Evidence of Risk Aversion in the Health and Retirement Study
 

By

 

Vickie L. Bajtelsmit

 

Department of Finance and Real Estate

Colorado State University
Fort Collins, CO 80523
(970) 491-0610 (Phone)
(970) 491-7665 (Fax)
vickie_bajtelsmit@biznet.cobus.colostate.edu
 
 
 

 

March 1, 1999

 

 

 

THIS IS A PRELIMINARY DRAFT AND SHOULD NOT BE QUOTED OR OTHERWISE DISTRIBUTED WITHOUT THE AUTHOR’S CONSENT.

 

 

Financial support for this research was provided by the Public Policy Institute of the American Association of Retired Persons.  However, the opinions expressed herein are solely the responsibility of the author.
  

 

ABSTRACT

 

This study reviews the literature on individual risk aversion and investment allocation.  Relative risk aversion is estimated using the 1994 wave of the Health and Retirement Study, a large nationally representative sample of households nearing retirement. After controlling for age, income, dependents, and other demographic characteristics, the results confirm earlier findings of decreasing relative risk aversion.  Single women are found to be relatively more risk averse than married couples.  Risky portfolio allocation is significantly lower for older households, for those with lower educational levels, and for black households, when housing is not included in the definition of wealth.  Examination of the wealth accumulation in this sample of households indicates excessive levels of debt and insufficient savings are common.  A smaller sample of individuals completed an experimental component of the survey designed to measure risk aversion with respect to gain or loss of income. The respondents’ self-professed risk aversion hasa positive impact on risky allocation but the significance level is low. 

 

I.                Introduction

 

The prevalence of self-directed pensions and the recent performance of the stock market have increased public awareness of the impact of asset allocation on portfolio accumulations.  While investment professionals have long been aware of the importance of taking risk for long term growth, the “common wisdom” is that individuals, on average, are more risk averse investors.  The social security reform debate has put the spotlight on this issue since the essence of the argument for privatization is that retirement income goals can be more easily achieved when returns on payroll taxes are invested in higher return (and higher risk) assets.  If certain groups of individuals tend to be more risk averse than others, there may be adverse and unintended consequences.  For example, if women and minority groups are more risk averse than men, the current disparities in working income will be exacerbated in retirement.  Women’s greater average longevity implies that they actually need to have a greater accumulation at retirement to support the same level of retirement income as men.

 

The purpose of this study is to examine household wealth allocations by individual characteristics, to estimate relative risk aversion, and to test for differences by gender and other characteristics.  The Health and Retirement Study, a unique nationally representative sample of households on the verge of retirement, provides the necessary financial and demographic information.  A thorough literature review of the previous research related to risk aversion and individual asset allocation is provided in Section II.  Section III presents the theoretical and empirical models as well as the results of the various estimations.  Conclusions and policy implications are given in Section IV.

 

II.              Literature Review

A.     Studies of Risk Aversion and Wealth

 

There have been a number of studies that have attempted to empirically estimate the relationship between relative risk aversion and wealth within the framework of expected utility theory. One of the earliest studies of risk aversion and wealth is by Friend and Blume [1975].  Their measure of risk aversion depends on the individual investor’s portfolio allocation between risky and risk-free assets, according to the following:

 

ak = [E(rm - rf )/s 2m] (1/Ck)

 

where ak is the proportion of net worth that investor k places in risky assets, E(rm - rf) is the expected difference between the return on the market portfolio of risky assets (rm) and the return on the risk free asset (rf), s 2m is the variance of the return on the market portfolio, and Ck is the Pratt-Arrow measure of relative risk aversion.[1]

 

Friend and Blume estimate the relationship between ak and wealth with cross sectional data from the 1962 and 1963 Federal Reserve Board Surveys of the Financial Characteristics of Consumers and Changes in Family Finances.  Their results are sensitive to the way that wealth is defined.  The narrowest definition of wealth excludes the value of houses, cars, and human capital, since these asset categories violate the assumptions of divisibility and liquidity which are inherent in the model.  On the basis of this definition of wealth, they find evidence of decreasing relative risk aversion (DRRA), ie. individuals invest a larger proportion of their wealth in risky assets as wealth increases.  When wealth is defined to include the value of houses, cars and human capital, they find evidence of constant relative risk aversion (CRRA).

 

Following the methodology of Friend and Blume, several studies find evidence of DRRA.  For example, Morin and Suarez [1983] use data from the 1970 Canadian Survey of Consumer Finances and find DRRA when wealth is defined exclusive of housing.  Bellante and Saba [1986], building on the work of Morin and Suarez and  using data from the U.S. Department of Labor’s Consumer Expenditure Survey for 1972-73, find evidence of DRRA when wealth is defined to include the value of housing but not the value of human capital. When the definition of wealth includes human capital as well, they find that the result of DRRA still holds but is significantly weaker.  Confining their sample to less wealthy households they find evidence of increasing relative risk aversion (IRRA), ie. individuals invest a smaller proportion of their wealth in risky assets as wealth increases. 

 

Other studies find similar results.  Siegel and Hoban [1982] find evidence of DRRA among wealthy households and IRRA among less wealthy households, when wealth is defined exclusive of housing.   Riley and Chow’s [1992] study of the 1984 panel of the Survey of Income and Program Participants finds evidence of DRRA when wealth is defined inclusive of houses but exclusive of human capital.

 

Most of these studies estimate the relationship between an individual’s investment in risky assets and wealth in a simple equation that excludes the effects of individual and household characteristics.  They then estimate the relationship using a more complex equation which includes a wide range of control variables at the individual and household level that have been hypothesized to influence an individual’s degree of risk aversion.  These characteristics are not included to test the theory but rather to fill in gaps in the theory in terms of variables in addition to wealth that seem to explain risk aversion.

B.     Studies of Risk Aversion and Individual Characteristics

 

  1. Risk aversion and gender

 

Researchers have only recently explored the issue of differences in risk aversion by gender.  Anecdotal evidence suggests that women are more risk averse than men.  A number of studies have confirmed this finding even when controlling for the effects of other individual characteristics such as age, education, and wealth.  Jianakoplos and Bernasek [1998] use the framework of Friend and Blume [1975] to look for evidence of gender differences in financial risk taking.  They use data from the Federal Reserve’s Survey of Consumer Finances (1989) and estimate relative risk aversion by gender.  They find that single women were relatively more risk averse than single men and married couples. The proportion held in risky assets was found to increase with wealth(DRRA) but for single women the effect was significantly smaller than for single men and married couples.

 

Palsson’s [1996] study of Swedish households also finds evidence that women are more risk averse than men when she examines the effects of a wide range of household variables on financial risk taking.  Riley and Chow [1992] also look at the effects of a broad range of individual and household variables on risk aversion and find a small but significant gender difference in risk taking with women being more risk averse than men.  In their study, never married women were less risk averse than married women, who were less risk averse than widowed and separated women.

 

Other studies have explored gender differences in risk aversion in the context of non-financial decisions.  These studies also find evidence of women’s greater risk aversion.  Hersch [1996] finds that, on average, women made safer choices than men in a number of risky consumer decisions such as smoking, seat belt use, preventative dental care and having regular blood pressure checks.  Hersch [forthcoming 1998] looks at gender- specific estimates of illness and injury incidence rates for different industries and occupations and concludes that women are more risk averse than men based on the observation that women are paid a higher compensating wage differential for accepting a given job-injury risk.  Brinig [1994], analyzing data on speeding convictions, finds that women appear to be less willing than men to be caught and convicted of speeding.

 

Despite the focus on the existence of gender differences, none of these studies addresses the question of why such differences exist.  Bajtelsmit and Bernasek [1996] review the literature on gender differences in risk taking, paying particular attention to risk taking and investing for retirement.  They suggest a conceptual framework for understanding why it is that women invest differently than men.  They work backwards from differences in wealth and income, to labor market experience, to discrimination, human capital, and finally to the effects of socialization and biological difference. 

 

If women are systematically more risk averse than men, the implication is that women will earn lower rates of return on their investments than men at the same wealth level.  This implies that they will accumulate less wealth than men over time, a conclusion that is compounded by the fact that women, on average, have lower income and wealth than men and are less likely to have private pensions. Looking at this from the perspective of retirement income adequacy, women will have less accumulated wealth at retirement with which to support a retirement period which is generally greater than that of their male counterparts (due to greater average longevity). Ensuring that women are not poor in their retirement years thus requires that we better understand why they are more risk averse than men.

 

  1. Risk aversion and age

 

Age is a demographic characteristic that has long been hypothesized to affect an individual’s degree of risk aversion.  The lifecycle risk aversion hypothesis predicts that risk aversion will increase over the lifecycle – the older a person gets, the more risk averse they become.  The underlying explanation for this lies in the relative importance of labor income and asset income over the lifecycle.  It is believed that the further a person is from retirement the more risk they are willing to accept in their investments since the number of paychecks they expect to get is large and labor income can offset any adverse investment outcomes.  The closer to retirement a person gets, the fewer paychecks they have to cover any such adverse investment outcomes.

 

Several studies that have considered the effects of age on risk aversion claim to test the lifecycle risk aversion hypothesis but do not.  Most studies have used cross sectional rather than longitudinal data and therefore can only draw inferences about the effects of age across a cross section of the population – at any given time younger people may be more or less risk averse than older people.  For example, Morin and Suarez [1983] conclude that risk aversion increases with age such that older people are more risk averse than younger people.  Palsson [1996] finds the same results.  Riley and Chow [1992] find that risk aversion decreases with age up to 65 years, then increases significantly.  Bellante and Saba [1986] attempt to distinguish between the effects of human capital and age on risk aversion and find evidence of increasing relative risk aversion with human capital but decreasing relative risk aversion with age.  Although they interpret their results as evidence of a pure lifecycle effect of age that is independent of the human capital effect, the cross sectional nature of their study cautions against such a conclusion.

 

A rare study using time series data, Bakshi and Chen [1994] find evidence to support the lifecycle risk aversion hypothesis.  Focusing on the effects of demographic changes on capital markets, they find an increase in the risk premium associated with an increase in the average age of investors.

 

The effects of age on risk aversion are further complicated by the possibility of cohort effects.  There has been some suggestion that young people today may be less risk averse than young people a decade ago, for example.  A study by Brown [1990] examines the effect of the distribution of wealth across age cohorts on security prices taking into account the non-marketability of human capital earnings.  He finds that middle age investors were less risk averse than young investors and that older investors were more risk averse than middle age investors.

              

Jianakoplos and Bernasek [1998] attempt to disentangle cross sectional, lifecycle and cohort effects of age on women’s risk aversion.  They find that younger women in 1983 and in 1995 are less risk averse than older women in the same years, 30-41 year old women were less risk averse in 1995 than in 1983, and that in 3 out of 4 stages in the lifecycle, relative risk aversion decreases with age.

 

  1. Risk Aversion and race/ethnicity

 

Very little research has been done on the effects of race/ethnicity on risk aversion.  In her study of risky consumer decisions, Hersch [1996] finds that, overall, whites make safer choices than blacks but that the racial gap closes considerably when education and wealth are controlled for.  Within racial categories women are found to exhibit safer behavior than men.  The conclusion Hersch comes to is that race is not as important a determinant of risk taking as other individual characteristics such as age, education, and wealth.

 

Jianakoplos and Bernasek [1998] in their study of financial risk taking find that black single women are significantly less risk averse than white single women, and are less risk averse than black single men and  married couples.  This is in contrast to their finding that white single women are more risk averse than white single men and married couples.

 

Comparing MBA students at the University of Houston and the Madrid School of Business, Zinkhan and Karande (1991) find that the Spanish students were less risk averse as a whole than the American Students.  (This study also finds significant gender differences, an indication that the gender effect exists cross-culturally as well).

 

  1. Risk aversion and education

 

A number of studies have examined the effects of formal education on risk aversion.  A common concern in interpreting the results of these studies is that education, income and wealth tend to be highly correlated.  The results on the effects of education on risk taking are mixed.  Riley and Chow [1992] find that financial risk aversion decreases with education.  Jianakoplos and Bernasek [1998] find the opposite – that risk aversion increases with education, without any significant difference between women and men.  Hersch [1996] finds that risk aversion increases with education when considering risky consumer choices.

 

In the context of financial risk taking, it would seem that a more relevant effect to measure would be access to financial knowledge rather than education in general.  A study by Bayer, Bernheim and Scholz [1996] examines the effects of financial education in the workplace on participation in and contributions to voluntary savings plans.  They find that measures of savings activity are significantly higher when employers offer retirement seminars and the effects are greater for lower paid employees than for higher paid employees.

 

C.  Experimental Studies of Risk Aversion

 

Another avenue for investigating risk taking behavior has been through the study of games and the use of games as experiments.  Examples of this are:  Gertner’s [1993] study of risk taking behavior in the context of the television game show “Card Sharks”; Metrick’s [1995] study of people’s attitudes to risk and their ability to play best-responses in the game show “Jeopardy”; Altaf’s [1993] experiment to test the extent to which risk preferences are context dependent; and Levy’s [1994] experiment in which students had to choose between investing in risky and riskfree assets in a series of ten decision-making stages.  The results of these experiments are mixed.  Most find evidence that people’s behavior is inconsistent with the predictions of expected utility theory.

 

Focusing specifically on risk taking by gender, Brinig [1994] conducts an experiment to compare the behavior of women and men in a game that does not involve any possible loss.  Her experiment involves drawing a winning ball from one of three jars which represent different risk-return combinations.  She finds no difference in the risk taking behavior of women and men when gender alone is considered.  When gender is combined with age however, she finds that women are more risk averse than men before age forty, then they are less risk averse until age forty-five, and beyond age forty-five women and men are found to have the same tendencies for risk taking.  The fact that participants do not face any risk of loss in the experiment cautions against drawing any strong conclusions from Brinig’s results.

              

Jianakoplos and Bernasek undertake an experiment to test for differences in risk taking by gender, which, like Brinig’s does not have any possibility of loss. They do not find any statistically significant difference in risk taking by gender.  Using the same game as Altaf [1993] they invite students to participate in an experiment where they played a game which pays $25 to the winner of the game.  Individuals have to choose between rolling a die and tossing a coin, each of which involves certain payoffs in the form of points. The objective is to accumulate the greatest number of points in the fewest possible plays of the game.  The expected payoffs to a coin toss and a roll of the die are the same, but the variance is different -- rolling the die is the riskier option.  Their measure of willingness to take risks is given by the proportion of plays of the game that a person chose to roll the die.  

 

One of the issues that comes up with experiments is whether or not there is any down-side risk.  If there is not then the results derived from such experiments may not be generalizable to people’s behavior in the real world.  Another issue is the small sample size of most of these experiments.  The Jianakoplos and Bernasek experiment, for example, had only 37 participants.  With such small sample sizes it is difficult to draw general conclusions.

 

C.     Individual Investment Allocation

Theoretically, the optimal portfolio for all individuals is a combination of the market portfolio and the risk-free asset. (Markowitz, 1952) Differences in risk aversion are manifested in differing proportionate allocations between these two investment choices.  However, in practice, we know that individuals do not all “hold the market”.

 

Several studies have been conducted looking at individual investment allocation.  However, most of these are flawed in that they look at a particular aspect of the individual’s portfolio without considering the whole.  This is typical of studies  that have been conducted by private pension providers since these firms do not have access to very detailed information on household income and wealth.  The literature reviewed in this section therefore comes with the caveat that the conclusions are largely descriptive and comparative rather than statistically validated.

 

1.      Pension Surveys

 

Observation of plan level data has generally yielded fairly consistent conclusions.  Individuals tend to pick fairly conservative pension portfolios. A 1993 study by Hewitt Associates found that when guaranteed investment contracts (GICs) were offered, they accounted for almost half of all employee contributions. Equities and balanced funds accounted for only 21 percent and 13 percent respectively.  A Fidelity Investments study including over 1500 plans and 2 million participants in 1994, found that when employer stock was offered, it accounted for about 16 percent of plan assets.  Nearly half of the funds were allocated to non-employer stock and 28.7% in GICs.  When employer stock was not available, the percentage in both equities and GICs increased. 

 

Goodfellow and Schieber (1997) tabulated the investment allocations for a sample of more than 36,000 participants in 24 defined contribution plans holding nearly $1.4 billion in total assets.  They find that fixed income investments are about 58 percent of total funds and that stocks represent approximately 28 percent. The percent in fixed income increases with age and the percent in stocks declines.  Higher income individuals are more inclined to invest in stocks, as are men.

 

A study by Bajtelsmit and VanderHei (1997) used individual plan data on 20,000 employees of a single U.S. firm. Account allocations in that study were 41 percent employer stock, 14.2 percent equity, and 44.8 percent GICs for the men in the sample.  Regression analysis indicated that women were less inclined to invest in employer stock and equities.

 

The largest pension fund in the world, TIAA-CREF has provided participants with investment choices since 1952.  In the early years, there were only two choices, the TIAA traditional guaranteed annuity and the CREF equity account.  Internal studies over many years indicated that most participants allocated their premiums 50-50 and did not regularly reallocate over time, even when the actual account balances differed substantially from the original 50-50 mix.  In more recent years, TIAA-CREF has expanded the asset choice set to include equity accounts of differing risk and return characteristics as well as money market, bond, and real estate choices.  At the same time, the firm has attempted to increase participant knowledge through educational programs.  The end result is that in 1996, the proportion of participants allocating some portion of their premiums to equities has steadily increased and 22.2% are 100% in equity.  The 50-50 allocation strategy is still popular (24.6%) and the proportion investing entirely in the guaranteed fund (9.0%) is half what it was in 1986. (TIAA-CREF, 1997). The allocation patterns by age have also changed over the last decade. In 1986, nearly 30% of participants over age 55 were invested entirely in the TIAA guaranteed annuity account, whereas in 1996, that percentage had dropped to only16.1%.  The younger aged participants are on average less conservative than in 1986 as well, with more than half of the under-35 participants having at least 50% of their premiums allocated to equities (TIAA-CREF, 1997) compared to only 11% in 1986.

 

Hinz, McCarthy, and Turner (1997) examined the 1990 allocation patterns of federal government workers in the Thrift Savings Plan.  Although their primary research question was related to gender differences, it is interesting to note that the observed patterns of allocations is very similar to that observed for other types of pensions. These workers were allowed to allocate up to 60% of their contributions to common stock and fixed income funds (the remainder to be in a fund of Treasury securities).  Only 28% of women compared to 45% of men participated in the common equity fund.  Overall, 13.4% of funds were allocated to the fund (average 8.9% for women and 15.3% for men.

 

2.      Special issues

 

Empirical analysis of investment allocation presents several special problems given the limitations of currently available data.  The studies surveyed above are all based on in-house pension fund data and, as such, lack valuable explanatory information on the  participants’ overall financial condition.  Some specific issues that deserve mention here are the household versus individual observation unit, gender, age and cohort patterns, and differences between what people say and what they do.

              

a.       Household vs. individual

 

As previously discussed, the data typically collected by plan sponsors are limited to plan specific information such as allocation percentages, account balances, and loans for individual participants.  Although the Pension and Welfare Benefits Administration of the Department of Labor collects and disseminates information on pension plans, these data are limited to aggregate plan information, most notably from the IRS Form 5500 annual report.  Two large cross-sectional data sets that have been used to examine financial decision-making are the Surveys of Consumer Finances (SCF) and the Current Population Surveys (CPS), which both include weights to make them representative of the U.S. population.  The most recent new survey is the Health and Retirement Study (HRS) which follows a representative sample of individuals who were age 51-61 in the first year of the survey (1992) and their spouses.

 

There is some question as to whether studies of financial decision-making should have the individual or the household as the unit of measurement.  While in many households, spouses or partners keep all finances completely separate, there are many in which the finances are combined. Therefore, examination of one spouse’s pension allocation may show a very conservative allocation of funds, but the other spouse’s pension may be in stocks.   Consideration of these individuals separately would thus yield incorrect conclusions regarding the risk-preferences of the household.  The SCF, CPS, and HRS surveys do not include any information on who makes financial decisions for the household[2]. 

 

b.      Gender differences

 

Although several studies have purported to find gender differences in investing patterns between men and women (Bajtelsmit and VanDerhei, 1997; Hinz, et al., 1997; Goodfellow and Schieber, 1997), the problems discussed above make it difficult to make definitive conclusions.  When this issue is examined with controls for income, wealth, and demographic characteristics, Bajtelsmit, Bernasek, and Jianakoplos (1997) find significant gender differences remain.  In order to avoid the issue of household decision-making, the study considered single households of men and women separately and compared them to married couples’ investments.  The main problem with the study however is that the SCF survey includes limited pension information. Although pension balance information is provided on each of their three largest pensions, allocation information for defined contribution plans is more limited.  For each pension, respondents were asked to indicate whether they allocated their pension to (1) mostly stocks, (2) mostly interest bearing investments, or (3) mixed. For participants in the 1989 SCF who had defined contribution plans and wealth in excess of $1000, Bajtelsmit et al. (1997) find that women are relatively more risk averse than men and that women’s  percentage wealth allocations to risky pensions decrease with wealth (increasing relative risk aversion).   The conclusions of this study is limited by the fact that the survey does not indicate whether the respondent or the respondent’s employer had allocation decision-making authority for their account. Although self-directed plans are increasingly common, there are still many defined contribution plans for which participants do not make allocation decisions.  Lastly, as in most studies, the household decision-maker is not identified.

 

Another gender related issue is that women and men may differ in their tendency to say one thing and do another (see below).  Jianakoplos and Bernasek (1998) consider actual risk-taking compared to self-professed risk-taking and find that women say they are more risk averse than their investment allocations would indicate.  Women who said they were “unwilling to take any risk at all” in their investments were still invested in risky assets. 

 

c.      Investment patterns over the life cycle

 

Financial planners often recommend a life-cycle approach to investment allocation.  The so-called “Rule of 70” suggests that investors should subtract their age from 70 and invest that portion of their portfolio in equities with the remainder in fixed income securities.  There is actually no theoretical basis for such a rule and, in fact, research on time diversification suggests that the investor’s age is less important than his or her investment time horizon (Siegal, 1996). Neither the private pension surveys nor the SCF and CPS data sets are particularly useful for examining investment patterns over the life cycle.  Although each includes information on age of participants, this tells us only what individuals of different ages are doing at a particular point in time.  There is no longitudinal survey that follows the same set of individuals over a long period of time and includes sufficient financial information. However, many studies have attempted to draw life cycle conclusions  or inferences based on cross-sectional data.  Comparison of cross-sections of the SCF, CPS, or Survey of Income and Program Participation (SIPP) have shown that cohorts do seem to exhibit patterns of wealth accumulation and decumulation.[3]  Limitations in the financial data  make it difficult to  make strong conclusions regarding the asset mix.  Even if there were a good source of longitudinal data on individual financial decision-making, a potential problem is the bias introduced by the researcher.  By answering financial questions every few years, the participants in the survey are probably more aware of the issues than the average individual and may tend to make different financial decisions as a result. The psychometric literature shows that once an individual is made aware of a risk, they are more likely to take it into consideration. 

 

It is difficult to separate the age effects from cohort effects.  The term cohort refers to a group of people in a certain age group at a particular point in time.  For example, the observation that a baby boomer couple carries a higher risk portfolio than their parents at the same age, may be due to their age or it may be to the greater conservatism of people in a cohort that has lived in the post-depression era.  Several studies examine cohort differences in investing and seem to find patterns that support the financial planner models that recommend lower risk at higher ages.  Poterba (1997) tabulates 401(k) eligibility and participation data for different cohorts and finds, not surprisingly, that younger cohorts are more likely to be eligible for 401(k) pension plans, with highest eligibility for the 35-45 year old group.  However, the participation rates, given eligibility, do not differ substantially across cohorts and average about 70%. 

 

Bajtelsmit and VanDerhei (1997) find significant cohort effects in the allocations of plan participants as do Hinz et al. (1997), with participants in older age cohorts having more conservative portfolios.  However, since private pensions were less common for earlier cohorts, direct comparison of asset portfolios in more comprehensive data sets does not necessarily make sense.  In fact, the lack of detail in the SCF survey regarding private pension assets mix can be attributed in part to the fact that, until recently, participants usually had no choices.

 

The HRS study, which has more complete financial information, essentially follows a single cohort through time, although only three waves of the study are complete at this time. To the extent that there are some survey participants who are older or younger spouses of the target survey group, there may be some evidence of cohort effects, but the respondent pool does not have a representative sample of those age cohorts.

 

d.      What people say is not always what they do

 

Survey data is the primary source of data for most studies of risk aversion, investment and preparation for retirement.  Some surveys ask for information on their wealth and their assets and liabilities.  Some surveys however, ask for answers to hypothetical questions.  For example, in the Survey of Consumer Finances (1989) respondents were asked how much risk they would be willing to take for certain returns on a hypothetical investment.  Jianakoplos and Bernasek [1998] find that what people said in answer to that question was not consistent with how they actually allocated their wealth among risky and risk free assets.  Caution is warranted in drawing conclusions from studies based on what people say rather than what they do.

 

Despite the growing body of knowledge related to individual risk-taking and investment allocation, there is still much that we do not understand.  As public policy makers consider changes to public and private pension regulation, it is increasingly important that there be a clear understanding of the factors that influence individual investment choices.


III.  Data and Empirical Methodology

 

A.  The Health and Retirement Study

           

          1.  General information

 

The Health and Retirement Study  (HRS) is a nationally representative longitudinal data collection effort begun in 1992 focusing on Americans who are close to retirement (aged 51-61 in 1992) and their spouses.  The survey investigates aspects of these households’ finances, health, and retirement decisions.  The intent is to follow the same group of respondents through their retirement years. For the purposes of this report, the second wave of the survey, conducted in 1994, will be used.  Future research on these topics might benefit by making use of the longitudinal nature of the survey although there is some risk that the behavior of the households surveyed might be influenced by the survey itself.

 

This survey is particularly well-suited to the study of retirement savings since it includes information on all aspects of household wealth and income as well as key demographic information that researchers need for control variables.  The investigation of investment risk-taking in many previous studies has been limited to examination of investment portfolios without consideration of the rest of the household portfolio.

  

2.      Asset information in the HRS

 

The HRS survey includes extensive asset and debt information for each of 6,979 households.  Respondents provide information on their primary residence and second homes as well as investment real estate.  They also give estimated values for personal property, self-owned businesses and farms, IRA and Keogh accounts, stock and bond investments (outside of tax deferred pensions), checking and savings accounts, money market funds, CDs, and government securities. Household debt, both secured and unsecured, is also summarized.

 

In addition to asset and debt information, the HRS includes substantial employment and pension information (e.g. type of pension plan for current and previous employers as well as characteristics of the plan and the expected benefits). As with the Survey of Consumer Finances, the survey is somewhat deficient in its information on defined contribution[4] pension investment allocations.  The respondent provides information on each of his or her three “most important” defined contribution plans. In addition to an estimate of the pension balance, the respondents are asked to indicate whether the funds in these plans are invested in “mostly or all stocks”, “mostly or all interest earning (or bonds)”, or “split”.  This is a bit too vague to allow inferences about pension investment risk-taking and asset allocation.

 

For investment allocation questions, an important consideration is whether the participants in a plan can direct the investment allocation.  Of the 11,596 respondents, only 350 had an employer-provided defined contribution pension. For the pension designated their most important, 185 indicate that they can choose the way the money in the account is invested and 129 said that they invested the pension in either a mostly stock portfolio (48) or split between stocks and interest earning investments (81).

 

Table 2 provides a summary of wealth allocations to particular asset categories for households in the survey.  The households are separated by marital status. These allocations can exceed 100% because many households have negative housing equity. [5] The standard deviations are also included in the table to illustrate the wide variation in allocations across households in the sample.

 

Table 2 Sample Weighted Asset Allocations by Marital Status

(Note:  Denominator is total assets including housing equity, investments, and pension accumulations.)[6]

Asset Category
Single Men
Single Women
Married Couples

 

Mean

Stand. Dev.

Mean

Stand. Dev.

Mean

Stand. Dev.

Residences

.295

.368

.414

.405

.414

.549

Stock (Non-pension)

1.207

17.258

4.942

89.706

.760

31.468

Bonds

.064

.704

3.381

149.29

.027

.664

CDs, Govt Securities

1.018

24.157

1.123

20.715

.115

2.760

IRA, Keoghs

1.163

7.675

15.735

457.793

.606

21.126

Investment Real Estate

24.441

837.126

11.211

345.541

1.052

22.578

DC Pension Accum.

.128

.307

.126

.303

.111

.279

Checking/Savings

2.965

43.689

8.394

160.717

.532

9.744

Automobiles

.175

.287

.140

.269

.109

.233

Source:  Author’s tabulations of the Health and Retirement Study Wave 2.

Note:  Columns will not sum to 100%.

 

The wide variation in allocations across the sample can also be seen by comparing the allocations across wealth quartiles.  The sample was divided into four groups based on their sample weighted net wealth (total assets less household debt).  Table 3 provides the asset allocation mean and standard deviations for the different asset categories.

 

 Table 3 Sample Weighted Asset Allocations by Wealth Quartile

(Note:  Denominator is total assets including housing equity, investments, and pension accumulations.)[7]

Asset Category
Wealth Quartile 1
Wealth Quartile 2
Wealth Quartile 3
Wealth Quartile 4

 

Mean

St.Dev

Mean

St.Dev

Mean

St.Dev

Mean

St.Dev

Residences

.428

.395

.508

.276

.395

.219

.340

2.242

Stock (Non-pension)

1.777

30.026

.174

1.004

.096

.389

.038

.108

Bonds

.079

1.009

.032

.423

.020

.378

.005

.032

CDs, Govt Securities

.335

3.614

.049

.319

.024

.099

.007

.039

IRA, Keoghs

.876

4.426

.168

.531

.114

.222

.038

.101

DC Pension Accum.

.055

.186

.046

.139

.038

.126

.328

.449

Automobiles

.256

.287

.099

.086

.061

.059

.411

.871

Checking & Savings

.775

3.432

.114

.304

.069

.157

.018

.050

Source:  Author’s tabulations of the Health and Retirement Study Wave 2.

Note:  Columns will not sum to 100%.

 

3.       Preparation for Retirement

 

How well prepared for retirement are these households?  Given the age of the target households, one would expect them to have already accumulated a substantial amount toward their retirement.  However, this is not the case.  Examination of the wealth of these households leads to the conclusion that many households have little or no savings to draw upon for retirement.  The bottom quartile based on net wealth have less than $77,000 in total net wealth (including housing equity and pension accumulations). Fully 50% of the sample have less than $201,000.  This still implies that the “three legged stool” of retirement income (pensions, savings, and social security) is being left to stand on less than two legs—primarily social security benefits. 

 

Table 4 details the wealth accumulations for the four wealth quartiles and the distributions of wealth within each quartile.

 

Table 4  Sample Weighted Distribution of Wealth in the Health and Retirement Study Sample by Wealth Quartile

Wealth=Total assets including real estate equity and pension balances less personal debt.

Wealth Quartile

25th Percentile

50th Percentile

75th Percentile

100th Percentile

1 (25%)

$12,359

$32,690

$53,000

$77,000

2 (50%)

$103,600

$130,000

$161,000

$201,000

3 (75%)

$246,851

$306,000

$395,000

$542,000

4 (100%)

$862,610

$9,869,741

$10,100,000

$20,600,000

 

 

 

 

 

Source:  Author’s calculations based on the Health and Retirement Study Wave 2.

 
Since the older households in the sample are closer to retirement and have had more years to accumulate wealth to support their retirement, Table 5 details the wealth distribution of the sample by age category. 
 
Table 5  Sample Weighted Distribution of Wealth in the Health and Retirement Study by Average Age of the Household

Wealth = Total assets including real estate equity and pension balances less personal debt.

Average Age
25th Percentile
50th Percentile
75th Percentile
100th Percentile
Less than 50
$30,687
$145,519
$453,677
$31,200,000
50-54
$57,500
$158,229
$417,656
$30,100,000
55-59
$55,000
$172,000
$513,000
$30,900,000
60-64
$66,000
$214,700
$563,000
$30,100,000
Over 65
$85,200
$222,186
$494,500
$30,000,000
 
 
 
 
 
 
As can be seen from Table 5, the lowest 50th percentile of all age groups has very little accumulated wealth.  This is particularly problematic for the households who are very near retirement.  An accumulation at age 65 of $200,000 in wealth earning 6% per year will provide an income of only $17,437 for twenty years (without assuming any increase for cost of living each year). 
 
In light of the descriptive statistics provided above, it seems clear that a better understanding of individual savings and investment behavior is warranted.  In the following sections, an empirical methodology is which allows comparison of the investment behavior of this survey group based on household characteristics.  

 

B. Methodology

 

1.      Theoretical framework
 

Expected utility theory implies that the proportion of risky assets in an investor’s portfolio will be a function of their wealth and their degree of risk aversion.  The convex shape of utility functions implies that risk aversion is also dependent on wealth in that individuals will have different attitudes toward risk as wealth increases.  The relationship between risk preferences and wealth was originally developed by Pratt (1964) and Arrow (1971), who define measures of absolute risk aversion (change in dollar allocation to risky assets as wealth increases) and relative risk aversion (change in portfolio allocation to risky assets as wealth increases).

 

Based on empirical and experimental studies of individual decision-making under risk, there is now general consensus that absolute risk aversion declines with wealth.  That is, individuals will invest a higher dollar amount in risky assets as their wealth increases. The characteristics of individual relative risk aversion are not as clear and appear to exhibit systematic differences by some characteristics such as age and income. Gender differences in relative risk aversion are considered in a recent paper by Jianakoplos and Bernasek (1998), who find evidence that relative risk aversion decreases with wealth and that single women in the 1989 Survey of Consumer Finances exhibit greater relative risk aversion than single men.  In other words, they find that the percentage of wealth invested in risky assets is greater for those with greater levels of wealth, but the increase in risky allocation is smaller for women than for men as wealth increases.

 

As discussed in Section II, Friend and Blume (1975) developed a theoretical and empirical framework for the estimation of relative risk aversion[8]. In their study, an individual investor’s portfolio allocation between risky and risk-free assets, in the absence of taxes[9], is defined according to the following equation:

 

ak = [E(rm - rf )/s 2m] (1/Ck)                                                                                        (6)

 

where ak is the proportion of net worth that investor k places in risky assets, E(rm - rf) is the expected difference between the return on the market portfolio of risky assets (rm) and the return on the risk free asset (rf),[10] s 2m is the variance of the returns on the market portfolio, and Ck is the Pratt-Arrow measure of relative risk aversion[11].  This equation implies that individuals allocate their wealth based on the markets’ risk/return tradeoff and their own relative risk aversion.

 

Other studies using this methodology include Morin and Suarez (1983), Bellante and Saba (1986), Siegel and Hoban (1982), Riley and Chow (1982), and Jianakoplos and Bernasek (1998).[12]  The relationship between portfolio allocation to risky assets and individual or household wealth is generally estimated using an equation which includes a range of control variables at the individual and household level that have been hypothesized to influence an individual’s degree of risk aversion.

 

The model used in this report employs the theoretical framework discussed above with some modifications.  Since the model has its foundation in capital market theory, it assumes that financial assets are infinitely divisible and can be traded with zero transaction costs.  This is clearly not the case for such assets as housing wealth and human capital.  Although pension wealth is also not tradeable per se, tax laws allow individuals to access some pension wealth with a penalty.

 

Consistent with Bernasek and Jianakoplos (1998), human capital is incorporated by reformulating equation (6) to take into account the dependence of ak on the covariance between the return on the market portfolio (rm) and the return on human wealth (rh). This results in the following specification for allocation to risky assets:

                                                       (7)

where hk is the ratio of investor k’s human wealth to net wealth, and bh,m is the ratio of the covariance of rm and rh to s2m. This equation can be simplified by making use of the findings of Liberman (1980) and Fama and Schwert (1977) that bh,m  is zero.  Then Equation (7) becomes:

                                                                                             (8)

This equation forms the basis for estimating the coefficient of relative risk aversion in household investment portfolios.

2.       Empirical model

Based on equation (8), the estimating equation takes the following specification:

                 (9)

where RISKYij is the ratio of the dollar value of risky asset holdings to net household wealth (HHWEALTHj), which is the total dollar value of all reported asset holdings (risky and non-risky) less the dollar value of household debt.  This wealth measure is calculated with and without housing wealth since it is not clear whether houses are accumulated for investment purposes in addition to their consumption purposes. Low risk assets include dollar balances of savings, checking, money market accounts, certificates of deposit, the cash value of life insurance, US savings bonds and Treasury securities. Risky assets include the net value of stock accounts, stock mutual funds, owned businesses, bond accounts (corporate, municipal, government, foreign), pension vehicles (IRAs, Keoghs, 401(k) plans, 403(b) plans) not invested in money market securities, other assets (jewelry, IOUs, collectibles, etc.) and non-housing real estate equity.

Other variables include: the average age in years of the members of the household (AGE); age squared (AGESQ, to test for non-linear age effects); the respondent’s education level (LOWEDUC = 1 if the respondent’s highest educational level is high school equivalency or less)[13]; the number of children under the age of 18 (KIDS); a dummy variable for single females (FEMSING)[14]; a dummy variable for whether the respondent or spouse has a defined benefit plan in addition to other retirement savings (HASDB); a dummy variable for whether the respondent has high school level of education or less (LOWEDUC); and a race variable (BLACK = 1 if the respondent reports race as black). 

Table 6 provides sample weighted summary statistics for selected variables used in this study. After preliminary empirical analysis, the original equation given in equation (9) was altered slightly.  The squared age term was not significant in any of the regressions and was therefore dropped.  Given the relatively narrow range of ages represented in this sample, this is not surprising.  To capture specific age effects, the AGE variable was dropped in favor of age categories as indicated in the table below.


TABLE 6 Sample Weighted Summary Statistics for the Health and Retirement Study Wave 2 (n=11609)

Variable

Mean

Stand. Dev.

Minimum

Maximum

WEALTH1

1,318,120

3,253,241

1,008a

3.04x 107

WEALTH2

754,522

2,506,655

1,008a

3.03x107

RISK1

.802

.266

-1.19

11.96

RISK2

.557

.381

-.414

11.11

BLACK

.094

.292

0

1

FEMSING

.142

.349

0

1

HASDB

.214

.410

0

1

KIDS

.194

.613

0

12

AGE

57.55

5.25

25

84

AGESQ

3339.77

597.48

625

7056

LOWEDUC

.607

.488

0

1

Source:  Author’s calculations based on the 1994 Wave 2 of the Health and Retirement Study.

a The empirical sample was limited to those with household wealth greater than $1000.

 

Human capital is usually defined as the present discounted value of this stream of earnings discounted at the long term real rate of interest. For example, in Jianakoplos and Bernasek (1998) , human capital was calculated by assuming that each individual’s current wages, salaries, and/or self-employment earnings continued unchanged until retirement. The income stream was discounted using a 2% rate[15]. If the individual was still working and between the ages 65 and 69, current earnings were assumed to continue for four more years; if between 70 and 74, to continue for three more years; if between 75 and 79, to continue for two more years; and if over 79, for one more year. Human capital for a household was the sum of the human capital calculated for each spouse.  Although this method could be applied to the current dataset as well, there are some problems.  Unlike the Survey of Consumer Finances, which represents the full spectrum of adult ages, the HRS households include at least one individual who is 53 to 63 in 1994 and many are already retired.  Because of this, the income-based measure of human capital is highly correlated with household income. However, neither explanatory variable turns out to be significant in the main regressions. Since household income is significant in the later model which compares actual allocations to experimental measures of risk aversion, for consistency, household income is included as a proxy for human capital in the regressions reported below.

 

C.  Results

 

Table 7 presents the estimated coefficients and t-statistics for equation (9) estimated with and without including housing wealth in the WEALTH and RISKY variables.  Since the dependent variable, the percentage of wealth allocated to risky assets, is a naturally censored variable, a tobit regression is used.

 

The estimated coefficient on ln(HHWEALTH) provides an estimate of the inverse of the coefficient of relative risk aversion (Ck) up to a positive multiplicative constant. A positive coefficient indicates that individuals with greater wealth in this sample allocate a larger portion of their wealth to risky assets than those with less wealth, i.e. decreasing relative risk aversion. Based on the signs and significance of the control variables, the percentage allocation to risky assets is also shown to be lower for those with lower education levels and for those with greater pension balances. The effect of the other control variables depend on whether housing wealth is included in the measure of household wealth. When housing is not included in the equation, blacks have lower allocations to risky assets and single women have higher allocations.  When housing wealth is included, single women do not have a significantly different allocation but blacks have a positive coefficient, which can be interpreted to imply that black households tend to have a larger proportion of their wealth in housing equity than other households.

 

As compared to the oldest age category (over 65), younger groups allocate a greater proportion to risky assets with the most significant difference being for those in the 50-55 age group.  As compared to the highest wealth quartile, lower wealth quartiles allocate a lower proportion to risky assets when housing wealth is not included, but a higher proportion when housing wealth is included.  Similar to the results for the black households, this simply implies that housing wealth is a larger proportion of total wealth for the less wealthy. 

 

Given the significance of the single female dummy in the regression which excludes housing wealth, further investigation of this issue was warranted.  Table 8 reports the result of regressions run for each marital status category separately with sample weighting. The coefficients for the single men and married couples equation are also statistically compared to the coefficients for the single women.  Any coefficient market marked with a j is significantly different from the single female coefficients at the 10% level.

 

 


Table 7 Censored Tobit Regression Coefficient Estimates and t-statistics ( )

Dependent variable = household (HH) portfolio allocation to risky assets

Explanatory Variables
Including Housing

(n=10,412)

Not Including Housing

(n=9,927)

Constant

-.251

(-3.451)***

-.139

(-1.499)

ln(HHWEALTH)

.079

(16.373)***

.073

(10.976)***

HUMAN

(Household Income)

2.03x10-12

(.153)

3.11x10-13

(.022)

LOWEDUC

-.014

(-1.850)*

-.046

(-5.507)***

SINGFEM

.010

(.890)

.051

(3.978)***

KIDS

# of Children Under 18

.007

(.999)

.002

(.315)

HASDB

(Household has DBPension)

-5.84x10-9

(1.340)

.002

(.311)

BLACK

(% Black spouses)

.035

(2.585)***

-.054

(-3.454)***

OWNHOME

 

N/A

-.028

(-2.349)**

Age <50

-.012

(-.435)

.042

(1.362)

Age 50-54

.049

(2.461)**

.071

(3.287)***

Age 55-59

.027

(1.413)

.051

(2.397)**

Age 60-64

.022

(1.123)

.022

(1.016)

Wealth Quartile 1

.152

(6.203)***

-.192

(-5.934)***

Wealth Quartile 2

.107

(6.168)***

-.097

(-4.554)***

Wealth Quartile 3

.059

(4.145)***

-.028

(-2.349)**

Pseudo R2

Log Likelihood

.085

-4281.014

.218

-4865.762

*significant at the 10% level

**significant at the 5% level

*** significant at the 1% level

 


 Table 8 Sample Weighted Tobit Regression Coefficient Estimates and t-statistics

Dependent variable = portfolio allocation to risky assets not including housing

Explanatory Variables

Single Men

Regression

Single Women

Regression

Married Couples

Regression

Constant

-1.63**

(-2.422)

-2.499***

(-7.801)

.109

(1.029)

ln(HHWEALTH)

.208***

(6.625)

.259***

(11.951)

.534***j

(6.961)

HH Income

-5.45x10-10

(-.069)

-6.78x10-10*

(-1.866)

8.00x10-13

(.055)

LOWEDUC

-.077**j

(-1.961)

.006

(.200)

-.052***

(-5.554)

KIDS

.065**

(2.083)

.056*

(1.766)

-.007j

(-.813)

HASDB

-.031

(-.0769)

.034

(1.205)

-.001j

(-.118)

HH BLACK

.071j

(1.152)

-.051

(-1.264)

-.073***

(-3.884)

HH Pension Balance

-3.69x10-8***

(-3.322)

-5.05x10-8***

(-6.667)

9.04x10-10j

(.394)

Own Home

-.116***

(-2.927)

-.062**

(-2.051)

-.010j

(-.638)

Age <50

-.402

(-.709)

-.207

(-.921)

.056*j

(1.777)

Age 50-54

-.255

(-.477)

-.031

(-.256)

.082***j

(3.661)

Age 55-59

-.242

(-.452)

-.074

(-.619)

.063***j

(2.839)

Age 60-64

-.255

(-.476)

-.099

(-.836)

.023j

(1.038)

Wealth Quartile 1

.129

(.806)

.482***

(4.457)

-.234*** j

(-7.222)

Wealth Quartile 2

.257**

(2.369)

.415

(5.392)***

-.152

(-6.357)*** j

Wealth Quartile 3

.218***

(2.568)

.237***

(3.749)

-.058***

(-3.324)

N

524

1088

8315

Pseudo R2

Log Likelihood

.368

-291.210

.226

-743.277

.196

-4243.8114

Source:  Author’s calculations based on the 1994 Wave 2 Health and Retirement Study.

*** Significant at the 1% level;  ** Significant at the 5% level;  *  Significant at the 10% level 

j Coefficients are signficantly different from the single female coefficients.

 


Although all three groups exhibit statistically significant decreasing relative risk aversion (investing a larger proportion of wealth in risky assets as wealth increases), single women have a significantly smaller coefficient than married couples. Although their coefficient is slightly higher than single men, the difference is not statistically significant. The explanatory variables have the expected effects and are consistent across groups with some exceptions.  Household income (HUMAN) is insignificant in all but the single female group where it has a small negative effect on risky allocation. Having children under age 18 is significant only for the singles where it increases the risky allocation, perhaps due to aggressive saving for college.  The lower age categories do not effect risk allocation for the singles, but have proportionately more risky assets than the over 65 group for the married couples.  This is consistent with “common wisdom” suggesting that portfolios should be reallocated to lower risk assets as retirement approaches.[16]

 

Respondents with high school or less education (LOWEDUC) have lower allocations to risky assets in all but the single female group.  Single men and married couples with at least one black spouse also have lower risk household portfolios. Having a defined benefit plan does not impact the risky allocation, but since that variable is defined as equal to one regardless of the size or generosity of the plan, not a lot can be read into that result. The balance in the combined household defined contribution plans (which is included in both the numerator and denominator of the risk allocation variable) has a negative impact on risk allocation for the singles but does not impact the married couples.

 

Separate regressions were also estimated using the alternative definition of wealth and risky allocation (including housing) with somewhat similar results (not reported here).  Although the coefficients obviously differed, the significance and signs of explanatory variables were largely comparable.  The female interaction terms indicated significant differences between single women and both other groups with respect to the homeownership dummy.

 

In interpreting all of these results, some care must be taken in comparing the actual coefficients.  Since the constant terms are not the same for all equations, the differences that we observe may be explained as either an intercept or a slope difference. Thus, even though the ln(WEALTH) coefficient in Table 8 is larger for single women than for single men (-.259 compared to -.208) and both coefficients are individually significant, we cannot conclude that the women are relatively less risk averse because the difference is not statistically significant. The constant in the single female equation is less than the single male constant (-2.49 compared to –1.63) so the larger wealth coefficient is not making as big a change in risky allocation as would seem by looking at the coefficients in isolation.  In contrast, the constant in the married couple regression is actually positive (.109), so that the large coefficient on the wealth variable makes a much bigger difference in risky allocation and is significantly different than that of the single women. The calculated significance level of this difference p=.002 (but in the regression including housing wealth it is .067). 

 

D.    Experimental Evidence of Income Risk Aversion

 

1.      Explanation of the experimental questions

 

As a separate module of the HRS survey, the researchers asked some experimental questions related to risk aversion.  Although it probably would have made more sense in the context of expected utility theory to ask questions related to wealth, the survey module focused on the respondent’s aversion to taking risk that affected his or her income.  The number of people participating in this module was much smaller than that for the full survey so the responses cannot necessarily  be interpreted as being representative of the US population as a whole. 

 

The questions were designed to estimate the individual’s tradeoff between risk and certainty equivalents with respect to income.   The respondent was told to assume that he or she had an adequate income that was virtually risk free.  Then, he or she was presented with the opportunity to take a risk (in the form of a new job) that would have a 50% chance of paying double the former income.  Each of the questions changed the scenario only in the outcome for the other 50% chance and asked in each  case whether the respondent would choose to take the risky job opportunity.  The alternative outcome ranged from a decrease in income of only 10% (compared to the original starting point) to a decrease in income of 75%.  The expected value of income is in all cases positive.

 

Table 9 summarizes the distribution of responses for the different scenarios presented.  Based on these responses, a dummy variable was created to represent income risk aversion.  Although this can be done in several ways, the results reported below use a risk aversion dummy which is equal to one if the individual indicated they would not take any of the gambles, and zero otherwise. 

 

Table 9  Responses to the Risk Aversion Module

in the Health and Retirement Survey Wave 2

Good Outcome

(50% Chance)

Bad Outcome

(50% Chance)

Incremental # Who Would

Take the Risk*

 

 

 

Double your income

Lose 10% of your income

137

Double your income

Lose 20% of your income

101

Double your income

Lose 33% of your income

112

Double your income

Lose 50% of your income

56

Double your income

Lose 75% of your income

30

Note:  319 respondents were not willing to take any of the gambles. 

* Each successive line in the table indicates the number of individuals from the previous line who were willing to take the next most risky alternative.

 

 

2.       Wealth and Investment Allocation by Levels of Risk Aversion

 

There is some evidence that individuals are not always consistent between what they say and what they do.  To test this hypothesis as well as consider the differences between risk taking with respect to income versus wealth, this section considers asset allocation by individuals with differing levels of stated income risk aversion. Cross-tabulations of several variables by risk aversion level and wealth quartile are presented in Table 10.  Based on the descriptive statistics, there does not appear to be a strong relationship between the income risk aversion measure and  allocation to risky assets.  Except for the lowest wealth quartile, the means and standard deviations for both groups are relatively similar. 

 

Nevertheless, since descriptive statistics often lead to faulty conclusions due to interactions between variables, the regression analyses reported in the previous section are re-estimated for this smaller sample.  The risk aversion dummy is included as a test of whether income risk aversion is a predictor of risky investment decision making.   As before, equation (9) is estimated in a censored tobit regression.  When housing wealth is not included, the risk aversion dummy (and alternative dummy formulations were not significant).  Table 11 reports the regression results using the full measure of wealth (including housing and net of personal debt) as the dependent variable. 

 

 

 

 


Table 10  Mean and Standard Deviation of Variables

by Level of Income Risk Aversion

(based on Experimental Module from the Health and Retirement Study Wave 2)

Variable

Less Income Risk Averse

More Income Risk Averse*

 

Mean

St. Dev.

Mean

St. Dev.

Risky alloc (incl. House)

      Wealth Quartile 1

      Wealth Quartile 2

      Wealth Quartile 3

      Wealth Quartile 4

 

.622

.822

.847

.925

 

.517

.174

.128

.102

 

.870

.801

.844

.915

 

.731

.149

.159

.142

Risk alloc (not incl. House)

      Wealth Quartile 1

      Wealth Quartile 2

      Wealth Quartile 3

      Wealth Quartile 4

 

.274

.547

.743

.810

 

.418

.370

.433

.255

 

 

.444

.465

.773

.804

 

.548

.324

.486

.239

Wealth (incl. House)

      Wealth Quartile 1

      Wealth Quartile 2

      Wealth Quartile 3

      Wealth Quartile 4

 

$22,923

$105,740

$298,432

$4,479,950

 

$16,629

$38,333

$89,147

$4,838,324

 

$27,565

$110,696

$305,131

$4,339,391

 

$18,155

$35,471

$93,905

$4,731,938

Wealth (not incl. House)

     Wealth Quartile 1

      Wealth Quartile 2

      Wealth Quartile 3

      Wealth Quartile 4

 

$13,849

$57,475

$176,852

$2,543,052

 

$23,775

$41,250

$88,878

$3,675,499

 

$28,666

$57,066

$176,799

$2,137,779

 

$102,361

$39,629

$97,336

$3,433,285

Housing Equity

     Wealth Quartile 1

      Wealth Quartile 2

      Wealth Quartile 3

      Wealth Quartile 4

 

$4,410

$51,608

$121,580

$2,027,671

 

$59,771

$30,653

$78,795

$3,843,460

 

$5,757

$56,042

$128,331

$2,380,461

 

$83,465

$37,435

$87,240

$4,100,527

Education Category (0-3)

     Wealth Quartile 1

      Wealth Quartile 2

      Wealth Quartile 3

      Wealth Quartile 4

 

1.16

1.52

1.83

1.84

 

.75

.81

.89

.94

 

1.22

1.53

1.77

1.90

 

.95

.82

.92

.98

 

 

 

 

 

*  This is the group of individuals who were not willing to take any of the risks offered in the experimental module.  The number of individuals represented in this table are smaller than the total number in the experimental module because not all of the households met the wealth >$1000 limitation for the

 

 


Table 11  Censored Tobit Regression Results

Dependent Variable:  Percent of Net Wealth Allocated to Risky Investments

(n=681 HRS Respondents who completed the risk aversion module)

Variable

Estimated Coefficient

(t-statistic)

Constant

 

Ln(WEALTH)

 

Wealth Quartile 1

 

Wealth Quartile 2

 

Wealth Quartile 3

 

College Degree Dummy

 

Risk Averse Dummy

 

Single Female

 

Age 50-54

 

Age 55-59

 

Age 60-64

 

Age 65+

 

Pseudo R2 = .126

Log Likelihood=-256.92

-.219

(.341)

.083***

(5.421)

.205**

(2.334)

.147**

(2.432)

.084*

(1.706)

.085**

(2.550)

.038

(1.446)

.001

(.021)

-.105**

(-2.033)

-.138***

(-2.712)

-.142***

(-2.656)

-.122*

(-1.707)

 

                        *** significant at the 1% level

** signficant at the 5% level

*significant at the 10% level

 

In this model, the risk aversion dummy is significant at the 15% level and is positive.  This indicates that the individuals who indicated greater levels of income risk aversion in the survey are actually investing larger proportions of their wealth in risky assets. Separate regressions (not reported here) estimated for different cross-sections of this sample (by educational level, by marital status, and by age) yield consistent results.  The risk aversion dummy has relatively low significance but is always positive.  Adding the risk aversion dummy does not improve the overall significance of the model nor does it change the effects or significance of the other explanatory variables.

 


 

V.              Conclusions

 

A.  Summary of the Main Results of this Study

 

In this paper, we have reviewed the literature related to investment allocation and risk-taking. Although this area of research is in a developmental stage, the bulk of the empirical work suggests that individuals do not always allocate their portfolios in the ways that might be suggested by theory. In addition, studies indicate that there may be characteristic differences in the allocation decisions made by particular groups, most notably by age and gender. 

 

The empirical study presented in Sections III and IV examines these issues by using the Health and Retirement Study, a nationally representative survey of households with at least one member aged 53-63 in 1994.  This survey includes extensive financial and demographic information, making it possible to consider questions of investment allocation in the context of a complete household portfolio.  The results of this study confirm earlier studies suggesting that demographic characteristics may indeed be predictors of behavior. 

 

We find that while all individuals exhibit decreasing relative risk aversion, the relative risk aversion of single women is significantly greater than that of married couples.  This is also true when housing wealth is included in the definition of wealth, although the significance of the difference is somewhat lower.  Other characteristics which are found to influence the risky allocation decision negatively (when housing wealth is not included) include lower education, black race, the size of the household’s pension accumulation, and homeownership.  Compared to the oldest group in the sample (over 65), the younger households have higher allocations to risky assets.  As would be expected, the lower wealth quartiles have lower allocations to risky assets than the richest in the sample.  However, when housing wealth is included in the definition of wealth, the lower wealth quartiles have higher allocations, indicating that housing wealth is a more significant component of their risky portfolio than it is for the wealthiest quartile.

 

An experimental module of the HRS survey was used to consider the question of whether perceived or stated individual risk aversion is consistent with observed asset allocation.  Based on the available data, we do not find evidence to support this hypothesis.  Individuals with higher measures of risk aversion (based on income risk) are found to have higher risky allocations of wealth after controlling for other factors, although the statistical significance of this result is fairly low.  This result is consistent with the work of Jianakoplos and Bernasek (1998) who find that stated risk tolerance in the Survey of Consumer Finances is not correlated with the same individuals’ portfolio choices.

 

B.    Implications for Public Policy

 

1.      Retirement Income Adequacy

 

The results of this study are important because they cast light on the behaviors of individuals and households who are at or near retirement age.  On average, these households have accumulated wealth that will be sufficient to support their retirement, but the focus on averages ignores the fact that a large percentage of these households have very little wealth.  The bottom quartile of households has less than $77,000 in total household wealth (including pension accumulations, housing equity, and net of household debt).  Fifty percent of these households have less than $201,000 in total net wealth.  Without including housing equity, their wealth levels are even lower.  Given that this sample is conservatively within fifteen years of retirement, it seems unlikely that these individuals will be able to accumulate sufficient savings to fully replace their pre-retirement earnings.  This behavior might be rational if the households are planning to rely on social security benefits and/or defined contribution pension plan benefits which are not measurable with this data. In addition, it is possible that individuals in this age group might be anticipating sizable bequests from elderly relatives.

 

2.      Public Policy Toward Pensions

 

The findings of this research study are consistent with conclusions that have been made by other researchers using a variety of techniques and datasets.  A large proportion of the households in this sample have insufficient savings and pensions to allow them to maintain their pre-retirement standard of living.  In order to shore up the “three-legged stool of retirement income”, public policymakers must direct their attention to five areas.

 

a.       Increase savings:  First and foremost, the level of savings must increase, particularly for those in the lowest wealth quartiles.  Tax incentives such as the Roth IRA may begin the movement toward a change in savings attitudes.

 

b.      Increase financial knowledge:  To get the most “bang for the buck”, young people need to understand the basic concepts of risk and return so that long term earnings can be maximized.

 

c.      Maintain a safety net:  At least for the lowest income and wealth groups, there is clearly a need for government provision of pension income.  A move toward privatized accounts might have the additional advantage of increasing public awareness of savings and investments.

 

 

d.      Encourage employer pensions:  A fairly small proportion of this sample is covered by a pension plan and pension accumulations are, on average, a small component of total savings.  The tax preferences offered by employer plans and the penalties associated with early withdrawal make them a desirable option for retirement savings.

 

e.      Discourage debt accumulation: Careful examination of this sample leads to the conclusion that many households have excessive levels of debt, particularly given that they are nearing retirement age. Although for the purposes of examining asset allocation, these households were excluded from the sample, many of the households in this sample have negative net wealth. 

 

V.  References

Altaf, M. A. "Attitude towards risk: An empirical documentation of context dependence," Journal of Economic Behavior and Organization, 1993, 91-98.

 

Arrow, K.J.  Essays in the Theory of Risk Bearing.  Chicago: Markham Publishing company, 1971.

 

Allais, Maurice, 1979, “The Foundations of a Postive Thoery of Choice Involving Risk and a Criticism of the Postulates and Axioms of the American School”, in Allais and Hagen (1979).

 

Allais, Maurice  and Ole Hagen, 1979, Expected Utility Hypotheses and the Allais Paradox, Dordrecht, Holland:  D. Reidel.

 

Bajtelsmit, V. and A. Bernasek. 1996. “Why Do Women Invest Differently Than Men?” Financial Counseling and Planning, Vol. 7, 1-10.

 

Bajtelsmit, Vickie L. and Jack L. VanDerhei, 1997, “Risk Aversion and Pension Investment Choices”, Positioning Pensions for the Twenty-first Century, Pension Research Council and University of Pennsylvania Press: Philadelphia, 45-66.

 

Bakshi, G. and Z. Chen.  “Baby Boom, Population Aging, and Capital Markets”, Journal of Business, Vol. 67, No. 2, 1994: 165-202.

 

Bayer, P.J., P.D. Bernheim and J.K. Scholz.  “The Effects of Financial Education in the Workplace: Evidence from a Survey of Employers” National Bureau of Economic Research, Working Paper 5655, 1996.

 

Bellante, D. and R. Saba.  “Human Capital and Life-Cycle Effects on Risk Aversion”, Journal of Financial Research, Spring 1986: 41-51.

 

Bernasek, Alexandra, and Vickie L. Bajtelsmit, 1997,  “Gender and Perception of Risk”, Colorado State University Working Paper, presented at the 1997 Midwest Finance Association Meeting, Chicago, Illinois.

 

Bradbury, J.  “The Policy Implications of Differing Concepts of Risk”, Science, Technology and Human Values, Vol. 14, No. 4 1989: 380-399.

 

Brown, D.  “Age Clienteles Induced by Liquidity Constraints”, International Economic Review, Vol. 31, No. 4, 1990: 891-912.

 

Chew, Soo Hong, 1983, “A Generalization of the Quasilinear Mean with Applications to the measurement of Income Inequality and Deicison Theory Resolving the Allais Paradox,” Econometrica, (July) 51: 1065-1092.

 

Edwards, Ward, 1955, “The Prediction of Decisions Among Bets”, Journal of Experimental Psychology, (Sept.)50:201-214.

 

Elton, Edwin, and Martin J. Gruber, 1991, Modern Portfolio Theory and Investment Analysis, New York:  John Wiley and Sons, Inc.

 

Federal Reserve Board of San Francisco, 1998, “The Baby Boom, the Baby Bust, and Asset Markets, Economic Letter, 98-20: 1-3.

 

Fishburn, Peter C., 1983, “Transitive Measurable Utility”, Journal of Economic Theory, Dec(31): 293-317.

 

Friend, I. and M.E. Blume.  “The Demand for Risky Assets”, American Economic Review, December 1975: 900-22.

 

Gertner, R. "Game Shows and Economic Behavior: Risk Taking on 'Card Sharks'". Quarterly Journal of Economics, May 1993, 507-521.

 

Goodfellow, Gordon P., and Sylvester J. Schieber, 1997, “Investment of Assets in Self-Directed Retirement Plans”, Positioning Pensions for the Twenty-first Century, Pension Research Council and University of Pennsylvania Press: Philadelphia, 67-90.

 

Hersch, J. “Smoking, Seat Belts and Other Risky Consumer Decisions: Differences by Gender and Race”, Managerial and Decision Economics, Vol. 17, 1996: 471-481.

 

Hersch, J.  “Compensating Differentials for Gender Specific Job Injury Risks”, American Economic Review, forthcoming.

 

Hinz, Richard P., David D. McCarthy, and John A. Turner, “Are Women Conservative Investors? Gender Differences in Participant-Directed Pension Investments”, Positioning Pensions for the Twenty-first Century, Pension Research Council and University of Pennsylvania Press: Philadelphia, 91-103.

 

Jianakoplos N. A. and A. Bernasek.  “Are Women More Risk Averse”, Economic Inquiry, forthcoming 1998.

 

Jianakoplos N.A. and A. Bernasek.  “Female Risk Aversion: By Age, Across Cohorts and Over the Lifecycle” working paper, Colorado State University, 1998.

 

Kahneman, Daniel and Amos Tversky, “ Prospect Theory:  An Analysis of Decision Under Risk”, Econometrica. March (47): 263-291.

 

Karmarkar, Uday S., 1978, “Subjectively Weighted Utility:  A Descriptive Extension of the Expected Utility Model”, Organizational Behavior and Human Performance, Feb.(21): 61-72.

 

Levy, H.. "Absolute and relative risk aversion: An experimental Study." Journal of Risk and Uncertainty, May 1994, 289-307.

 

Machina, Mark J., 1982, “Expected Utility Analysis without the Independence Axiom”,  Econometrica, March, 50: 277-323.

 

_______________, 1992,  “Choice Under Uncertainy:  Problems Solved and Unsolved”, in Foundations of Insurance Economics,  Boston: Kluwer Academic Publishers, p.  49-82.

 

Markowitz, Harry M.  “Portfolio Selection.”  Journal of Finance 6: 77-91 (March 1952).

 

Metrick, A. "A Natural Experiment in "Jeopardy!" American Economic Review, March 1995, 240-253.

 

Mitchell, Olivia S., Jan A. Olson, and Thomas Steinmeier, “Construction of the Earnings and Benefits File (EBF) for Use with the Health and Retirement Survey,” Forecasting Retirement Needs and Retirement Wealth, Pension Research Council 1998 Symposium.

 

Moore, James F., and Olivia S. Mitchell, Projected Retirement Wealth and Savings Adequacy in the Health and Retirement Study,” Forecasting Retirement Needs and Retirement Wealth, Pension Research Council 1998 Symposium.

 

Morin, R.A. and F. Suarez.  “Risk Aversion Revisited”, Journal of Finance, September 1983: 1201-16.

 

Otway, H.J., and K. Thomas.  “Reflections on risk perception and policy”, Risk Analysis, Vol. 2, 1982: 69-82.

 

Poterba, James M., 1997, “The Growth of 401(k) Plans: Evidence and Implications,” Public Policy Toward Pensions, Sylvester Schieber and John Shoven, eds., MIT Press:  Cambridge, 177-196..

 

Pratt, J.W.  “Risk Aversion in the small and large”, Econometrica, 1964: 122-36.

 

Quiggin, John, 1982, “A Theory of Anticipated Utility”, Journal of Economic Behavior and Organization, (Dec) 3: 323-343.

 

Riley, W.B. and K.V. Chow.  “Asset Allocation and Individual Risk Aversion”, Financial Analysts Journal, November/December 1992: 32-7.

 

Samwick, Andrew and Jonathan Skinner, 1997, “Abandoning the Nest Egg?  401(k) Plans and Inadequate Pension Saving,” Public Policy Toward Pensions, Sylvester Schieber and John Shoven, eds., MIT Press:  Cambridge,197-218.

 

Scheiber, Sylvester and John B. Shoven, 1997, “The Consequences of Population Aging on Private Pension Fund Saving and Asset Markets,” Public Policy Toward Pensions, Sylvester Schieber and John Shoven, eds., MIT Press:  Cambridge, 219-246.

 

Siegel, F.W. and J.P. Hoban.  “Relative Risk Aversion Revisited”, Review of Economics and Statistics, August 1982: 481-87.

 

Slovic, P., B. Fishoff and S. Lichtenstein.  “Perceived risk: Psychological factors and social implications”, Warner, F. and D. Slater (editors) The assessment and perception of risk, London: Royal Society, 1981: 17-34.

 

Stiglitz, J.E.  “The effects of income, wealth, and capital gains taxation on risk taking” Quarterly Journal of Economics, Vol. 83, May 1969: 263-283.

 

TIAA-CREF, 1997, “Premium Allocations and Accumulations in TIAA-CREF—Trends in Participant Choices Among Asset Classes and Investment Accounts”,  Research Dialogues, 51: 1-11.

 

Tobin, James.  “Liquidity Preference as Behavior Towards Risk.” Review of Economic Studies 26: 65-86 (February 1952).

 

Tversky, Amos and Daniel Kahneman, 1974, “Judgement Under Uncertainty:  Heuristics and Biases, Science, (September): 185: 1125-1131.

 

__________________,  1986, “Rational Choice and the Framing of Decisions”, Journal of Business, 4(2) 251-278.

 

Venti, Steven F. and David A. Wise, 1997, “The Wealth of Cohorts:  Retirement Saving and the Changing Assets of Older Americans,” Public Policy Toward Pensions, Sylvester Schieber and John Shoven, eds., MIT Press:  Cambridge, 85-130.

 

Von Neumann, J. and O. Morgenstern.  Theory of Games and Economic Behavior, Princeton: Princeton University Press, 1953.

 

Warshawsky, Mark.  “Private Annuity Markets in the U.S.: 1919-1984.”  Journal of Risk               and Insurance 55: 518-528 (September 1988).

 

World Bank.  Averting the Old Age Crisis.  Oxford University Press, (1994).

 

Zinkhan, G.M. and K.W. Karande. 1991. “Cultural and gender differences in risk-taking behavior among American and Spanish decision makers”. The Journal of Social Psychology. 131(October): 741-742.

 



[1]  The market risk premium E(rm-rf) divided by the variance of the market return is the market price of risk, a term that also appears in the standard Capital Asset Pricing Model.  See Elton and Gruber (1991, p. 292) for a discussion of the implications of using the variance as opposed to the standard deviation in the denominator of the CAPM formula.

[2]  A new privately sponsored survey of TIAA-CREF participants includes decision-making information, although the sample is not representative of the population and the survey has incomplete information on the household.

 

[3] See Venti, Steven F. and David A.  Wise (1997) for a study using the SIPP to examine retirement wealth.   They use a method of analysis based on comparing “like families” between 1984 and 1991.

[4] A defined contribution plan is defined as any type of plan in which money is accumulated in an account for the respondent.  (These include 401(k), 403(b), ESOP, SRA, thrift/savings, stock/profit sharing, and money purchase plans.) Defined benefit plans are defined as those plans in which benefits are based on a formula usually involving age, years of service, and/or salary.

[5] It is interesting to note that these allocations are very consistent with the Markowitz portfolio model which predicts that some households will invest more than their total wealth in risky securities by investing borrowed funds in the market.

[6] Although the regressions in this study consider household wealth net of all debt, these ratios are the asset category divided by total assets.  Included in assets are housing equity, automobiles, stocks, bonds, checking and savings, pension plan balances,and other marketable investments.  Human capital is not included.  Total wealth (net of debt) is highly negative for many households in the sample.

[7] Although the regressions in this study consider household wealth net of all debt, these ratios are the asset category divided by total assets.  Included in assets are housing equity, automobiles, stocks, bonds, checking and savings, pension plan balances,and other marketable investments.  Human capital is not included.  Total wealth (net of debt) is highly negative for many households in the sample.

[8] Constant relative risk aversion (CRRA) is defined as investing the same proportion of wealth in risky assets as wealth increases.  Investing a higher or lower proportion of wealth as your wealth increases is increasing relative risk aversion (IRRA) or  decreasing relative risk aversion (DRRA), respectively.

[9]  The effects of taxes are ignored in this estimation.  Other studies have shown that taxes do not significantly impact results. (Bellante and Saba, 1986; Friend and Blume, 1975).  Since the differences in tax rates across individuals for the sample period (1995) are relatively small compared to earlier time periods, these differences should have an even smaller effect in this case.

[10]  The market risk premium E(rm-rf) divided by the variance of the market return is the market price of risk, a term that also appears in the standard Capital Asset Pricing Model.  See Elton and Gruber (1991, p. 292) for a discussion of the implications of using the variance as opposed to the standard deviation in the denominator of the CAPM formula.

[11] Relative risk aversion Ck = [-U”(Wk)/U’(Wkt)]Wkt where Wkt is investor k’s wealth in period t. U’(W) and U”(W) are the first and second derivatives of the utility function with respect to wealth. U’(W) is generally assumed to be positive in the expected utility model (utility increases with wealth) and the second derivative is generally assumed to be negative (the rate of increase in utility for a given increase in wealth is declining).

[12] Using data from the Canadian Survey of Consumer Finances for 1970 Morin and Suarez (1983) find evidence of decreasing relative risk aversion (DRRA) when wealth is defined exclusive of housing.  Bellante and Saba (1986) use data from the U.S. Department of Labor’s Consumer Expenditure Survey for 1972-73 and find evidence of DRRA when wealth was defined to include the value of housing but not the value of human capital. When the definition of wealth includes human capital as well, they find that the result of DRRA still holds but is less significant.  Confining their sample to less wealthy households they find evidence of increasing relative risk aversion (IRRA), ie. individuals invest a smaller proportion of their wealth in risky assets as wealth increases. Hoban (1982) found evidence of DRRA among wealthy households and IRRA among less wealthy households, when wealth was defined exclusive of housing.   Riley and Chow’s (1992) study of the 1984 panel of the Survey of Income and Program Participants finds evidence of DRRA when wealth is defined inclusive of houses but exclusive of human capital.

 

 

[13] Other alternative measures for education include actual years of education, an education category dummy and a dummy for those with higher education.  Empirical tests showed the low education dummy reported here and the college education dummy were the most significant in the models.  This is an indication that the relationship between risk taking and education is not linear but has a “tail” effect. 

[14] This includes those who are separated, divorced, widowed and never married.  Although it would seem that the never married group is more likely to exhibit different investment behaviors than the others, there are only a small number of women in the sample who have never been married. 

[15] Implicit in this method of calculation of human capital is the assumption of a constant growth rate in earnings.  Thornton, Rodgers and Brookshire (1997) show that, contrary to the usual assumption of a u-shaped earnings profile, longitudinal data is actually more consistent with a constant growth rate pattern.

[16] A possible reason for the insignificance of the age result is that there is very little variation in the ages of the single groups.  The average age of the married couples exhibits more variation since the age eligible spouse may be married to a much younger or much older person.