosen
43
6
7
REFERENCES Agnew, J., Balduzzi, P., Sunden, A., 2003. Portfolio Choice and Trading in a Large 401 (k) Plan. American Economic Review 93, 193-215 Agnew, J.R., 2006. Do Behavioral Biases Vary across Individuals? Evidence from Individual Level 401(k) Data. Journal of Financial and Quantitative Analysis 41, 939 Baxter, M., Jermann, U.J., 1997. The international diversification puzzle is worse than you think. American Economic Review 87, 170-180 Benartzi, S., Thaler, R.H., 2001. Naive Diversification Strategies in Defined Contribution Saving Plans. American Economic Review 91, 79-98 Bertaut, C., Starr-McCluer, M., 2002. Household Portfolios in the United States. MIT Press. Campbell, J.Y., 2006. Household Finance. The Journal of Finance 61, 1553-1604 Campbell, J.Y., Lettau, M., Malkiel, B.G., Xu, Y., 2001. Have Individual Stocks Become More Volatile? An Empirical Exploration of Idiosyncratic Risk. Journal of Finance 56, 1-43 Canner, N., Mankiw, N.G., Weil, D.N., 1997. An Asset Allocation Puzzle. American Economic Review 87, 181-191 Cavaglia, S., Brightman, C., Aked, M., 2000. The Increasing Importance of Industry Factors. Financial Analysts Journal 56, 41-54 Cohn, R.A., Lewellen, W.G., Lease, R.C., Schlarbaum, G.G., 1975. Individual Investor Risk Aversion and Investment Portfolio Composition. The Journal of Finance 30, 605-620 Curcuru, S., Heaton, J., Lucas, D., Moore, D., 2004. Heterogeneity and Portfolio Choice: Theory and Evidence. Dwyer, P.D., Gilkeson, J.H., List, J.A., 2002. Gender differences in revealed risk taking: evidence from mutual fund investors. Economics Letters 76, 151-158 French, K.R., Poterba, J.M., 1991. Investor Diversification and International Equity Markets. American Economic Review 81, 222-226 Friend, I., Blume, M.E., 1975. The Demand for Risky Assets. American Economic Review 65, 900-922
44
Goetzmann, W.N., Kumar, A., 2008. Equity Portfolio Diversification. Review of Finance Huberman, G.U.R., Jiang, W.E.I., 2006. Offering versus Choice in 401 (k) Plans: Equity Exposure and Number of Funds. The Journal of Finance 61, 763-801 Kalra, R., Stoichev, M., Sundaram, S., 2004. Diminishing gains from international diversification. Financial Services Review 13, 199-214 Kelly, M., 1995. All their eggs in one basket: Portfolio diversification of US households. Journal of Economic Behavior and Organization 27, 87-96 King, M.A., Leape, J.I., 1998. Wealth and portfolio composition: Theory and evidence. Journal of Public Economics 69, 155-193 Lewis, K.K., 1999. Trying to Explain Home Bias in Equities and Consumption. Journal of Economic Literature 37, 571-608 Malkiel, B.G., 1996. A random walk down Wall street 6 thed. WW Norton & Company, New York. Polkovnichenko, V., 2004. Limited stock market participation and the equity premium. Financial Services Letter 1, 24-34 Polkovnichenko, V., 2005. Household Portfolio Diversification: A Case for RankDependent Preferences. Review of Financial Studies 18, 1467 Read, D., Lowenstein, G., 1995. Diversification Bias: Explaining the Discrepancy between Combined and Separate Choices. Journal of Experimental Psychology 1, 7-59 Riley, W.B., Chow, K.V., 1992. Asset allocation and individual risk aversion. Financial Analysts Journal 48, 32-37 Rosen, H.S., Wu, S., 2004. Portfolio choice and health status. Journal of Financial Economics 72, 457-484 Shefrin, H., Statman, M., 2000. Behavioral Portfolio Theory. Journal of Financial and Quantitative Analysis 35, 127-151 Shlomo, B., Richard, H.T., 2001. Naive diversification strategies in defined contribution saving plans. American Economic Review 91, 79 Simonson, I., 1990. The Effect of Purchase Quantity and Timing on Variety-Seeking Behavior. Journal of Maketing Research 27, 150-62 Statman, M., 2004. The Diversification Puzzle. Financial Analysts Journal 60
45
Sunden, A.E., Surette, B.J., 1998. Gender differences in the allocation of assets in retirement savings plans. American Economic Review 88, 207 Welch, I., 2000. Views of Financial Economists on the Equity Premium and on Professional Controversies*. The Journal of Business 73, 501-537
46
Appendix A - Questionnaire 1. Gender: Male Female 2. Age: 20-29 30-39 40-49 50-59 60 or above 3. Racial or Ethnic Group(s): (To which racial or ethnic group(s) do you most identify? Select more than one if applicable) African-American (Non-Hispanic) Asian/Pacific Islanders Caucasian (non Hispanic) Latino or Hispanic Native American, Aleut or Aboriginal Peoples Other 4. For how long have you lived in the United States? Since birth Less than 10 years 10 years or more 5. Marital Status Single Married or Living with partner 6. Do you and your spouse invest jointly or separately? Jointly Separately 7. Who has greater responsibility for making savings and/or investment decisions in your household? Me My Spouse 8. How many children under age 18 do you have in your household? None 1 2 More than 2
47
9. What is the approximate value of your house? Less than $100,000 $100,000 - $249,999 $250,000 - $499,999 $500,000 or more 10. What is the approximate value of your tangible assets other than your home (e.g., jewelry)? Less than $50,000 $50,000 - $99,999 $100,000 or more 11. If you own real estate other than your personal residence, what is the combined approximate value? Not applicable $100,000 - $249,999 $250,000 - $499,999 $500,000 or more I do not own a home 12. Do you currently own a firm? Yes No 13. What is the approximate value of your outstanding unsecured loans and other liabilities (including credit cards)? Less than $25,000 $25,000 - $99,999 $100,000 - $249,999 $250,000 - $499,999 $500,000 or more 14. What is your Current Household Income? Less than $75,000 $75,000 - $149,999 $150,000 and above 15. How long have you been a Faculty/Instructor? Less than 3 years More than 3 years 16. Are you a tenured professor? Yes No 17. Which of the following expressions best describes your short-term expectations of the market? I expect a bull period I expect a bear period I expect a normal (or flat) period
48
18. Which of the following statements best characterize your recent investment experience? On average, I have experienced a loss on my investments On average, my gains are just about as much as my losses On average, I have experienced a gain on my investments. 19. Have you ever invested in any of the following? Choose as many as apply. U.S. Govt. Bills and Bonds Federal Agency Bonds or Municipal Bonds U.S. Corp. bonds or bond mutual funds U.S. High-yield junk bond or bond mutual funds U.S. Large-cap stocks or stock mutual funds U.S. Small-cap stocks or stock mutual funds Foreign stocks/bond or foreign mutual funds Futures and options Managed futures or commodity pools Private Hedge Funds Privately managed Accounts REIT’s None of the Above 20. Please indicate what percentage of your total wealth is currently invested in each of the following categories (The total must sum to 100): Checking, Savings, CDs, Govt. Bills and Bonds Federal Agency Bonds and Municipal Bonds Corporate Bonds Mutual Funds Stocks REIT’s Derivatives 21. When was the last time you invested in the stock market? I currently invest in the stock market The last time I invested in the stock market was within the last 5 years The last time I invested in the stock market was more than 5 years ago I have never invested in the stock market 22. Which of the following statements best characterize your last investment in the stock market? I made a gain on my investment I made a loss on my investment Not Applicable 23. How many stocks do you currently own (excluding mutual funds)? None Less than 5 Between 5 and 15 Greater than 15
49
24. Which of the following sectors do you own stocks in? (Choose as many as apply) Oil & Gas Basic Materials Industrials Consumer Goods Health Care Consumer Services Telecommunications Utilities Financials Technology None of the Above 25. Do you currently invest in a retirement plan? Yes No Plan 26. When did you start investing in your retirement plan? Less than 5 years ago 5-20 years ago More than 20 years ago 27. When do you anticipate withdrawing money from your plan? Later than 25 years 10-25 years Within 10 years 28. Please indicate the percentage of your total retirement asset invested in each of the following (Total must sum to 100): Equities - Domestic Equities - International Real Estate Fixed Income Money Market Accounts Guaranteed Income Multi-Asset Investments 29. How often do you change the composition of your retirement plan? Never Every 5 years or more Every 2-5 years At least once every 2 years 30. Excluding my primary residence, my retirement plan represents ___% of my investment holdings. less than 20 percent 20 percent to 49 percent 50 percent to 79 percent 80 percent or more
50
31. How do you rank the following in order of Riskiness? (0=No/Least Risk, 6=Most Risk) Checking, Savings, CDs, Govt. Bills and Bonds Federal Agency Bonds and Municipal Bonds Corporate Bonds Mutual Funds Stocks REIT’s Derivatives
51
Appendix B: SCF Data, 2004 - Descriptive Statistics Income, Equity and Financial Assets are in Thousands, Gender is 1 for male, 2 for female; Age is in Years, Educ is years of formal education, Children is number of children under 18, Race is a categorical variable from 1 to 5 for each of the 5 Federal classification, 1 is White
All Households VARIABLE
N
MIN
MAX
MEAN
STD
GENDER
4519
1
2
1.22
0.41
AGE
4519
18
95
50.74
15.7
MARRIED
4519
1
2
1.34
0.47
EDUC
4519
1
17
13.97
2.89
CHILDREN
4519
0
8
0.84
1.16
RACE
4519
1
5
1.41
0.91
INCOME
4519
0
105069.9
792.14
3914.71
EQUITY
4519
0
202657.4
1891.1
10824.7
FIN
4519
0
577788
3382.7
17512.6
Households with no Financial Assets VARIABLE
N
MIN
MAX
MEAN
STD
GENDER
233
1
2
1.425
0.495
AGE
233
18
91
42.176
14.403
MARRIED
233
1
2
1.597
0.492
EDUC
233
1
17
9.936
3.3
CHILDREN
233
0
6
1.116
1.438
RACE
233
1
5
2.039
0.939
INCOME
233
0
129.39
17.185
15.112
EQUITY
233
0
0
0
0
FIN
233
0
0
0
0
Households with Financial Assets VARIABLE
N
MIN
MAX
MEAN
STD
GENDER
4286
1
2
1.2
0.4
AGE
4286
18
95
51.2
15.63
MARRIED
4286
1
2
1.33
0.47
EDUC
4286
1
17
14.19
2.69
CHILDREN
4286
0
8
0.83
1.14
RACE
4286
1
5
1.37
0.9
INCOME
4286
0
105070
834.3
4015.45
EQUITY
4286
0
202657
1994
11105.85
FIN
4286
0
577788
3567
17964.16
52
CAN DIVERSIFICATION BE LEARNED? Abstract This paper investigates the role of financial education in household portfolio allocation decisions using data from a survey of 1,385 professors at universities across the United States. The results suggest that knowledge of finance increases the likelihood that an investor will efficiently allocate his direct investments across the major asset classes, invest in foreign assets and hold a diversified equity portfolio. However, there is no evidence that investors who are more financially sophisticated make superior allocation decisions in their retirement savings. In particular, we find that irrespective of age and other domestic factors, Finance professors are more likely to allocate more than 70% of their retirement savings to Domestic Equities. We also find that English professors are more likely to practice a naïve diversification strategy of choosing a subset of the available funds and allocating equal proportion of their portfolio to each of the chosen funds.
JEL category: G11, D10, D31 Keywords: portfolio choice, diversification, behavioral finance
2
1.
Introduction The benefits of diversification have been recognized and documented in the finance
literature for decades. Many chapters in finance textbooks have been devoted to portfolio theory, which focuses on how an investor should diversify his investments across stocks, bonds and other assets to maximize return and reduce risk. However, Bertaut & Starr-McCluer (2002) note that “the portfolio decisions of households in the United States is not very well understood”. Further, Statman (2004) acknowledges that the level of diversification observed in the equity portfolios of households in the United States presents a “puzzle”. In this paper, by comparing the investment behavior of individuals proficient in finance to those who have little knowledge of finance, we investigate whether knowledge of the benefits of diversification helps investors minimize risk. We survey Finance and English professors at universities across the United States to investigate the extent to which members of these two groups pursue diversification benefits. Since Finance professors have advanced knowledge of the benefits of diversification, if they make superior asset allocation decisions it may be attributed to their education in finance. On the other hand, if the investment patterns of Finance and English professors are found to be similar and they don’t hold diversified portfolios, then this would provide evidence that investment behavior is based more on psychological factors. In other words, rather than using the theories in finance textbooks, investors construct their portfolios based on their sentiments. We investigate if the individuals in our sample diversify across broad asset classes and within their equity portfolios. Since a number of diversification strategies may be justified for asset allocation, we ensure that the model is tractable by examining two indirect tests of active diversification. The first test investigates if individuals allocate greater than 70% of their direct
3
investments to mutual funds or a mix of Stocks, Bonds and Cash. We find that after controlling for economic and demographic factors, individuals with knowledge of finance are more likely to efficiently allocate the majority of their direct investments. We also perform a similar study of allocations in retirement savings. For the faculty sample, we ask respondents to provide the breakdown of their retirement savings based on the TIAA-CREF® funds. Specifically, using the investments in five of the major funds and two sub-categories of the equities funds, we find no evidence that knowledge of finance increases the likelihood that an investor will invest the majority of his retirement savings either in Multi-asset investments or a mix of at least three of the available funds. While our asset allocation measure is admittedly crude, most financial professionals use heuristic measures in making recommendations to their clients. One such measure is based only on the age of the investor, whereby he allocates [100 – Age]% of his personal wealth to a diversified equity portfolio (see Malkiel (1996) p. 418). In the second test, we investigate the extent to which knowledge of finance increases the likelihood that an investor will seek the benefits of international diversification. We consider the inclusion of foreign stocks or bonds in an individual’s portfolio to be an indicator of international diversification. Lewis (1999) suggests that a US investor with mean-variance preferences should invest at least 40% of his portfolio in foreign stocks. We find that that after controlling for economic and demographic factors, Finance professors are more likely to invest in foreign stocks/bonds or foreign mutual funds and allocate a larger share of their retirement savings to international equities. To study whether knowledge of finance helps investors diversify their equity portfolio, we investigate three proxy measures of equity diversification. Each measure is conditional on the respondent investing a positive amount directly in individual stocks. The first measure of equity
4
diversification is the probability of investing in more than 15 stocks; the second measure is the probability of investing in stocks from four or more sectors and the third measure is a combination of the first two, i.e., the probability of investing in 15 or more stocks from four or more sectors. Friend & Blume (1975), Kelly (1995) and Polkovnichenko (2005) use the Federal Reserve’s Survey of Consumer Finances (SCF) 1 data and find that among households that hold stocks directly, the median number of stocks held was less than three, suggesting a lack of diversification in investors’ equity portfolios. Our analysis shows that knowledge of finance increases the likelihood that an investor will diversify within his equity portfolio. However, after controlling for income and age, the impact is significantly reduced and is more related to the number of sectors chosen than the number of stocks held. We also investigate two diversification strategies that have received attention in the literature recently: A naïve diversification strategy or “framing 1/n heuristic” 2 in which the individual invests an equal proportion of his portfolio in each of the available asset categories; and a “conditional 1/n heuristic” diversification strategy in which the investor chooses a subset of the available asset categories and invests an equal proportion in each of the chosen categories. The framing 1/n heuristic strategy is considered irrational since the number of categories chosen depends on the number of choices available, while the conditional 1/n heuristic may be deemed rational. Agnew (2006) investigates the extent to which participants in a 401(k) plan practice each of these diversification strategies and finds that demographic factors are significant predictors in each of her models. We investigate whether after controlling for demographic factors, investors who have knowledge of finance are less likely to practice these naïve
1
The Survey of Consumer Finances is a triennial survey of US household balance sheet and demographic factors conducted by the Board of Governors of the Federal Reserve System.
2
See Shlomo and Thaler (2001) for a detailed description of these strategies.
5
diversification strategies. We find that both Finance and English faculty are equally likely to practice the framing 1/n heuristic but the English professors are more likely to practice the conditional 1/n heuristic. This finding suggests that knowledge of finance does not necessarily lead to a reduction in less than fully rational behavior. 2.
Related Literature and Motivation
2.1. Household Portfolio Asset Allocation Decisions According to King & Leape (1998), the empirical literature on household savings behavior has focused primarily on the total amount of savings rather than relative allocations among different types of assets. Nonetheless, there is ample evidence of hetergeneity in household portfolio allocation decisions (see for example Curcuru et al. (2004)). This heterogeneity may be justified purely on the basis of differential risk tolerance. Canner et al. (1997) examine popular advice on portfolio allocation among cash, bonds, and stocks and find that the advice is not consistent with the mutual-fund separation theorem, which states that all investors should hold the same composition of risky assets. They find that popular advisors recommend that aggressive investors hold a lower ratio of bonds to stocks than conservative investors. However, in addition to the traditional variables such as age, income and wealth, some researchers have found that some seemingly “unlikely” candidates are contributory factors in the household portfolio allocation decision. These include marital status, gender and health status. Sunden & Surette (1998) use SCF data from 1992 and 1995 to investigate how individuals allocate assets in defined contribution plans and find that after controlling for a wide range of demographic, financial and attitudinal characteristics, gender and marital status are still important factors in the household portfolio allocation decision. They find that single women are
6
less likely to invest a significant portion of their retirement savings in risky assets. They argue that with the increasing trend toward defined contribution (DC) plans, such sub-optimal portfolio allocation decisions could adversely impact the accumulated retirement wealth. Rosen & Wu (2004) analyze the role of health status in the household portfolio decision and find that the probability of holding different types of assets and the share of wealth allocated in each asset category is affected by the health status of members of the household. Their results suggest that households in poor health are less likely to own retirement accounts, bonds and risky assets. They point out that the health status effect does not seem to operate through the individual’s attitude towards risk. In his presidential address to the American Finance Association, Campbell (2006) acknowledges that even though “many households seek advice from financial planners and other experts, some households make decisions that are hard to reconcile with this advice or with any standard model.” While he hesitates to advocate expansion of financial education to avoid the potential mistakes that households make in their portfolio allocation decision, our basic motivation is to investigate whether this would be a plausible solution. In particular, we use two groups of investors who are similar in all respects except for their knowledge of finance. This allows us to investigate if individuals with superior knowledge of finance are more likely to make efficient portfolio allocation decisions.
2.2. International Diversification Researchers have considered the lack of investment in foreign stocks to be inconsistent with the standard theory of portfolio choice. Baxter & Jermann (1997) argue that the divergence between diversified portfolios and observed portfolios, the “international diversification puzzle” is wider than was thought. They suggest that whereas in the past this phenomenon could be
7
explained by the lack of financial integration and national barriers to capital flows, the growth and integration of markets over recent years has not seen similar portfolio reallocations. For example, French & Poterba (1991) report that U.S. investors hold about 94% of their financial assets in the form of U.S. securities, and for Japan, the United Kingdom, and Germany, the portfolio share of domestic assets in each case exceeds 85%. More recently Lewis (1999) suggests that a US investor with mean-variance preferences should invest at least 40% of his portfolio in foreign stocks. However, Kalra et al. (2004) examine the effectiveness of international diversification in the presence of periodic rebalancing and associated transaction costs and find that the benefits of international diversification are much smaller than previously understood; they suggest that only a small allocation (10%) of domestic investor’s portfolio to international securities may be justified. In our empirical investigation, we quantify the differential impact of increased financial knowledge on international diversification ceteris paribus.
2.3. Equity Diversification There has been ample evidence in the finance literature of investors holding undiversified equity portfolios. We discuss a few of the more recent studies here. Goetzmann & Kumar (2008) study more than 40,000 stock accounts at a brokerage firm in the 1991-96 period and find that the mean number of stocks in a portfolio was four and the median number was three. In their sample, more than 25% of investor portfolios contain only one stock, more than 50% contain fewer than three stocks and in any given monthly time-period only 5-10% of the portfolios contain more than 10 stocks. The above investment behavior sheds some light on why investor portfolios have extremely high volatility and exhibit worse risk-return trade-off than randomly constructed portfolios.
8
Polkovnichenko (2004) use SCF household data for the years 1983, 1989, 1992, 1995, 1998 and 2001 and find that most households that invest directly in stocks (i.e., not through mutual funds) had portfolios consisting of one to five stocks, with the median being between one and two. They also find that more wealthy investors hold more directly held stocks than the less wealthy. However, they conclude that most direct stockholders invest substantial fractions of their wealth in undiversified portfolios of individual stocks and often combine such investments with well-diversified mutual funds. Polkovnichenko (2004) suggests that while standard expected utility theories cannot reconcile these observations, they can be explained by rankdependent preference models. Statman (2004) argues that the levels of diversification in U.S. investors’ equity portfolio presents a puzzle, since based on the rules of mean-variance portfolio theory, optimal levels of stocks exceeds 300, but the average investor holds only three or four stocks. However, he acknowledges the finding of Campbell et al. (2001), who provide evidence that most of the benefits of equity diversification is obtained with a portfolio of 20 stocks. Statman (2004) suggests that the diversification puzzle can be solved in the context of Shefrin & Statman (2000) behavioral portfolio theory, wherein investors construct their portfolios as layered pyramids in which the bottom layers are designed for downside protection and the top layers are designed for upside potential. In our empirical investigation, we expand the scope of analysis beyond the number of individual stocks held and also include the number of sectors where the stocks are from. Cavaglia et al. (2000) examine five years of data from the twenty-one countries that comprise the current MSCI World Developed Markets and find that diversification across industries provides greater risk reduction benefits than diversification across countries.
9
2.4. Naïve Diversification With the proliferation of mutual funds, most investors have been able to achieve the benefits of diversification indirectly. However, there is still empirical evidence of sub-optimal asset allocation and naïve diversification strategies being the norm rather than the exception. Benartzi & Thaler (2001) investigate diversification strategies in defined contribution plans and find that many investors follow a simple naïve strategy of dividing their contributions equally among all available investment alternatives and suggest that the diversification benefits achieved is a function of the available choices. Huberman & Jiang (2006) investigate the records of over half a million participants in more than 600, 401(k) plans and find that participants tend to allocate their contributions evenly across the funds they use with the tendency weakening with the number of funds used. They find that participants typically invest their savings in a small number of funds (between three and four), irrespective of the number of funds offered, (which is typically between four and fiftynine.) They suggest that their results are at odds with the finding that investors have a “propensity to diversify”, in studies such as Simonson (1990) and Read & Lowenstein (1995). In addition, unlike Benartzi & Thaler (2001) who find that participants follow the 1/n rule in defined contribution (DC) plans which would be irrational, Huberman & Jiang (2006) find that participants allocate 1/n to each of the chosen funds, which they consider to be consistent with K-fund separation theories. Agnew (2006) investigates behavioral biases in individual 401(k) investments by using data from an anonymous large benefits provider which includes detailed individual demographic and contribution data. The overall sample includes 73,699 eligible employees and the sub-sample of active participants includes a total of 22,979 employees with contribution allocations, where
10
an employee is considered active if a contribution was made to the plan during the first two weeks of August 1998. Agnew (2006) investigates three naïve diversification strategies, the framing 1/n heuristic, the modified 1/n heuristic and the conditional 1/n heuristic. 3 In the framing 1/n heuristic, individuals distribute their contributions equally among the n choices available. In the modified 1/n heuristic, investors treat their company’s stock as a separate asset class and divide the remainder of their investment equally among the other asset classes. In the conditional 1/n heuristic, the individual divides his allocations evenly among the funds chosen, where the funds chosen may be less than the total offered. Agnew (2006) finds that salary and other demographic factors such as gender are significant predictors in each of these choices. She acknowledges that while the data used overcomes the common disadvantage of aggregation inherent in most studies involving plan data, her study still has the drawback of missing information on the participant’s assets outside the plan. In addition, variables that have been shown to impact asset allocation decisions such as marital status, education and financial literacy are missing from the dataset. In our empirical study, we use a broader set of control variables.
2.5. Survey of Finance Academicians A number of previous studies have used surveys of finance academicians to investigate financial economic theories. One of the most widely cited is the study done by Welch (2000) who use a survey of 226 academic financial economists to investigate if they are trend followers like most individual investors or do they instead rely on academic studies in forming their predictions of the market? Welch (2000) identifies a high level of heterogeneity in predictions of the equity premium puzzle among the respondents in his study even though they had similar information. He also finds that on average, there was a downward bias in the prediction versus 3
Agnew (2006) also investigates other allocation biases such as investing in company stock and choosing not to participate in the DC plan.
11
historical values. As suggested by Welch (2000), this finding is “striking” since the equity premium is of fundamental importance in both asset pricing and corporate finance. 3.
Data and Empirical Methods
3.1. Survey of professors The data used in this study is from a survey of professors across the United States. During the summer of 2007, we manually collected the names and email addresses of Finance and English faculty at universities in the United States. We use a questionnaire to collect actual portfolio holdings and demographic information from each of the individuals selected. In Appendix A we provide the questionnaire used in our survey. The questionnaire was emailed to 4,381 finance professors and 4,447 English professors. To increase the rate of participation, two follow-up emails were sent to individuals who had not responded after one week and after two weeks respectively. We received responses from 1,430 of the finance professors and 414 of the English professors 4 for a response rate of 33% and 9% respectively. The survey includes information on their total investments in financial and non-financial assets, retirement savings and demographic variables. Since our primary aim is to investigate whether the Finance professors exhibit a greater propensity to diversify, we only include respondents that invest in financial assets either directly or through their retirement savings. The final sample consists of 1,147 finance professors and 238 English professors who own financial assets. The sample of respondents who currently invest in a retirement plan includes 1,074 Finance and 168 English professors. For the direct investments, we include an extensive set of categories that would be as 4
We also received email responses from some of the subjects citing reasons why they are unable or unwilling to participate. The reasons include being ill, being on sabbatical, being too busy to participate and having privacy concerns.
12
inclusive as possible and also provide the granularity to identify any inherent sophistication. The first category includes safe assets; Checking Accounts, Savings Accounts, CDs and Government Bills and Bonds (hereafter referred to as Cash). The second category includes Federal Agency Bonds and Municipal Bonds. There are three separate categories for Corporate Bonds, Mutual Funds and Stocks and two categories for REITs and Derivatives. For the retirement savings, we use the funds offered by TIAA-CREF 5 . The TIAA-CREF has six major categories for investments but we give seven options in our question. Five of the options are the same as the five major categories of TIAA-CREF funds, (1) Fixed Income, (2) Guaranteed Income, (3) Money Market Investments, (4) Multi-Asset Investments and (5) Real Estate Funds. We separate the sixth TIAA-CREF category of Equities funds into two sub-categories of (1) EquitiesDomestic and (2) Equities-International 6 . Table 1 provides summary statistics for the overall sample as well as the sub-sample of Finance and English professors respectively. The number of participants who invest in each category and the mean allocation in each category are given for direct investments and retirement savings. Not surprisingly, Panel A shows that Cash is the most widely used category with 88.6% of the Finance faculty holding some Cash and 91.6% of the English faculty holding cash as part of their overall portfolio. For both groups, the largest allocation is to Mutual Funds. On average, the mean allocation to mutual funds is 60% for Finance professors and 51% for English professors. However, whereas Finance professors invest the second largest share of their portfolio in stocks, a mean of 34%, the second largest share of the English professors’ portfolio is held in Cash accounts, a mean of 46%. The mean allocation to Stocks by the English faculty is 5
TIAA-CREF is the largest manager of defined contribution retirement plans for employees of educational organizations.
6
We separate the Equities fund into Domestic Equities and International Equities to investigate international diversification in Section 2.3.3
13
the same as that by the Finance faculty but ranks third in order of preference. Panel A also shows that relative to their Finance counterparts, English professors invest a larger share of their portfolio in Federal Agency Bonds and Municipal Bonds while the opposite holds for corporate bonds. In addition, Finance professors are twice as likely to invest in REITs and three times as likely to invest in derivatives as English Professors. The results for the retirement savings in Panel B are more similar between the Finance and English professors. Domestic Equities is the most widely used category for both the Finance and English professors, where on average the largest share is allocated; 55% by the Finance professors and 48% by the English professors. In addition, similar to the domestic equities, Finance professors invest slightly more in international equities than their English counterpart. On the other hand, the English professors invest a larger share in all of the other categories, i.e., in Real Estate, Fixed Income, Money Market, Guaranteed Income and Multi-Asset Investments. In summary, Table 1 provides preliminary evidence that the Finance professors are more likely to invest in “riskier” products and will invest a larger share of their portfolio to these assets than their English counterparts.
3.2. Asset Allocation Decisions We start our empirical investigation by comparing how the respondents allocate their portfolios across the major asset categories. We group Federal Agency Bonds, Municipal Bonds and Corporate Bonds into a new category and name it Bonds. We then investigate the extent to which the respondents allocate a significant share of their portfolio to each of the four major categories, i.e. Cash, Stocks, Bonds and Mutual Funds. Since there is a wide spectrum of allocation strategies employed by the individuals in other similar studies, deciding on a basis for comparison is inherently subjective. First, we define the “majority” of the individual’s portfolio
14
as being 70% or more. We then compare the asset categories that account for 70% or more of each of the respondents’ direct investments and their retirement savings 7 . We define two strategies to serve as proxies for active diversification. For direct investments, the two strategies are: i. Invest 70% or more in Mutual Funds ii. Invest 70% or more in a mix of Cash, Bonds and Stocks For retirement savings, we consider the following two strategies to indicate active diversification: i. Invest 70% or more in Multi-Asset Investments ii. Invest 70% or more in a mix of at least three of the seven Categories Table 2 and Figure 1 compare the number of participants in allocations that account for 70% or more of the direct investments and the retirement savings. We also provide the relative participation in each of the diversification strategies defined above. For direct investments, the most significant difference between the sub-samples is among those who invest the majority of their portfolio in Mutual funds, Cash and Stocks. A larger proportion of the Finance professors invest the majority of their portfolio in mutual funds and stocks, 38.9% and 13.9%, compared to the English professors who invest 26.8% in mutual funds and 7.7% in stocks. On the other hand, a significantly larger proportion of the English professors (31.1%) allocate the majority of their direct investments to Cash than the Finance professors (7.3%). While a substantial portion of both sub-samples allocate the majority of their portfolio to a mix of Cash, Stocks and Bonds (38.8% of the Finance professors and 34.0% of the English professors), this difference is statistically insignificant. Only 4% of both groups allocate the majority of their direct
7
Since some categories, e.g., REITs and derivatives do not account for 70% of any of the respondents’ portfolios they are automatically eliminated as subjects for this investigation.
15
investments to Bonds. Panel A of Table 2 presents the proportion of individuals in each group that employ either of the diversification strategies defined above, i.e., invest the majority of their portfolio in Mutual Funds or a mix of Cash, Stocks and Bonds. We also report results of the Mantel-Haenszel Chi-Squared test which confirms that Finance professors are 22.6% more likely to employ either of these strategies than English professors. The results in Panel B of Table 2 suggest that both groups of respondents invest the majority of their retirement savings either in a mix of at least three of the seven available choices or in Equities: 61.8% of the Finance professors allocate the majority of their retirement savings to equities and 30.6% allocate the majority to a mixture of at least three of the available choices. Among the English professors, 41.3% allocate the majority of their retirement savings to a mix of at least three of the available choices and 40.1% allocate the majority of their portfolio to Equities. A significantly larger proportion of the English professors invest the majority of their portfolio in Multi-Asset investments (6.6% vs. 2.1%) and Money Market Instruments (4.2% vs. 1.1%). Only a small number of both groups invest most of their retirement savings in the Real Estate fund. We also compare the diversification strategies defined for the retirement savings between the Finance and English professors. We find that the English professors are significantly more likely to invest the majority of their retirement savings in Multi-Asset Investments or a mix of at least three of the available choices. The preliminary findings of Table 2 and Figure 1 suggest that compared to their English counterparts, Finance professors are more likely to diversify in their direct investments but are less likely to diversify in their retirement savings. However, it may be argued that these results are driven by other factors such as income, age or gender (see Cohn et al. (1975); Riley & Chow (1992); Dwyer et al. (2002); Agnew et al. (2003)). To investigate the likelihood that our results
16
are driven by other factors, we perform a cross-sectional multivariate regression analysis of the probability of the respondents employing either of the diversification strategies outlined above. Table 3 provides summary statistics for the control variables included in the analysis. The proportion of women in the English sample (42%) is much larger than that in the Finance sample (16%). The age distribution is similar across both groups with each sample split almost perfectly in half at the 50-year old mark. Caucasians dominate both samples but there is more diversity in the finance sample, due primarily to the large proportion of Asians and Pacific Islanders (12%). Most of the respondents in both samples are married or live with a partner. The number of single English professors (26%) is slightly higher than the number of single Finance professors (16%). The majority of the households in both samples have no children under 18 years old but the proportion is significantly higher in the English sub-sample. Most of the finance professors (55%) are in the highest household income category, earning more than $150,000 while most of the English professors (46%) are in the $75,000 - $150,000 household income bracket. Finally, in both samples most of the households have minimal unsecured debt. The proportion of Finance and English professors having less than $100,000 in unsecured debts is 83% and 88% respectively. For our cross-sectional analysis, we estimate the following probit regression model:
Pr ( Diverse = 1) = α + α Faculty + α Gender + α Married + α Age i
0
1
i
2
i
3
i
4
i
(1)
+ α Race + α Children + α Income + α Debt + e 5
i
6
i
7
i
8
i
i
We estimate the model separately for the direct investments and for the retirement savings. For the direct investments, the dependent variable, Diverse is “1” if the respondent invests 70% or more of his portfolio in mutual funds or a mix of Cash, Stocks and Bonds and “0” otherwise. For the retirement savings, Diverse is “1” if the respondent invests 70% or more of his retirement savings in Multi-asset investments or a mix of at least three of the seven funds available. The
17
results of the estimation of Equation 1 are given in Table 4. Panel A provides the results for the direct investments and Panel B provides similar results for the retirement savings. We estimate the model separately for the Finance and English sub-sample as well as for the combined sample. The indicator variable Faculty which takes a value “1” if the respondent is in the Finance sample and “0” otherwise is included only in the full-sample regression. The results in Panel A of Table 4 shows that for the full sample, the faculty variable is positive and significant, suggesting that Finance faculty are more likely to actively seek diversification benefits in their direct investments. There is a significantly positive relation between the propensity to diversify and the income level. Older respondents and those who are married are more likely to diversify their direct investments, but as the level of unsecured debt increases the probability of holding a diversified portfolio decreases. Panel A also shows that within the Finance sample, age is the most important predictor and women are more likely to diversify than men. However, in this sub-group, the income level does not have a significant impact on the propensity to diversify by holding mostly mutual funds or a mix of Cash, Stock and Bonds. English professors who are older, Caucasian and earn higher income are significantly more likely to invest most of their portfolio either in mutual funds or a mix of Cash, Stocks and Bonds. The full-sample results in Panel B of Table 4 show that the faculty variable is negative and significant suggesting that Finance professors are less likely to diversify in the retirement savings than English professors. Within the Finance sub-sample, women, older respondents and individuals who are married or live with a partner are significantly more likely to invest the majority of their retirement savings either in Multi-Asset Investments or a mix of at least three of the seven available funds. Finance professors are less likely to diversify as the number of
18
children in their household increases. For the English sub-sample, the probability of diversifying within the retirement savings increases with income and men in this group are more likely to diversify than women. To investigate if knowledge of finance helps individuals to manage their retirement savings more efficiently, we extend the model to include four additional variables; Changeplan, PlanAge, YrstoRet and Planratio. ChangePlan is the frequency with which the respondent changes the composition of his retirement plan, PlanAge is the number of years the respondent has been investing in the retirement plan, YrstoRet is the number of years remaining until retirement and PlanRatio is the percentage of the household total assets that the retirement plan represents. The respective values for these variables are: ChangePlan: 0=Never, 1=Every 5 years or more, 2=every 2-5 years, 3=at least once every 2 years. PlanAge: 1=less than 5 years ago, 2=5-20 years ago, 3=more than 20 years ago. YrstoRet: 1=within 10 years, 2=10-25 years, 3=later than 25 years. PlanRatio: 1=less than 20 percent, 2=20 percent to 49 percent, 3=50 percent to 79 percent and 4=80 percent or more. The extended model is given by:
Pr ( Diverse = 1) = α + α Faculty + α Gender + α Married + α Age i
0
1
i
2
i
3
i
4
+ α Race + α Children + α Income + α Debt 5
i
6
i
7
i
8
+ α Changeplan + α PlanAge + α Yrsto Re t 9
i
10
i
11
i
(2) i
i
+ α PlanRatio + e 12
i
i
We expect a positive relation between the frequency with which an investor changes the composition of his plan and the probability that he holds a diversified portfolio. However, the relation between the other variables and the probability of holding a diversified portfolio is not unambiguous. For example, an investor who has most of his assets in his retirement savings (PlanRatio = 4), could conceivably be balancing the need to minimize risk and maximizing the
19
return on his major investment. Table 5 provides the results of the estimation of the model given by Equation 2 for the overall sample and each of the sub-samples. Of the three additional variables, the only one that is significant is the YrstoRet variable, which is negative and significant for the Finance sample. However, the age variable (Age) which was positively related to the probability of holding a diversified portfolio is now no longer significant. This suggests that the Age variable was a proxy for the remaining years to retirement and the relation is negative since an older respondent would have a shorter time remaining to retirement, consistent with a lower value for YrstoRet. In other words, Finance professors who have a shorter time remaining until retirement are more likely to diversify across different asset classes within their retirement savings. In summary, our findings on the allocation decisions of the households in this sample suggests that after controlling for economic and demographic factors, individuals who have knowledge of finance are more likely to actively seek the benefits of diversification in their direct investments but are more willing to hold less diversified portfolio in their retirement savings.
3.3. International Diversification In this section, we investigate a specific asset allocation decision, the propensity to invest in foreign assets. We use two measures of international diversification. Our first measure is obtained by asking respondents if they have ever invested in “Foreign stocks/bond or foreign mutual funds”. The top half of Figure 2 shows the respective proportion of Finance and English professors who indicate that they have ever invested in this category of financial asset. Finance professors are almost two times more likely than English professors to have ever invested in foreign stocks/bonds or foreign mutual funds (74.6% vs. 42.9%).
20
Our second measure of international diversification is the proportion of the respondent’s retirement savings that is invested in the International Equities funds. We form quintiles based on the percentage allocations to this fund category. The bottom half of Figure 2 compares the relative allocation of the sub-samples into each of the quintiles. Two-thirds of the English professors invest less than 20% of their retirement savings in international equities while more than half of the Finance professors invest less than 20% of their retirement savings in international equities. On the other hand, one-third of the finance professors and one-fourth of the English professors invest between 20% and 40% of their retirement savings in international equities respectively. We perform cross-sectional analysis to investigate which of the other economic and demographic factors affect the probability of seeking the benefits of international diversification. Since our first measure of international diversification is a dichotomous variable, we estimate the following probit regression model:
Pr ( Foreign = 1) = α + α Faculty + α Gender + α Married + α Age i
0
1
i
2
i
3
i
4
i
+ α Race + α Children + α Income + α Debt + e 5
i
6
i
7
i
8
i
(3)
i
The dependent variable, Foreign is “1” if the respondent has ever invested in foreign stocks/bond or foreign mutual funds and “0” otherwise. We estimate the model for the full sample and for the Finance and English sub-samples separately. We exclude the indicator variable, faculty, which is “1” if the respondent is a Finance professor and “0” otherwise from the sub-sample regressions. The results of the estimation are in Table 6. The full sample results of Table 6 shows that the probability that an individual will diversify internationally is positively related to his income and Finance professors are significantly more likely to have ever invested in foreign stocks/bond or foreign mutual funds than their English counterpart. Further inspection of Table 6 also shows that consistent with the 21
overall results, Finance professors who earn more are more likely to hold foreign investments. However, of the variables included in our investigation, the probability that an English professor will diversify internationally is only related to the age of the respondent. In this sample older professors are more likely to hold foreign investments. We investigate if the second measure of international diversification is affected by other economic and demographic factors by performing cross-sectional analysis using the following regression model.
Intl = α + α Faculty + α Gender + α Married + α Age i
0
1
i
2
i
3
i
4
i
+ α Race + α Children + α Income + α Debt + e 5
i
6
i
7
i
8
i
(4)
i
The dependent variable, Intl, is the percentage of the respondent’s retirement savings that is invested in International Equities. Since the dependent variable is bounded at 0 and 1, we estimate a two-limit censored (tobit) regression. The results provided in Table 7 confirm that Finance professors allocate a significantly larger share of their retirement savings to international equities. Among the Finance professors, the amount invested in international equities is positively related to income but decreases with age. We also find that female professors are less likely to invest in international equities. The findings of Tables 2-6 and 2-7 confirm the results in Figure 2, that after controlling for economic and demographic factors, Finance professors are significantly more likely to invest in foreign stock/bonds or foreign mutual funds and allocate a larger share of their retirement savings to international equities.
3.4. Equity Diversification In this section we investigate if respondents who invest directly in individual stocks hold
22
diversified stock portfolios. We use two proxy measures of equity diversification. The measures are based on the responses to the following two questions from the survey: (i) How many stocks do you currently own (excluding mutual funds)? (ii) Which of the following sectors do you own stocks in? (Choose as many as apply) Figure 3 provides the breakdown of the respondents based on the response to these two questions. The top section of Figure 3 shows that while more than half of the English professors (53.8%) do not invest directly in equities, the corresponding proportion of the Finance professors is 31.0%. The proportion of Finance professors in each of the other three buckets, i.e. invest in 15 stocks, invest in 5-15 stocks and invest in greater than 15 stocks, is approximately uniform while the proportion of the English sample decreases monotonically as the number of stocks increases. The lower section of Figure 3 shows that most respondents in both samples invest directly in stocks that are in the same sector but the proportion is much larger for the English sample than the Finance sample (30.0% versus 17.7%.) To investigate the extent to which investors in both samples diversify within their equity portfolio, we define two proxy measures of equity diversification: i. The respondent invests in more than 15 stocks ii. The respondent invests in stocks from at least 4 sectors. Panel A of Table 8 compares the probability that a respondent will practice each of these diversification strategies as well as a combination of the two, i.e., invest in more than 15 stocks from four or more sectors. Results of the Mantel-Haenszel Chi-squared test confirm that the respondents in the finance sample are 10% more likely to invest in more than 15 stocks, 17% more likely to hold stocks in four or more sectors and 11% more likely to practice both strategies.
23
We also investigate if these results hold after controlling for other economic and demographic factors. We estimate the following probit regression model:
Pr (Diverse = 1) = α + α Faculty + α Gender + α Married + α Age i
0
1
i
2
i
3
i
4
+ α Race + α Children + α Income + α Debt + e 5
i
6
i
7
i
8
i
i
(3.5)
i
The model is estimated separately for each strategy and in each model the dependent variable Diverse is “1” for respondents that employ the respective strategy and “0” otherwise. The results for each of the strategies are given in Panels B, C and D of Table 8. In Panel B, Diverse is “1” only for those respondents that invest directly in 15 or more stocks and “0” otherwise. In Panel C, Diverse is “1” for respondents who invest directly in stocks from four or more sectors and in Panel D, Diverse is “1” only for respondents who invest directly in more than 15 stocks from four or more sectors and “0” otherwise. Panel B of Table 8 shows that Finance professors who are older and have higher income are more likely to invest directly in 15 or more stocks. For the English sample, the probability that a respondent will invest in more than 15 stocks is positively related to the income level but unrelated to the other factors included in the model. Further, there is no significant difference between the likelihood that respondents in either of the two sub-samples will undertake this strategy. The results in Panel C of Table 8 indicate that Finance professors are significantly more likely to invest in stocks from four or more sectors. In both samples, respondents who are older and have higher income are more likely to diversify across sectors. Within the Finance group, men are more likely to invest directly in stocks from four or more sectors. Inspection of the results of the combined equity diversification strategy in Panel D of Table 8 shows that respondents in the Finance sample are more likely to hold more than 15 stocks from four or more sectors. The other results in Panel D are similar to the findings in Panels B and C, with income and age having a positive affect on this strategy for the Finance
24
professors and income being the main contributing factor among the English professors. Male English professors are also moderately more likely than their female counterpart to invest in more than 15 stocks from four or more sectors. Together the results in this section suggest that knowledge of finance increases the likelihood that investors will diversify within their equity portfolio. However, after controlling for income and age, the impact is significantly reduced and is more related to the number of sectors chosen than the number of stocks held.
3.5. Naïve Diversification Strategies We now investigate two naïve diversification strategies that have received attention in the literature recently. The first is the “framing 1/n heuristic” in which the individual invests an equal proportion of his portfolio in each of the available asset categories and the second is the “conditional 1/n heuristic” in which the investor chooses a subset of the available asset categories and invests an equal proportion in each of the chosen categories. Specifically, we investigate if investors with more knowledge of finance are less likely to employ either or both of these naïve diversification strategies. We use the individual’s allocations to his retirement savings for our empirical investigation. Since we ask respondents to indicate how they allocate their retirement savings to seven funds, the framing 1/n heuristic is synonymous with an individual investing one-seventh of his retirement savings in each of the seven available funds. The conditional 1/n heuristic is equivalent to the investor choosing between two and six funds and investing equal proportion in each of the funds chosen. For example, if two funds are chosen, 50% would be invested in each, if three funds are chosen, 33.33% would be invested in each fund. Figure 4 shows the distribution of the funds chosen by both the Finance and English
25
professors. The distribution closely approximates a normal distribution, rising from one fund to a maximum at three funds and then falling to a minimum at seven funds. In Table 9, we provide results of t-test that the mean allocation to each of the funds chosen is “1/n”. We provide results for the overall sample as well as for each of the two sub-samples. If the framing 1/n heuristic holds, when seven funds are chosen the mean allocation to each fund should be 14.3%. If the conditional 1/n heuristic holds, when two, three, four, five or six funds are chosen, the allocation to each fund should be 50%, 33.3%, 25%, 20% and 16.67% respectively. The results for the full sample in Panel A shows that for respondents who invest in all seven funds, the allocation to four of the funds is not statistically different from 14.3%. However, for those choosing between two and six funds, only the allocations to the Multi-Asset Investment are consistently indistinguishable from 1/nth of the number of chosen funds. This is a preliminary indicator that overall, investors seem to treat multi-asset investments as a separate asset class, invest 1/n in that category and then subjectively allocate the remainder of their retirement portfolio to the other (n-1) chosen funds. The results for the Finance sub-sample in Panel B are qualitatively similar to the overall results in Panel A. However, the results for the English sub-sample in Panel C suggests that when respondents in this group choose n funds, except for the allocations to Domestic and International equities and Real Estate, the allocations to the other funds are largely indistinguishable from 1/n. 8 Together the results in Table 9 suggest that both Finance and English faculty are equally likely to practice the framing 1/n heuristic but the English professors are more likely to practice the conditional 1/n heuristic. Since the framing 1/n heuristic is considered to be irrational but the 8
In the English sub-sample, it is not possible to make an assessment of the framing 1/n heuristic or the conditional 1/n heuristic when 6 funds are chosen since only 3 respondents chose all 7 funds and 6 funds respectively, in this group.
26
conditional 1/n heuristic may be perceived as being rational, the findings in this section suggest that knowledge of finance does not necessarily lead to a reduction in the likelihood of less than fully rational behavior. 4.
Conclusions In this paper we investigate if the household asset allocation and diversification decision is
influenced by the individual’s knowledge of finance. Using a survey of Finance and English academicians at universities across the United States, we examine the extent to which knowledge of finance results in investors holding more diversified portfolios. We study both the asset allocation decision, (to see how efficiently households in our sample choose among the major asset classes) as well as the extent to which they diversify within their equity portfolios. For the asset allocation decision, we employ two proxy measures of active diversification. The first one tests if individuals allocate the majority of their direct investments to mutual funds or a mix of Stocks, Bonds and Cash. Using cross-sectional probit regression models, we find that after controlling for economic and demographic factors, individuals who have more knowledge of finance are more likely to efficiently allocate the majority of their direct investments. Our second test investigates the extent to which knowledge of finance increases the likelihood that an investor will seek the benefits of international diversification. We find that Finance professors are significantly more likely to invest in foreign stock/bonds or foreign mutual funds and allocate a larger share of their retirement savings to international equities than their English counterparts. Conditional on an investor holding a positive amount directly in individual stocks, we employ three tests of equity diversification. The first test is the probability of investing in more than 15 stocks; the second test is the probability of investing in stocks from four or more sectors and the third test is a combination of the first two, i.e., the probability of investing in 15 or more
27
stocks from four or more sectors. We find evidence that knowledge of finance increases the likelihood that an investor will diversify within his equity portfolio. However, after controlling for income and age, the impact is significantly reduced and is more related to the number of sectors chosen than the number of stocks held. We also investigate asset allocation decision in retirement savings but find no evidence that knowledge of finance increases the likelihood that an investor will invest the majority of his retirement savings either in Multi-asset investments or a mix of at least three of the available funds. Specifically, we find that within the Finance sample, the propensity to diversify in the retirement savings is most related to the age of the respondent. Finally, we investigate two naïve diversification strategies, the “framing 1/n heuristic” in which the individual invests an equal proportion of his portfolio in each of the available asset categories and a “conditional 1/n heuristic” in which the investor chooses a subset of the available asset categories and invest an equal proportion in each of the chosen categories. Our empirical findings suggest that both Finance and English faculty are equally likely to practice the framing 1/n heuristic but the English professors are more likely to practice the conditional 1/n heuristic. We acknowledge that by using a cross-sectional dataset, we have investigated the portfolio allocation decision in a static framework. However when we include dummy variables in our model to capture subjective rebalancing/life-cycle effects, our results are largely unchanged. The main difference is that the respondent’s years to retirement seem to be a more precise factor than age in retirement savings allocation decisions. Notwithstanding this finding, a follow-up survey may provide useful insights.
28
Table 1: Portfolio Allocations of Finance and English faculty This table presents summary statistics of the allocation into each of the asset groups. We provide the number and percentage of respondents who invest in each group and the mean allocation. Finance and English are the results of a survey of Finance and English faculty at universities across the United States. Panel A provides the allocations for the direct investments and Panel B provides allocations for the retirement savings. The number of observations in Panel B is less than Panel A since some respondents do not have a retirement account. The categories in Panel B are based on the TIAA-CREF asset classes.
Panel A – Direct Investments Number of Participants All (1385)
Mean Allocation
Finance (1147)
English (238)
All
Finance
English
Checking, Savings, CDs, Govt. Bills and Bonds
1234
(89.1%)
1016
(88.6%)
218
(91.6%)
26.5%
22.4%
45.9%
Federal Agency Bonds and Municipal Bonds
445
(32.1%)
386
(33.7%)
59
(24.8%)
8.2%
7.6%
12.2%
Corporate Bonds Mutual Funds Stocks REITs Derivatives
481 1099 869 342 223
(34.7%) (79.4%) (62.7%) (24.7%) (16.1%)
446 933 755 313 208
(38.9%) (81.3%) (65.8%) (27.3%) (18.1%)
35 166 114 29 15
(14.7%) (69.7%) (47.9%) (12.2%) (6.3%)
9.9% 58.7% 33.9% 7.4% 2.7%
10.0% 60.0% 33.9% 7.7% 2.9%
8.8% 51.3% 33.6% 4.1% 0.0%
Panel B – Retirement Savings Number of Participants All (1242) Equities – Domestic Equities – International Real Estate Fixed Income Money Market Guaranteed Income Multi Asset Investment
1134 928 494 708 474 302 246
(91.3%) (74.7%) (39.8%) (57.0%) (38.2%) (24.3%) (19.8%)
Mean Allocation
Finance (1074)
English (168)
1001 830 423 645 412 255 196
133 98 71 63 62 47 50
(93.2%) (77.3%) (39.4%) (60.1%) (38.4%) (23.7%) (18.2%)
29
(79.2%) (58.3%) (42.3%) (37.5%) (36.9%) (28.0%) (29.8%)
All 54.3% 22.6% 14.5% 21.5% 16.3% 17.5% 25.1%
Finance
English
55.2% 22.7% 13.5% 21.0% 14.2% 15.7% 21.8%
47.9% 21.9% 20.8% 27.5% 30.0% 26.8% 38.0%
Table 2: Investment Strategies by Discipline In this table we compare how individuals allocate the majority of their financial assets. We provide the breakdown of the strategies that account for 70 percent or more of the respondents’ portfolios. The results for the Finance and English professors and the combined sample are given. Panel A provides the allocations for the direct investments and Panel B provides similar results for the retirement savings. We also perform Mantel-Haenszel Chi-Squared test that the proportion using each allocation is the same for both sub-samples; *, ** and *** denote significance at the 10%, 5% and 1% level respectively.
Panel A – Direct Investments Allocations
All
Finance
English
MantelHaenszel Chi-Squared
N (1) Invest 70% or more in Mutual Funds (2) Invest 70% or more in mix of Cash, Bonds and Stocks (3) Invest 70% or more in Cash (4) Invest 70% or more in Bonds (5) Invest 70% or more in Stocks
1385 36.8% 37.9% 11.3% 0.4% 12.8%
1147 38.9% 38.8% 7.3% 0.4% 13.9%
235 26.8% 34.0% 31.1% 0.4% 7.7%
13.057*** 2.248 106.834*** N/A 7.012***
Diversified Portfolios - (1) and (2) above
89.4%
93.2%
70.6%
32.234***
Panel B – Retirement Savings Allocations
Finance
N (1) Invest 70% or more in Multi-Asset (2) Invest 70% or more in mix of Categories (3) Invest 70% or more in Money Market Investments (4) Invest 70% or more in Fixed Income or Guaranteed Income (5) Invest 70% or more in Equities (6) Invest 70% or more in Real Estate
1241 2.7% 32.1% 1.5%
1074 2.1% 30.6% 1.1%
167 6.6% 41.3% 4.2%
10.584*** 7.263*** 8.960***
3.6%
3.3%
6.0%
3.016**
58.9% 1.1%
61.8% 1.0%
40.1% 1.8%
28.866*** 0.755
Diversified Portfolios - (1) and (2) above
34.8%
32.8%
47.9%
14.101***
30
English
MantelHaenszel Chi-Squared
All
Table 3: Summary Statistics for Control Variables This Table presents summary statistics for the result of our survey of Finance and English professors at universities across the United States. Finance
English
All
1106
279
1385
N Gender Male Female
967 180
84% 16%
139 99
58% 42%
1106 279
80% 20%
Age (Age) 20-29 30-39 40-49 50-59 60 or above
12 232 290 378 235
1% 20% 25% 33% 20%
9 59 51 58 61
4% 25% 21% 24% 26%
21 291 341 436 296
2% 21% 25% 31% 21%
17 142 906 18 6
1% 12% 79% 2% 1%
14 8 202 5 1
6% 3% 85% 2% 0%
31 150 1108 23 7
2% 11% 80% 2% 1%
53
5%
8
3%
61
4%
Marital Status (Married) Single Married or Living with partner
184 963
16% 84%
61 177
26% 74%
245 1140
18% 82%
Number of Children in Household (Children) None 1 2 More than 2
645 190 208 104
56% 17% 18% 9%
179 37 18 4
75% 16% 8% 2%
824 227 226 108
59% 16% 16% 8%
Income (Income) Less than $75,000 $75,000 - $149,999 $150,000 and above
41 467 628
4% 41% 55%
67 110 60
28% 46% 25%
108 577 688
8% 42% 50%
Unsecured Debts (Debt) Less than $25,000 $25,000 - $99,999 $100,000 - $249,999 $250,000 - $499,999 $500,000 or more
817 140 103 52 31
71% 12% 9% 5% 3%
167 44 21 6 0
70% 18% 9% 3% 0%
984 184 124 58 31
71% 13% 9% 4% 2%
Race/Ethnicity (Race) African-American (Non-Hispanic) Asian/Pacific Islanders Caucasian (non Hispanic) Latino or Hispanic Native American, Aleut or Aboriginal Peoples Other
31
Table 4: Analysis of Asset Allocation Decisions This table provides probit regression analysis for the combined faculty sample and the Finance and English sub-samples using the following model:
Pr (Diverse = 1) = α + α Faculty + α Gender + α Married + α Age + α Race + α Children i
0
1
i
2
i
+ α Income + α Debt + e 7
i
8
i
3
i
4
i
5
i
6
i
i
Panel A provides the results for direct investments and Panel B provides similar results for the retirement savings. In Panel A Diverse is “1” for individuals who invest more than 70 percent of their portfolio in either mutual funds or a mixture of at least Cash, Stocks and Bonds. In Panel B Diverse is “1” for individuals who invest more than 70 percent of their retirement savings in either multi-investment assets or a mix of at least three of the other categories. The faculty variable (0=English, 1=Finance) is omitted from the regressions of the sub-samples. The chi-squared values for each of the estimates are in parenthesis below the respective estimates. Significant estimates at the 10%, 5% and 1% level are denoted by *, ** and *** respectively.
Panel A – Direct Investments Faculty
Gender
Married
Age
Race
Children
Income
Debt
Intercept
Log Likelihood
N
0.687*** (15.76)
0.165 (1.00)
0.341** (3.98)
0.272** (18.40)
-0.078* (3.08)
0.066 (1.19)
0.301*** (7.63)
-0.152** (5.74)
-1.623*** (11.22)
-737.721
1371
Finance
0.406** (3.70)
0.384* (3.60)
0.242*** (10.74)
-0.044 (0.84)
0.050 (0.63)
0.199 (2.34)
-0.141** (4.26)
-1.004* (3.01)
-590.641
1134
English
-0.324 (1.23)
0.383 (1.25)
0.299** (4.11)
-0.338** (5.88)
0.138 (0.48)
0.525** (4.65)
-0.207 (1.17)
-1.101 (1.48)
-141.071
237
All
Panel B – Retirement Savings Faculty
Gender
Married
Age
Race
Children
Income
Debt
Intercept
Log Likelihood
N
-0.494*** (7.19)
0.264* (2.64)
0.453*** (6.16)
0.292*** (19.60)
-0.048 (1.06)
-0.138** (5.47)
-0.066 (0.36)
0.028 (0.19)
-2.095*** (15.42)
-764.380
1230
Finance
0.570*** (9.31)
0.676*** (9.89)
0.354*** (22.52)
-0.045 (0.81)
-0.131** (4.43)
-0.184 (2.15)
0.012 (0.03)
-3.277*** (29.06)
-643.268
1063
English
-0.607* (3.35)
-0.301 (0.58)
-0.163 (0.86)
-0.103 (0.48)
-0.180 (0.67)
0.589** (4.70)
0.076 (0.15)
0.754 (0.45)
-110.606
167
All
32
Table 5: Extended Model of Retirement Savings This table provides probit regression analysis for the combined faculty sample and the Finance and English sub-samples using the following model:
Pr ( Diverse = 1) = α + α Faculty + α Gender + α Married + α Age + α Race + α Children i
0
1
i
2
i
3
i
4
i
5
i
6
i
+ α Income + α Debt + α Changeplan + α PlanAge + α Yrsto Re t + α PlanRatio + e 7
i
8
i
9
i
10
i
11
i
12
i
i
The dependent variable, Diverse is “1” for individuals who invest more than 70 percent of their retirement savings in either multi-investment assets or a mix of at least three of the other categories. The faculty variable (0=English, 1=Finance) is omitted from the regressions of the sub-samples. ChangePlan is the frequency with which the respondent changes the composition of his retirement plan, PlanAge is the number of years the respondent has been investing in the retirement plan, YrstoRet is the number of years remaining until retirement and PlanRatio is the percentage of the household total assets that the retirement plan represents. The chi-squared values for each of the estimates are in parenthesis below the respective estimates. Significant estimates at the 10%, 5% and 1% level are denoted by *, ** and *** respectively.
ChangePlan: 0=Never, 1=Every 5 years or more, 2=every 2-5 years, 3=at least once every 2 years. PlanAge: 1=less than 5 years ago, 2=5-20 years ago, 3=more than 20 years ago. YrstoRet: 1=within 10 years, 2=10-25 years, 3=later than 25 years. PlanRatio: 1=less than 20 percent, 2=20 percent to 49 percent, 3=50 percent to 79 percent and 4=80 percent or more.
All
Finance
English
Faculty
Gender
Married
Age
Race
Children
Income
Debt
Change Plan
PlanAge
-0.598***
0.262
0.424**
0.016
-0.053
-0.127**
-0.085
0.035
0.072
(10.02)
(2.57)
(5.30)
(0.02)
(1.08)
(4.59)
(0.58)
(0.32)
(1.63)
0.558***
0.626***
0.099
-0.054
-0.115**
-0.192
0.022
(8.82)
(8.35)
(0.66)
(0.98)
(3.40)
(2.27)
(0.10)
Intercept
Log Likelihood
N
-0.066
-0.260
-757.345
1230
(1.06)
(0.11) -637.548
1063
-109.908
167
YrstoRet
PlanRatio
0.101
-0.428***
(0.59)
(10.14)
0.072
0.071
-0.422***
-0.079
-1.499*
(1.36)
(0.25)
(8.05)
(1.26)
(2.91)
-0.595*
-0.304
-0.366
-0.075
-0.199
0.581**
0.046
0.101
0.011
-0.344
0.040
1.925
(3.01)
(0.56)
(1.43)
(0.20)
(0.78)
(4.25)
(0.05)
(0.43)
(0.00)
(1.03)
(0.06)
(1.05)
33
Table 6: Analysis of Investment in Foreign Assets This table provides probit regression analysis for the combined faculty sample and the Finance and English sub-samples using the following model:
Pr (Foreign = 1) = α + α Faculty + α Gender + α Married + α Age + α Race + α Children i
0
1
i
2
i
+ α Income + α Debt + e 7
i
8
i
3
i
4
i
5
i
6
i
i
Foreign is “1” for individuals who have invested in foreign stocks/bonds or foreign mutual funds and “0” otherwise. The faculty variable (0=English, 1=Finance) is omitted from the regressions of the sub-samples. The chi-squared values for each of the estimates are in parenthesis below the respective estimates. Significant estimates at the 10%, 5% and 1% level are denoted by *, ** and *** respectively.
Log Likelihood
N
-1.150** (4.61)
-706.991
1230
-0.070 (1.01)
0.420 (0.50)
-596.948
1063
-0.094 (0.21)
-3.508*** (7.69)
-101.938
167
Faculty
Gender
Married
Age
Race
Children
Income
Debt
Intercept
1.136*** (37.51)
-0.136 (0.66)
0.003 (0.00)
0.080 (1.42)
-0.067 (2.17)
0.066 (1.17)
0.452*** (15.70)
-0.080 (1.53)
Finance
-0.181 (0.86)
-0.112 (0.28)
-0.002 (0.00)
-0.052 (1.12)
0.039 (0.39)
0.491*** (14.20)
English
-0.027 (0.01)
0.690 (2.56)
0.654*** (11.70)
-0.224 (1.57)
0.292 (1.75)
-0.008 (0.00)
All
34
Table 7: Proportion of Portfolio invested in International Equities This table provides results of two-limit censored (tobit) regression analysis for the combined faculty sample and the Finance and English sub-samples using the following model:
Intl = α + α Faculty + α Gender + α Married + α Age + α Race + α Children i
0
1
i
2
i
+ α Income + α Debt + e 7
i
8
i
3
i
4
i
5
i
6
i
i
Intl is the percentage of the individual’s retirement savings invested in International Equities. The faculty variable (0=English, 1=Finance) is omitted from the sub-sample regressions. The Qualitative Limited Independent Model procedure which uses a non-linear optimization is used for the estimation. The t-values for each of the estimates are in parenthesis below the respective estimates. Significant estimates at the 10%, 5% and 1% level are denoted by *, ** and *** respectively.
Faculty
Gender
Married
Age
Race
Children
Income
Debt
Intercept
Log Likelihood
N
0.057** (2.83)
-0.030 (-1.79)
-0.014 (-0.78)
-0.052*** (-7.92)
0.000 (-0.06)
0.003 (0.48)
0.028** (2.40)
0.005 (0.81)
0.252*** (4.66)
-192.206
1230
Finance
-0.047*** (-2.53)
-0.025 (-1.24)
-0.057*** (-8.11)
0.002 (0.33)
0.002 (0.34)
0.032*** (2.54)
0.004 (0.63)
0.353*** (6.27)
-130.917
1063
English
0.041 (1.01)
0.050 (0.98)
-0.011 (-0.49)
-0.025 (-1.29)
0.006 (0.24)
-0.017 (-0.49)
0.026 (1.06)
-0.028 (-0.19)
-53.255
167
All
35
Table 8: Analysis of Equity Diversification This table compares direct investment in equities. Panel A compares three diversification strategies: (i) Invest in greater than 15 stocks, (ii) Invest in stocks from at least 4 different sectors and (iii) a combination of (i) and (ii). Results of Mantel-Haenszel Chi-Squared tests that the proportion of respondents using each strategy is the same for both the Finance and English sub-sample are also given. We also perform probit regression analysis of each strategy using the following model;
Pr ( Diverse = 1) = α + α Faculty + α Gender + α Married + α Age + α Race + α Children i
0
1
i
2
i
+ α Income + α Debt + e 7
i
8
i
3
i
4
i
5
i
6
i
i
The results for each strategy are given in Panels B, C and D respectively. In each Panel Diverse is “1” for individuals who employ the respective strategy and “0” otherwise. For example, in Panel B Diverse is “1” for respondents who invest in greater than 15 stocks. We provide results for the overall sample and for the Finance and English sub-samples. The faculty variable (0=English, 1=Finance) is omitted from the regressions of the sub-samples. The chi-squared values for each of the estimates are in parenthesis below the respective estimates. In all panels, *, ** and *** denote significance at the 10%, 5% and 1% level respectively.
Panel A – Measures of Equity Diversification Mantel-Haenszel Chi-Squared
All
Finance
English
N Invest in greater than 15 stocks Invest in stocks from 4 or more sectors
1377 20.2% 35.8%
1137 21.5% 38.8%
240 13.8% 21.7%
7.473*** 25.251***
Invest in greater than 15 stocks from 4 or more sectors
18.2%
20.1%
8.8%
17.291***
Panel B – Invest in more than 15 stocks Faculty
Gender
Married
Age
Race
Children
Income
Debt
Intercept
Log Likelihood
N
0.133 (0.37)
-0.293 (2.13)
-0.131 (0.39)
0.256*** (12.05)
0.023 (0.22)
0.026 (0.16)
0.706*** (28.09)
0.087 (1.68)
-3.795*** (36.69)
-652.299
1363
Finance
-0.239 (1.11)
-0.044 (0.04)
0.247*** (9.58)
0.025 (0.23)
0.022 (0.11)
0.597*** (16.67)
0.071 (1.01)
-3.538*** (27.89)
-567.291
1125
English
-0.474 (1.19)
-0.437 (0.78)
0.170 (0.59)
-0.038 (0.04)
0.037 (0.01)
1.213*** (12.13)
0.221 (0.98)
-3.994*** (7.49)
-83.113
238
All
36
Table 8 contd. Panel C – Invest in stocks from 4 or more Sectors Faculty
Gender
Married
Age
Race
Children
Income
Debt
Intercept
Log Likelihood
N
0.551*** (8.95)
-0.394** (5.78)
-0.066 (0.15)
0.251*** (17.05)
-0.024 (0.30)
-0.028 (0.28)
0.434*** (16.89)
0.033 (0.32)
-2.432*** (23.55)
-843.922
1363
Finance
-0.456** (5.92)
-0.138 (0.54)
0.240*** (13.15)
-0.014 (0.09)
-0.041 (0.55)
0.410*** (12.17)
0.030 (0.24)
-1.574*** (8.68)
-727.690
1125
English
-0.212 (0.37)
0.278 (0.41)
0.296* (2.77)
-0.180 (0.88)
0.183 (0.74)
0.548** (4.02)
0.135 (0.45)
-3.739*** (9.27)
-114.063
238
All
Panel D – Invest in more than 15 stocks from 4 or more Sectors Faculty
Gender
Married
Age
Race
Children
Income
Debt
Intercept
Log Likelihood
N
0.558** (4.76)
-0.458** (4.22)
-0.146 (0.43)
0.277*** (12.56)
-0.036 (0.44)
0.029 (0.19)
0.751*** (27.80)
0.024 (0.11)
-4.100*** (36.02)
-604.761
1363
Finance
-0.293 (1.54)
-0.114 (0.23)
0.257*** (9.79)
-0.033 (0.36)
0.023 (0.12)
0.658*** (18.76)
0.028 (0.15)
-3.472*** (25.40)
-544.330
1125
English
-1.450** (4.73)
-0.198 (0.09)
0.399 (1.89)
-0.074 (0.07)
0.155 (0.17)
1.304*** (8.60)
-0.073 (0.06)
-4.477** (4.81)
-57.220
238
All
37
Table 9: Naïve Diversification Strategies This table compares two “naïve” diversification strategies. The first strategy is the “framing 1/n heuristic”, where individuals invest 1/n in each of the n funds available for their retirement savings. The second strategy is the “conditional 1/n heuristic” where the individual chooses a subset, n of the available funds and invests 1/n in each of the n chosen funds. We use 5 of the 6 major funds available via TIAA-CREF and 2 sub-categories of the 6th fund. Since the maximum number of funds is 7, the “framing 1/n heuristic” is analogous to individuals investing 1/7th in each of the 7 funds. Results are provided for the combined faculty in Panel A and for the Finance and English sub-samples in Panels B and C respectively. We test if the mean proportional allocation in each of the n funds chosen differs significantly from 1/n. For example, for respondents who invest in 2 funds, we perform t-test that the mean allocation in each of the 2 funds is 50% etc. *, ** and *** denote significance at the 10%, 5% and 1% level respectively.
Panel A – All Faculty Investment in each of the Funds Chosen Number of Funds Chosen
1
2
3
4
5
6
7
Equities Domestic
100
63.6***
56.0***
48.4***
41.5***
33.4***
26.5***
Equities International
100
35.5***
22.6***
19.0***
16.2***
16.3
11.8**
Real Estate
100
45.7
17.4
13.4***
12.6***
10.3***
11.8
Fixed Income
100
40.5***
22.9***
19.0***
15.5***
15.3
13.9
Money Market
100
44.4
22.5
13.1***
12.0***
8.7***
8.0***
Guaranteed Income
100
39.1**
26.4**
18.7***
14.5***
13.7
17.8
Multi Asset Investment
100
52.0
34.8
23.2
20.3
16.6
14.8
N
119
265
357
298
149
36
17
38
Table 9 contd. Panel B – Finance Faculty Investment in each of the Funds Chosen 3 4 5 6
Number of Funds Chosen
1
2
Equities Domestic
100
64.5***
56.2***
49.0***
44.1***
34.5***
30.0***
Equities International
100
35.4***
22.6***
18.8***
16.4***
15.8
12.1
Real Estate
100
44.7
18.0***
13.2***
10.9***
10.6***
11.9
Fixed Income
100
39.1***
22.1***
18.7***
15.3***
15.6
14.4
Money Market
100
41.0
21.4***
12.7***
11.4***
7.9***
7.9***
Guaranteed Income
100
36.7**
27.4*
18.4***
13.0***
13.9
9.9***
Multi Asset Investment
100
49.0
33.8
25.1
20.4
16.3
13.9
93
229
308
271
126
33
14
Number of Funds Chosen
1
2
3
4
5
6
7
Equities Domestic
100
55.7
54.1***
41.5***
27.7***
21.3
10.0
Equities International
-
36.4***
22.1***
21.2
15.4***
21.3
10.0
Real Estate
100
47.2
15.3***
15.4***
21.3
5.5**
11.7
Fixed Income
100
51.1
30.4
26.0
17.4
12.0
11.7
Money Market
100
55.8
27.3
17.4**
16.2
20.5
8.3
Guaranteed Income
100
46.4
21.4*
20.1
20.8
12.5
54.7
Multi Asset Investment
100
58.0
36.5
17.2**
20.0
18.3
19.0
26
36
49
23
3
N
7
Panel C – English Faculty Investment in each of the Funds Chosen
N
39
27
3
Figure 1: Relative Allocations by Discipline
Direct Investments
Invest 70% or more in Mutual Funds Invest 70% or more in mix of Cash, Bonds and Stocks Invest 70% or more in Cash
Invest 70% or more in Bonds
Invest 70% or more in Stocks 0.0%
5.0%
10.0%
15.0%
Finance
20.0%
25.0%
30.0%
35.0%
40.0%
English
Retirement Savings
Invest 70% or more in Multi-Asset Invest 70% or more in mix of Categories Invest 70% or more in Money Market Investments Invest 70% or more in Fixed Income or Guaranteed Income Invest 70% or more in Equities Invest 70% or more in Real Estate 0.00%
10.00%
20.00%
30.00%
Finance
40
English
40.00%
50.00%
60.00%
70.00%
Figure 2: Investment in International Equities
80.0%
Finance
English
70.0% 60.0% 50.0% 40.0% 30.0% 20.0% 10.0% 0.0% Has Invested in Foreign Stocks
70.0%
Finance
English
60.0% 50.0% 40.0% 30.0% 20.0% 10.0% 0.0%
≤20%
20 - 40%
40 - 60%
60 - 80%
Proportion in International Equities
41
≥80%
Figure 3: Direct Investment in Equities (a) Number of Stocks
Finance
60.0%
English
50.0% 40.0% 30.0% 20.0% 10.0% 0.0%
None
Less than 5
Between 5 and 15
Greater than 15
(B) Number of Sectors 30.0%
Finance
English
25.0% 20.0% 15.0% 10.0% 5.0% 0.0%
1
2
3
4
5
6
Number of Sectors
42
7
8
9
10
Figure 4: Number of Retirement Funds Chosen
30.0% Finance
English
25.0%
20.0% 15.0% 10.0%
5.0% 0.0% 1
2
3
4
5
Number of Funds Chosen
43
6
7
REFERENCES Agnew, J., Balduzzi, P., Sunden, A., 2003. Portfolio Choice and Trading in a Large 401 (k) Plan. American Economic Review 93, 193-215 Agnew, J.R., 2006. Do Behavioral Biases Vary across Individuals? Evidence from Individual Level 401(k) Data. Journal of Financial and Quantitative Analysis 41, 939 Baxter, M., Jermann, U.J., 1997. The international diversification puzzle is worse than you think. American Economic Review 87, 170-180 Benartzi, S., Thaler, R.H., 2001. Naive Diversification Strategies in Defined Contribution Saving Plans. American Economic Review 91, 79-98 Bertaut, C., Starr-McCluer, M., 2002. Household Portfolios in the United States. MIT Press. Campbell, J.Y., 2006. Household Finance. The Journal of Finance 61, 1553-1604 Campbell, J.Y., Lettau, M., Malkiel, B.G., Xu, Y., 2001. Have Individual Stocks Become More Volatile? An Empirical Exploration of Idiosyncratic Risk. Journal of Finance 56, 1-43 Canner, N., Mankiw, N.G., Weil, D.N., 1997. An Asset Allocation Puzzle. American Economic Review 87, 181-191 Cavaglia, S., Brightman, C., Aked, M., 2000. The Increasing Importance of Industry Factors. Financial Analysts Journal 56, 41-54 Cohn, R.A., Lewellen, W.G., Lease, R.C., Schlarbaum, G.G., 1975. Individual Investor Risk Aversion and Investment Portfolio Composition. The Journal of Finance 30, 605-620 Curcuru, S., Heaton, J., Lucas, D., Moore, D., 2004. Heterogeneity and Portfolio Choice: Theory and Evidence. Dwyer, P.D., Gilkeson, J.H., List, J.A., 2002. Gender differences in revealed risk taking: evidence from mutual fund investors. Economics Letters 76, 151-158 French, K.R., Poterba, J.M., 1991. Investor Diversification and International Equity Markets. American Economic Review 81, 222-226 Friend, I., Blume, M.E., 1975. The Demand for Risky Assets. American Economic Review 65, 900-922
44
Goetzmann, W.N., Kumar, A., 2008. Equity Portfolio Diversification. Review of Finance Huberman, G.U.R., Jiang, W.E.I., 2006. Offering versus Choice in 401 (k) Plans: Equity Exposure and Number of Funds. The Journal of Finance 61, 763-801 Kalra, R., Stoichev, M., Sundaram, S., 2004. Diminishing gains from international diversification. Financial Services Review 13, 199-214 Kelly, M., 1995. All their eggs in one basket: Portfolio diversification of US households. Journal of Economic Behavior and Organization 27, 87-96 King, M.A., Leape, J.I., 1998. Wealth and portfolio composition: Theory and evidence. Journal of Public Economics 69, 155-193 Lewis, K.K., 1999. Trying to Explain Home Bias in Equities and Consumption. Journal of Economic Literature 37, 571-608 Malkiel, B.G., 1996. A random walk down Wall street 6 thed. WW Norton & Company, New York. Polkovnichenko, V., 2004. Limited stock market participation and the equity premium. Financial Services Letter 1, 24-34 Polkovnichenko, V., 2005. Household Portfolio Diversification: A Case for RankDependent Preferences. Review of Financial Studies 18, 1467 Read, D., Lowenstein, G., 1995. Diversification Bias: Explaining the Discrepancy between Combined and Separate Choices. Journal of Experimental Psychology 1, 7-59 Riley, W.B., Chow, K.V., 1992. Asset allocation and individual risk aversion. Financial Analysts Journal 48, 32-37 Rosen, H.S., Wu, S., 2004. Portfolio choice and health status. Journal of Financial Economics 72, 457-484 Shefrin, H., Statman, M., 2000. Behavioral Portfolio Theory. Journal of Financial and Quantitative Analysis 35, 127-151 Shlomo, B., Richard, H.T., 2001. Naive diversification strategies in defined contribution saving plans. American Economic Review 91, 79 Simonson, I., 1990. The Effect of Purchase Quantity and Timing on Variety-Seeking Behavior. Journal of Maketing Research 27, 150-62 Statman, M., 2004. The Diversification Puzzle. Financial Analysts Journal 60
45
Sunden, A.E., Surette, B.J., 1998. Gender differences in the allocation of assets in retirement savings plans. American Economic Review 88, 207 Welch, I., 2000. Views of Financial Economists on the Equity Premium and on Professional Controversies*. The Journal of Business 73, 501-537
46
Appendix A - Questionnaire 1. Gender: Male Female 2. Age: 20-29 30-39 40-49 50-59 60 or above 3. Racial or Ethnic Group(s): (To which racial or ethnic group(s) do you most identify? Select more than one if applicable) African-American (Non-Hispanic) Asian/Pacific Islanders Caucasian (non Hispanic) Latino or Hispanic Native American, Aleut or Aboriginal Peoples Other 4. For how long have you lived in the United States? Since birth Less than 10 years 10 years or more 5. Marital Status Single Married or Living with partner 6. Do you and your spouse invest jointly or separately? Jointly Separately 7. Who has greater responsibility for making savings and/or investment decisions in your household? Me My Spouse 8. How many children under age 18 do you have in your household? None 1 2 More than 2
47
9. What is the approximate value of your house? Less than $100,000 $100,000 - $249,999 $250,000 - $499,999 $500,000 or more 10. What is the approximate value of your tangible assets other than your home (e.g., jewelry)? Less than $50,000 $50,000 - $99,999 $100,000 or more 11. If you own real estate other than your personal residence, what is the combined approximate value? Not applicable $100,000 - $249,999 $250,000 - $499,999 $500,000 or more I do not own a home 12. Do you currently own a firm? Yes No 13. What is the approximate value of your outstanding unsecured loans and other liabilities (including credit cards)? Less than $25,000 $25,000 - $99,999 $100,000 - $249,999 $250,000 - $499,999 $500,000 or more 14. What is your Current Household Income? Less than $75,000 $75,000 - $149,999 $150,000 and above 15. How long have you been a Faculty/Instructor? Less than 3 years More than 3 years 16. Are you a tenured professor? Yes No 17. Which of the following expressions best describes your short-term expectations of the market? I expect a bull period I expect a bear period I expect a normal (or flat) period
48
18. Which of the following statements best characterize your recent investment experience? On average, I have experienced a loss on my investments On average, my gains are just about as much as my losses On average, I have experienced a gain on my investments. 19. Have you ever invested in any of the following? Choose as many as apply. U.S. Govt. Bills and Bonds Federal Agency Bonds or Municipal Bonds U.S. Corp. bonds or bond mutual funds U.S. High-yield junk bond or bond mutual funds U.S. Large-cap stocks or stock mutual funds U.S. Small-cap stocks or stock mutual funds Foreign stocks/bond or foreign mutual funds Futures and options Managed futures or commodity pools Private Hedge Funds Privately managed Accounts REIT’s None of the Above 20. Please indicate what percentage of your total wealth is currently invested in each of the following categories (The total must sum to 100): Checking, Savings, CDs, Govt. Bills and Bonds Federal Agency Bonds and Municipal Bonds Corporate Bonds Mutual Funds Stocks REIT’s Derivatives 21. When was the last time you invested in the stock market? I currently invest in the stock market The last time I invested in the stock market was within the last 5 years The last time I invested in the stock market was more than 5 years ago I have never invested in the stock market 22. Which of the following statements best characterize your last investment in the stock market? I made a gain on my investment I made a loss on my investment Not Applicable 23. How many stocks do you currently own (excluding mutual funds)? None Less than 5 Between 5 and 15 Greater than 15
49
24. Which of the following sectors do you own stocks in? (Choose as many as apply) Oil & Gas Basic Materials Industrials Consumer Goods Health Care Consumer Services Telecommunications Utilities Financials Technology None of the Above 25. Do you currently invest in a retirement plan? Yes No Plan 26. When did you start investing in your retirement plan? Less than 5 years ago 5-20 years ago More than 20 years ago 27. When do you anticipate withdrawing money from your plan? Later than 25 years 10-25 years Within 10 years 28. Please indicate the percentage of your total retirement asset invested in each of the following (Total must sum to 100): Equities - Domestic Equities - International Real Estate Fixed Income Money Market Accounts Guaranteed Income Multi-Asset Investments 29. How often do you change the composition of your retirement plan? Never Every 5 years or more Every 2-5 years At least once every 2 years 30. Excluding my primary residence, my retirement plan represents ___% of my investment holdings. less than 20 percent 20 percent to 49 percent 50 percent to 79 percent 80 percent or more
50
31. How do you rank the following in order of Riskiness? (0=No/Least Risk, 6=Most Risk) Checking, Savings, CDs, Govt. Bills and Bonds Federal Agency Bonds and Municipal Bonds Corporate Bonds Mutual Funds Stocks REIT’s Derivatives
51
Appendix B: SCF Data, 2004 - Descriptive Statistics Income, Equity and Financial Assets are in Thousands, Gender is 1 for male, 2 for female; Age is in Years, Educ is years of formal education, Children is number of children under 18, Race is a categorical variable from 1 to 5 for each of the 5 Federal classification, 1 is White
All Households VARIABLE
N
MIN
MAX
MEAN
STD
GENDER
4519
1
2
1.22
0.41
AGE
4519
18
95
50.74
15.7
MARRIED
4519
1
2
1.34
0.47
EDUC
4519
1
17
13.97
2.89
CHILDREN
4519
0
8
0.84
1.16
RACE
4519
1
5
1.41
0.91
INCOME
4519
0
105069.9
792.14
3914.71
EQUITY
4519
0
202657.4
1891.1
10824.7
FIN
4519
0
577788
3382.7
17512.6
Households with no Financial Assets VARIABLE
N
MIN
MAX
MEAN
STD
GENDER
233
1
2
1.425
0.495
AGE
233
18
91
42.176
14.403
MARRIED
233
1
2
1.597
0.492
EDUC
233
1
17
9.936
3.3
CHILDREN
233
0
6
1.116
1.438
RACE
233
1
5
2.039
0.939
INCOME
233
0
129.39
17.185
15.112
EQUITY
233
0
0
0
0
FIN
233
0
0
0
0
Households with Financial Assets VARIABLE
N
MIN
MAX
MEAN
STD
GENDER
4286
1
2
1.2
0.4
AGE
4286
18
95
51.2
15.63
MARRIED
4286
1
2
1.33
0.47
EDUC
4286
1
17
14.19
2.69
CHILDREN
4286
0
8
0.83
1.14
RACE
4286
1
5
1.37
0.9
INCOME
4286
0
105070
834.3
4015.45
EQUITY
4286
0
202657
1994
11105.85
FIN
4286
0
577788
3567
17964.16
52
