Student Spring 2019
Master thesis I, 15 ECTS
Umeå School of Business and Economics
Which households hold risky assets?
A study on household investment choices in the United States
Kristin Bruksner
Abstract
This study uses U.S. data from the Survey of Consumer Finance (SCF) from year 2016 to examine how different characteristics of U.S. households affect the proportion of risky assets held by the household. The proportion of risky assets is calculated as the ratio of risky assets, such as stocks and bonds, to total assets. The SCF data is analyzed with a program in Stata called “scfcombo”, and the method used for the regression analysis is the ordinary least squares (OLS) method. The results of this study shows that a larger proportion of risky assets in the household portfolio are associated with a household that has a relatively large income, large net worth, owns a primary residence, and where the head of the household is male, not married, working, white or non- Hispanic, is willing to take on a financial risk, and has an education level of associate- or bachelor’s degree or higher.
Table of Contents
1. INTRODUCTION ... 1
1.1. BACKGROUND ... 1
1.2. PURPOSE ... 2
1.3. OUTLINE ... 3
2. LITERATURE REVIEW ... 4
3. ECONOMIC THEORY ... 7
3.1. RISK AVERSION ... 7
3.2. INVESTMENT DECISIONS ... 8
4. DATA ... 11
4.1.VARIABLE DESCRIPTION... 12
4.1.1. The dependent variable ... 12
4.1.2. The explanatory variables ... 13
5. METHOD ... 18
6. RESULTS ... 21
7. DISCUSSION ... 24
8. CONCLUSION AND IDEAS FOR FURTHER WORK ... 27
REFERENCES ... 29
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1. Introduction
Financial and economic risk is something that we deal with every day. Many people try to avoid risk as far as possible, but risk doesn’t always mean something negative, it can also create opportunities. Higher risk is associated with a higher expected return
(Markowitz, 1952), therefore risky assets are expected to have a higher return than risk free assets. Since the stock market has been shown to historically deliver a high return (Yahoo Finance, 2019), it is of interest to study why households does not participate in these markets. What decides how households invest? When a household does not participate in investing in risky assets, they risk missing out on the higher return associated with risky investments. Is it some specific characteristics of households that can explain their investment choices? The area of household’s investment choices is well studied, and several studies has been made to examine what effect different
household characteristics can have on the household’s investment decision. This area is of great interest to get more understanding on how different households invest, and what their investment decisions depends on.
1.1. Background
The disposable income that the household receive can be either consumed or saved. The individual may choose to save for personal future consumption or to donate the saved assets to loved ones. The decision between how much of the income that should be spent on consumption, and how much to save, is determined by how much the
individual values present and future consumption, assumed that the individual does not just save for the sake of saving (Romer, 2012). When an individual divide less of her income on saving in one period, it will imply less consumption in the future. The income that the individual chooses to save can be invested in many different kinds of assets, such as stocks, bonds, treasury bills, gold, etc. These assets can be divided into risky assets and risk-free assets. Risky assets are assets that result in an uncertain return, and risk-free assets are assets where the return is certain. How much of one’s savings that is invested in risky and risk-free assets may depend on several aspects such as the individual’s tolerance of risk, how long the money should be invested, and why the investment is made.
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In the book “Money, Banking and Financial Markets”, by Cecchetti and Schoenholtz (2015), risk in outcomes of financial and economic decisions is defined as: “Risk is a measure of uncertainty about the future payoff to an investment, assessed over some time horizon and relative to a benchmark.” They continue to define a risk-free asset as:
“an investment whose future value is known with certainty and whose return is the risk- free rate of return.” The expected payoff that you will receive from a risk-free asset is certain. On the opposite, if you invest in a risky asset, the return that you will receive is uncertain and can be more or less than the amount you invested (Brealey, Myers and Marcus, 2014). This uncertainty that comes with a risky asset may be worth the risk, since there is a chance that you will receive more than the amount you invested. A risk- averse investor would choose an investment with a certain return over an investment with an uncertain return, with the same expected return, and she would require the compensation of a risk premium to expose herself to the risk (Cecchetti and
Schoenholts, 2015). Hence, investors who are very risk-averse would prefer investments that are risk-free, such as government bonds or certificates of deposits, while investors that are less risk-averse accept higher levels of risk for the opportunity to earn higher returns.
1.2. Purpose
The purpose of this study is to examine what characteristics of American households that affect the proportion of risky assets held in the household’s portfolio with the contribution that the study examines the latest Survey of Consumer Finance (SCF) data for year 2016.
The data used is a cross-sectional data from the 2016 Survey of Consumer Finances (SCF) that includes financial information about households in the U.S. The SCF has a complex sample design, and a multiple imputation technique is used to deal with the problem of missing data. Because of the complexity of the data, this may cause a potential problem with the significance of the estimates and the standard errors in the regression. To deal with this, a program called “scfcombo” is used in Stata to account for the complexity of the data. This will be further discussed in the method section of this paper. For this study, a multiple regression model is used, and a regression analysis is conducted by using the ordinary least squares (OLS) method.
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The results of this study show that household’s that has a larger proportion of risky assets in their investment portfolios are associated with a household that has a relatively large income, large net worth, owns a primary residence. Furthermore, a large
proportion of risky assets held by the household is associated with a head of the household that is male, not married nor living with a partner, working in some way, willing to take on a financial risk, white or non-Hispanic, and has an education level of associate- or bachelor’s degree or higher. The results show that age and number of children in the household is not significantly correlated to the proportion of risky assets held.
1.3. Outline
This section of the paper has focused on the background and the purpose of this study.
In the second section previous research regarding risk behavior of households and individuals will be presented, followed by the third section where the economic theory related to this paper will be presented. The fourth section will present the data used for this study and describe the variables used in the model, and the fifth section will explain the method used for the study. Section six will present the results from the regression analysis, while section seven and eight will conclude the paper with discussions and ideas for further work.
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2. Literature review
The fields of risk and household investment decisions are common research areas in both economics and other areas. Many earlier empirical studies have studied the investment behavior of households and what factors that may affect their investment decisions. Results following the literature review has shown that some of the most important characteristics that explain portfolio choices and that are correlated with risk amongst individuals and households are age, wealth, gender and education.
Fratantoni (1998) used SCF data from year 1989 to study the relationship between homeownership and investment in risky assets. Fratantoni used the household’s financial assets (such as savings accounts, stocks and bonds) to calculate the share of risky assets that the household held. His study showed that married couples and
homeowners had a smaller share of risky assets. Grable (2000) studied risk-taking with data collected by responses of a financial risk-tolerance assessment questionnaire answered by faculty and staff members at a university. Grable found that some of the characteristics that are associated with financial risk tolerance1 are associated with gender, age, education, civil status, etc. Some of Grable’s conclusions showed that men are more risk averse than women, older individuals are more risk tolerant than younger individuals, and, opposed to Fratantoni’s results, married individuals are more risk tolerant than those who are single.
Age is usually controlled for when analyzing risk aversion since studies shows that age has an impact on how risk averse the individual is. In 1992, Riley and Chow (1992) used U.S. data from the Survey of Income and Program Participation (SIPP) to study individuals relative risk aversion. They found that relative risk aversion decreases with age, but only up until an age of 65, where it instead increases with age. Another study, using Swedish cross-sectional data, made by Pålsson (1996) examined how relative risk aversion varies with household characteristics, taking real assets into account in the household wealth. Pålsson’s study showed that households that are headed by older persons are generally more risk averse than those headed by younger persons. This can be explained by when reaching an age of retirement, the need for a steady income
1Risk tolerance is defined as an individual’s willingness to accept uncertainty when making financial decisions (Grable, 2000). In the SCF dataset risk tolerance is measured by asking the head of the household if he or she is willing to take financial risk when making investments.
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increases and there is less time to regain any potential loss resulted from risky investments. Therefore, investments should shift towards more risk-free assets when closer to retirement. Hanna and Wang (1997) used data from the SCF over the years 1983-89 to study the relationship between risk tolerance and age, where risk tolerance is measured by the ratio of risky assets to total wealth, and found that risk tolerance
increases with age.
Wealth is a factor that is often examined in studies regarding financial decisions taken by individuals and households. A study made by Cohn et al. (1975) regarding the effect of wealth on the proportion of risky assets in an individual’s portfolio showed a strong pattern of decreasing relative risk aversion when wealth increases. Riley and Chow (1992) also found a negative relationship between risk aversion and wealth, and risk aversion and income where risk aversion decreases significantly for the very wealthy individuals, and for households with higher income. Riley and Chow found evidence for the same negative relationship for education and risk aversion, which can be explained by the fact that individuals that are educated may to a larger extent be exposed to the various investment options that is available to them (Riley and Chow, 1992). Riley and Chow explained that young individuals under the age of 21 allocate most of their assets in personal property and checking account, and a small proportion of their assets in risky assets. Therefore, the proportion of wealth that is invested in risky assets increases with wealth and income, while the proportion invested in less risky assets such as bonds decreases with wealth and income.
Sung and Hanna (1996) used data from the 1989 SCF to examine the factors related to risk tolerance. They showed that, amongst other factors, education has a positive effect on risk tolerance, even after the effects of other variables are controlled for, where higher education results in higher risk tolerance. Jianakopolos and Bernasek (1998) also used data from the 1989 SCF to study the proportion of risky assets to wealth and found that single women are relatively more risk averse than single men, and that relative risk aversion decreases with increasing household wealth, excluding residential housing and human capital.
One characteristic that is well studied in risk aversion is gender. Most studies finds that women generally are more risk averse than men (Pålsson, 1996; Powell and Ansic,
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1997; Halek and Eisenhauer, 2001; Watson and Mcnaughton, 2007; Sapienza, Zingales and Maestripieri, 2009). The fact that men are generally less risk averse than women means that men expose themselves to more risky situations, such as investing a larger proportion of their wealth in risky financial assets. Halko, Kaustia and Alanko (2012) made a study in Finland regarding stock holdings and gender, and found significant results that women are less willing to take risks than men are.
When studying the relationship between ethnicity and risk tolerance, the vast majority shows that blacks and Hispanic have a lower risk tolerance compared to Whites. Yao, Gutter and Hanna (2005) used data from the SCF over several years to study the relationship between race and ethnicity and financial risk tolerance. They found that White respondents are more willing to take some financial risk than blacks and Hispanics. But when studying the willingness to take substantial risk, blacks and Hispanics are more willing to take on risk than Whites. Fang, Hanna and Chatterjee (2013) uses data from the University of Michigan Health and Retirement Study to study the relationship between race and ethnicity and risk aversion. They found, consistent with the study of Yao, Gutter and Hanna, that Blacks were more risk averse than Whites. But non-immigrant Hispanics were not different than Whites when it comes to risk aversion. Whereas Hispanics, and other immigrants (largely Asians) were more risk averse than Whites.
Yao, Gutter and Hanna (2005) mentions that a possible explanation to the result that Whites are more willing to take on financial risk compared to minority groups can be that Whites are more exposed to financial information from different kinds of sources as media, social marketing, and financial services. They continue to mention that
individuals that are foreign born may experience a language barrier and therefore experience limited exposure to financial concepts, which could help to explain the results.
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3. Economic theory
The households divides its income at each point in time between consumption and saving so as to maximize its lifetime utility (Romer, 2012). When a household is saving it can choose to invest their money in different kind of assets, such as stocks, bonds or certificate of deposits. These assets can be divided into risky assets or risk-free assets.
In this section I will present economic theories that is well known when it comes to risk, and portfolio decisions.
3.1. Risk Aversion
Risk aversion is defined as an unwillingness to be exposed to risk. Depending on an individuals’ attitude towards risk, the individual is said to be risk averse if he or she avoids risk and prefers the expected value of an investment or a game more than the utility of it, risk neutral if he or she is indifferent as long as the expected value of the investment or a game is the same as the utility of it, and risk loving if he or she prefers the utility of the investment or a game to its expected value (Varian, 1992). Arrow (1965) and Pratt (1964) developed a model to measure the risk aversion of an individual, called the Arrow-Pratt measure of absolute risk aversion:
𝑟(𝑤) = −𝑢′′(𝑤) 𝑢′(𝑤)
(1)
The individual’s utility function is defined as 𝑢(𝑤), where we assume 𝑢′(𝑤) > 0 and 𝑢′′(𝑤) < 0, and 𝑟(𝑤) relates to the curvature of the utility function. We divide the second derivative of the utility function with its first derivative to get a measure that is robust to affine transformations, given a certain level of wealth 𝑤. The more concave the expected utility function is, the more risk averse the individual is (Pratt, 1964;
Varian, 1992). Similarly, for a risk neutral individual the utility function will be linear, and for a risk loving individual the utility function will be convex. The Arrow-Pratt measure of absolute risk aversion shows that the larger the measure of absolute risk aversion, the greater will the utility loss of being exposed to risk by investing in risky assets be compared to what the expected value of the risky asset under perfect certainty will be. The measure of risk aversion can also be written as relative risk aversion by multiplying the measure of absolute risk aversion by wealth, 𝑤:
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𝑝(𝑤) = −𝑢′′(𝑤)𝑤 𝑢′(𝑤)
(2)
Where 𝑝(𝑤) is, similarly to absolute risk aversion, the curvature of the utility function.
Relative risk aversion is defined as bets or investments as a proportion of wealth (Danthine and Donaldson, 2005), while absolute risk aversion express bets or investments in absolute values (Varian, 1992). The degree of relative risk aversion determines the proportion of wealth an individual will choose to hold in risky assets given a certain level of wealth, 𝑤.
We can use the theories of risk aversion described above and analyze a simple portfolio problem.
3.2. Investment decisions
As mentioned previously, an individual can choose to invest its money in risky assets or risk-free assets. The decision between these two risk classes are affected by how risk averse the investor is, and how much wealth he or she has (Danthine and Donaldson, 2005). To prove this, we consider an investor that has a wealth level, 𝑊0, that faces a decision on the proportion of wealth that should be invested in risky assets, 𝑎, where the rate of return of the risky assets, 𝑟𝑟, is uncertain during a time horizon that is one period.
The alternative is to invest in risk-free assets that has a certain rate of return, 𝑟𝑓, which for simplicity will be assumed to be zero. As the rate of return on the risky asset is uncertain, the investors wealth at the end of the time period is uncertain and given by:
𝑊̃1 = (1 + 𝑟𝑓)(𝑊0− 𝑎𝑊0) + 𝑎𝑊0(1 + 𝑟𝑟) = 𝑊0+ 𝑎𝑊0𝑟𝑟 (3)
Where the decision problem the investor needs to solve for her investment decision to maximize her expected utility can be expressed as:
max𝑎 𝐸𝑈( 𝑊̃1) = max 𝐸𝑈(𝑊0+ 𝑎𝑊0𝑟𝑟) (4)
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Where 𝑈(∙) is the investors’ utility function and 𝐸 is the expectations operator
(Danthine and Donaldson, 2005). The necessary and sufficient first-order condition for the investor’s maximization problem under risk aversion (𝑈′′(𝑊) < 0) is given by:
𝐸[𝑈′(𝑊0+ 𝑎𝑊0𝑟𝑟)𝑊0𝑟𝑟] = 0 (5)
If we assume 𝑈′(𝑊) > 0 and 𝑈′′(𝑊) < 0 and let 𝑎∗ represent the maximization problem solution, we can write:
𝑎∗ > 0 ⟺ 𝐸𝑟𝑟 > 𝑟𝑓 𝑎∗ = 0 ⟺ 𝐸𝑟𝑟 = 𝑟𝑓
(6) (7)
Which indicates that a risk averse investor will invest in risky assets if the expected rate of return of the risky assets exceeds the rate of return of the risk-free assets (Danthine and Donaldson, 2005). The optimal investment that the investor can make will satisfy the first-order condition stated in equation (5) which requires that the expected elasticity of marginal utility of wealth will be equal to zero (Varian, 1992).
To see how the proportion that is invested in risky assets, 𝑎, changes when wealth, 𝑊0, changes, we can examine the comparative statics of this problem (Varian, 1992). If we let 𝑎(𝑊0) be the optimal choice of 𝑎 as a function of 𝑊0, this must satisfy the first- order condition:
𝐸[𝑈′(𝑊0+ 𝑎𝑊0𝑟𝑟)𝑊0𝑟𝑟]≡0 (8)
If we differentiate this equation with respect to 𝑊0, it gives us:
𝐸[𝑈′′(𝑊0+ 𝑎(𝑊0)𝑊0𝑟𝑟)𝑊0𝑟𝑟[1 + 𝑎′(𝑊0)𝑊0𝑟𝑟]] ≡ 0 (9)
Or, rearranged:
𝑎′(𝑊0) = − 𝐸[𝑈′′(𝑊0+ 𝑎(𝑊0)𝑊0𝑟𝑟)𝑊0𝑟𝑟] 𝐸[𝑈′′(𝑊0+ 𝑎(𝑊0)𝑊0𝑟𝑟)(𝑊0𝑟𝑟)2]
(10)
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The second-order condition will be satisfied since risk aversion implies that 𝑈′′(𝑊) < 0, therefore the denominator is negative. From this we can see that:
𝑠𝑖𝑔𝑛 𝑎′(𝑊0) = 𝑠𝑖𝑔𝑛 𝐸[𝑈′′(𝑊0+ 𝑎(𝑊0)𝑊0𝑟𝑟)𝑊0𝑟𝑟] (11)
The sign of the expression on the right-hand side is determined by the absolute risk aversion, 𝑟(𝑤) (Varian, 1992). Varian (1992) shows that the right-hand side will be positive, negative, or zero as the absolute risk aversion, 𝑟(𝑤), is decreasing, increasing or constant. Pratt and Arrow hypothesized that an individual’s investment in a risky asset will increase in wealth as risk aversion decreases in wealth (Varian, 1992). The more risk-averse a person is, the higher reward he requires to engage in risky
investments.
If we consider an investor that is risk-neutral, i.e. does not care about risk, how much of her wealth will be invested in the risky asset? The simple answer is that all of her wealth will be invested in the risky asset. To prove this, we assume that the utility function of the risk-neutral investor is written 𝑈(𝑊) = 𝛽 + 𝛾𝑊, where 𝛽 and 𝛾 is constants, and 𝛾 > 0. We also assume that 𝐸𝑟𝑟 > 𝑟𝑓. We can write the risk-neutral investors
maximization problem as:
max𝑎 𝐸(𝛽 + 𝛾 (𝑊𝑜(1 + 𝑟𝑓) + 𝑎(𝑟𝑟− 𝑟𝑓))
= max
𝑎 [𝛽 + 𝛾 (𝑊0(1 + 𝑟𝑓)) + 𝛾𝑎(𝐸𝑟𝑟− 𝑟𝑓)]
(12)
Since we assume that 𝐸𝑟𝑟 > 𝑟𝑓, this expression is increasing in 𝑎 which means that if we assume the risk-neutral investor cannot borrow any money, she will invest her wealth in risky assets until 𝑎 = 𝑊0, i.e. until all of her wealth is invested in risky assets (Danthine and Donaldson, 2005).
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4. Data
The data used in this study is a cross-sectional data from the 2016 SCF. This is a survey data that includes information about the finances of households in the U.S. The SCF data provides detailed information on assets and liabilities of U.S. households as well as information on employment and demographic characteristics of the households. The SCF is sponsored by the Federal Reserve Board and is made in cooperation with the Department of the Treasury and collected by the NORC at the University of Chicago (Federal Reserve Board, 2017a). The SCF is a triennial survey where the 2016 wave is the latest survey made, and all the dollar variables are inflation-adjusted to 2016 dollars (Federal Reserve Board, 2018). The sample is chosen randomly and is attempting to sample households from all economic strata. The SCF consists of a complex sample design and is not an equal-probability design since it oversamples the relatively wealthy families in the U.S. since wealthy respondents are less likely to respond (Kennickell, 2001). The sample is intended to provide a good coverage of the population in the U.S.
as a whole, and due to the disproportional inclusion of wealthy families, weights should be used when interpreting the data (Federal Reserve Board, 2016b).
The dataset used is the “Summary extract public data” which is extracted from the “Full public data set” by the SCF to produce the summary values of different variables2.
The 2016 dataset originally consists of 6248 observations, but to deal with the problem of missing data, which is common in survey data, a multiple imputation technique has been used to replace the missing and incomplete data. In multiple imputations,
stochastic multivariate methods are used to replace each of the missing values with two or more values which has been generated to simulate the sampling distribution of the missing values (Montalto and Sung, 1996). This technique has been used with SCF since 1989 where each missing value has been replaced with five values. The multiple imputations technique used is developed for the SCF and produces five complete data sets which is referred to as “implicates” (Montalto and Sung, 1996). This means that the final dataset consists of 31 240 observations, five times more than the actual
observations. The data in the survey is intended to represent a household, with the head of the household as the respondent. The head of the household is defined as the male in
2 To see how the extract variables were created, see (Federal Reserve Board, 2016a))
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a mixed-sex couple, or as the older person in a same-sex couple. If the person is single, that person is defined to be the head of the household (Federal Reserve Board, 2016b).
Since this study has the purpose to examine households’ investments in risky assets, households that has less than 1.000 USD in assets are excluded from the data, this is consistent with previous studies in this area. This means that 1 597 observations are excluded, and 29 643 observations are left in this dataset to observe. Additionally, one observation was excluded since the proportion of risky assets of that household was less than zero. This means that a total of 29 642 observations are left to be analyzed.
When studying household assets, one can analyze the household’s total assets, which includes both financial and non-financial assets, or only the financial assets when studying the household’s proportion of risky assets held. An argument for using total assets is that real estates and other nonfinancial assets normally are a big part of the household’s wealth (Pålsson, 1996). Since most previous studies uses the household’s total assets in their analysis (see for example Pålsson, 1996; Jianakopolos and Bernasek, 1998; Liu, Yang and Cai, 2016) this study also takes the households total assets into account when analyzing the proportion of risky assets that the household has in their investment portfolio.
4.1. Variable description
The variables included in this study are variables that are frequently used in previous studies, mentioned in the literature review section, and that are of interest to explain characteristics of households. These variables are expected to correlate with the
proportion of risky assets that households hold. In the next sections descriptions of the variables included in the model is presented.
4.1.1. The dependent variable
The dependent variable in this model is the proportion of risky assets to total assets that the household has in their portfolio. The proportion of risky assets is calculated as the total value of risky assets divided by the total value of assets (excluding value of principal residences) held by the household.
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𝑝𝑟𝑜𝑝𝑜𝑟𝑡𝑖𝑜𝑛 𝑜𝑓 𝑟𝑖𝑠𝑘𝑦 𝑎𝑠𝑠𝑒𝑡𝑠 = 𝑟𝑖𝑠𝑘𝑦 𝑎𝑠𝑠𝑒𝑡𝑠 𝑡𝑜𝑡𝑎𝑙 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑎𝑠𝑠𝑒𝑡𝑠
(13)
This study follows the definition of risky assets according to Jianakopolos and Bernasek (1998) and Schooley and Worden (1996) who also used the SCF data to study the proportion of risky assets as the dependent variable. The assets included as risky assets are the total values of directly held pooled investment funds, stocks, bonds, equity in quasi-liquid retirement assets, equity interest in trusts and annuities, other financial assets (loans from the household to someone else, royalties, non-public stocks, etc.), net equity in nonresidential real estate, businesses with either active or non-active interest, and the total value of other nonfinancial assets (such as precious metal, antiques, oil/gas/mineral investment or leases, and other miscellaneous assets). Similar to the study of Jianakopolos and Bernasek (1998), this study does not include the value of principal residence as risky assets, but instead uses a measure of this as an explanatory variable. This since it is unclear whether households own their principal residences for investment purposes or for consumption. As Modigliani and Brumberg (2013) stated in their article about the life-cycle theory; a house ownership is a source of a current service and it may be used to fund the consumption after retirement, or it may be bequeathed. Therefore, the total assets exclude the values of principal residence in this study.
4.1.2. The explanatory variables
Several different factors can be assumed to explain why and if households invest in risky assets, for example how risk averse they are or how large income they have. The explanatory variables included in this model is chosen based on previous research, discussed in the literature review section, as characteristics that is expected to explain the risk behavior of households. The explanatory variables used in this study is: age, gender, education, ethnicity, marriage, children, employment, net worth, income, pension available, house ownership and if the head of the household is willing to take any financial risk.
Age squared is added to allow for non-linear age effects since previous research has shown that risk-aversion may increase closer to pension (see for example Wang and
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Hanna, 1997). Children squared is included to allow for non-linear effects for the number of children in the household, the assumption is that when the number of children increases the marginal effect decreases.
The variable for education level has been regrouped to six different values by compromising one of the included variables for highest completed grade originally consisting of 15 different values. All other explanatory variables are used in their original form in the data set.
Table 1 below shows the definition of all variables that are included in this study and the values they can take on, and table 2 shows the descriptive statistics of all the included variables.
Table 1. Variable definition.
Variable Name Abbreviation Variable Definition Values Proportion of risky
assets
prisky Proportion of risky assets held of total assets
0-1
Age age Age of head of household 19-95
Age squared age2 The square of the variable age 361-9025
Gender gen Gender of head of household 0=Male
1=Female Owning houses hou Have owned principal
residence
0=No 1=Yes Financial risk fin Respondent willing to take
financial risk
0=Not willing to take financial risk 1=Willing to take financial risk Any pension pen Pension exists for either head
of household or spouse
0=No type of pension exists 1=Pension exists
Marriage mar Marital status of head of
household
0=Neither married nor living with partner 1=Married / Living with partner
Employment emp Labor force participation of head of household
0=Not working
1=Working in some way
Children chi Total number of children in
household
0-7
Children squared chi2 The square of the variable children
0-49
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Table 2. Descriptive statistics.
Variables Mean Median Std. Dev. Minimum Maximum
Proportion of risky assets 0,292 0,162 0,322 0 1
Age 51,812 52 17,215 19 95
Gender 0,255 0 0,436 0 1
Education 3,178 3 1,329 1 6
Ethnicity 1,503 1 0,866 1 4
Marriage 0,592 1 0,492 0 1
Children 0,770 0 1,113 0 7
Employment 0,719 1 0,449 0 1
Income percentile groups 3,219 3 1,550 1 6
Net worth percentile groups 2,695 3 1,260 1 5
Financial risk 0,042 0 0,202 0 1
Any pension 0,595 1 0,491 0 1
Owning houses 0,670 1 0,470 0 1
Number of observations: 29 642
Note: The median value is included since the data has very large values for a relatively small part of the population.
Using the median therefore shows the “typical” holding, whereas the mean is more sensitive to outliers (Bricker et al., 2012).
Income percentile groups
inc Income percentile groups.
Income is the household income for previous calendar year.
1=0-20 2=20-39,9 3=40-59,9 4=60-79,9 5=80-89,9 6=90-100 Net worth percentile
groups
nw Net worth percentile groups.
Net worth is the difference between assets and debt.
1=0-24,9 2=25-49,9 3=50-74,9 4=75-89,9 5=90-100
Ethnicity eth Race/ethnicity of head of
household
1=White non-Hispanic 2=Black / African American 3=Hispanic
4=Other
Education edc Highest completed grade by
head of household
1=No high school diploma/GED 2=High school diploma or GED 3=Some college but no degree
4=Associate degree or bachelor’s degree 5=Master's degree
6=Doctorate or professional school degree
16
The descriptive statistics shows that the mean proportion of risky assets held by households are 29%, while the median is 16%. The average education level is “some college but no degree”, where the largest fraction, 34%, have an associate or bachelor’s degree, and the smallest fraction, 4%, have a doctorate or professional school degree.
The average and median age of the head of household is 52 years, with the youngest in the sample being 19 and the oldest being 95 years old. The head of household is male in 74% of the cases, and 59% of the head of household is married or living with partner.
Only 4% of the households are willing to take any financial risk, and 59% of the households has any existing pension. The average number of children are 0,7, where 59% of the sample has zero children, and 0,06% has 7 children. When it comes to labor force participation, 28% are not working at all while 72% are working in some way. A relatively large fraction of households, 67%, owns any principal residence.
Table 3. Risky assets for different income groups.
Income percentile group Holds any risky assets Mean proportion of risky assets held
0-20 30% 13%
20-39,9 48% 19%
40-59,9 64% 24%
60-79,9 81% 34%
80-89,9 93% 44%
90-100 98% 59%
In table 3 above, we can see that the mean proportion of risky assets held increases with income. While the smallest income percentile groups mean proportion of risky assets in their portfolio is 13%, the largest income percentile group has a mean proportion of 59% of risky assets in their portfolio. We can also see that the proportion of households that holds any risky assets increase with higher income. Income is therefore expected to have a positive effect on the dependent variable in the regression analysis.
In table 4 below, we can see that if men are the head of the household, the mean proportion of risky assets held are higher than if the head of the household is a female, the same goes if the head of household is married or living with partner, compared to if he or she is not married nor living with partner.
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Table 4. Household portfolios of gender and civil status.
Mean proportion of risky assets held
Male 32%
Female 23%
Married/Living with partner And Female
And Male
32%
28%
32%
Not married nor living with partner And Female
And Male
25%
22%
29%
As seen in figure 1 below, the mean proportion of risky assets held increase with age, with a small dip in the age group 65-74 years.
Figure 1. Mean proportion of risky assets held by age group.
0%
10%
20%
30%
40%
50%
<35 35-44 45-54 55-64 65-74 ≥75
Mean proportion of risky assets held
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5. Method
The SCF uses a multiple imputation technique to replace missing values. Because of this the dataset consists of five complete datasets (called implicates) instead of just one (Kennickell, 1998). To be able to analyze the data this can be corrected by using the
“repeated-imputation-inference” (RII) technique, which is a technique that uses information from all five implicates. The RII method combines the results across the five datasets by calculating the means and variances of the results from the five separate implicates (Montalto and Sung, 1996)3, and thereby corrects for the extra variability due to the multiple imputations and shows more accurate levels of significance. The SCF provides a data file including 999 bootstrap replicates and sampling weights for each replicate. These are used to bootstrap the standard errors, which should deal with the heteroscedasticity problem and the sample design by incorporating these problems into the estimates (Pence, 2006). The weights are included to compensate for the
oversampling of wealthy households and reflects each household’s probability of being included in the sample (Federal Reserve Board, 2016b).
The appropriate method to use for the regression analysis would be the generalized linear model (GLM) since the dependent variable is a proportion and the observations takes on values within the interval [0, 1], with a large fraction of the observations taking on the value 0 and 1. This indicates that the relationship is non-linear, and therefore GLM should be used (Baum, 2008). However, because of the complex dataset that the SCF is, the Federal Reserve Board recommends using the RII technique when analyzing the data (Federal Reserve Board, 2016; Montalto and Sung, 1996). To do this in an easy way, Karen Pence (2015) designed a program to use when analyzing all five implicates in the SCF data, called “scfcombo”. The “scfcombo” program is used to make sure that the correct standard errors estimates are calculated because of the multiple imputations.
If an ordinary regression command would be used, the regression would treat each of the observations as independent observations and this would lead to non-correct values of the standard errors and the significance of results (Federal Reserve Board, 2017b).
The “scfcombo” program only gives the coefficients and standard errors, and is, to my best knowledge, not flexible enough to incorporate the options needed when using the GLS method for my model. A GLM regression were made (without using the RII
3 See Montalto and Sung (1992) for a deeper explanation about the RII method.
19
technique) which showed that the signs of the coefficients were consistent with the signs using OLS with the “scfcombo” program. Fewer estimates were significant when using OLS with the RII technique, which is consistent with the information regarding the technique used (Montalto and Sung, 1996). Therefore the analysis are conducted by using ordinary least squares (OLS) regression in Stata/IC 15 to be able to use the
“scfcombo” program to calculate and combine the imputation uncertainty and
bootstrapped standard errors (Pence, 2015).4 One problem with using the OLS method when the dependent variable is a proportion, is that the values may be outside the interval [0, 1]. Since the purpose of this study is not to predict any values, but to observe the effect of the household characteristics, and because of the arguments stated above considering the imputation uncertainty, the OLS method will be used together with the program “scfcombo” for the regression analysis.
Lindamood, Hanna and Bi (2007) analyzed different articles dealing with SCF data focusing on how they dealt with different problems arising when using the data. When discussing the methods for dealing with the multiple imputation method used in the SCF, they stated that even though it is possible to use only one of the implicates to make an analysis the results may be biased, and that the RII technique should be used with all five implicates when possible. For this reason, all five implicates are used in this study. The descriptive statistics are measured using weights to correct for the oversampling of wealthy households and to account for sampling errors of the estimates calculated, and the regression is made with the OLS method using the “scfcombo”
program that uses the RII technique with weights and bootstraps.5
A VIF-test has been made to check for multicollinearity between the variables. No multicollinearity was found except between the variables age and age squared. These variables are expected to have this kind of problem since the squared variable is calculated from the original variable. All other variables have VIF-values under 7, which is less than the generally accepted level of multicollinearity (VIF <10) (Hair Jr et al., 2014).
5 The SCF Codebook brings up the possible problem of using weights in regressions and explains that weighted estimates may be dramatically less efficient than unweighted estimates (Federal Reserve Board, 2016b). A regression was made without the use of weights and no substantial difference was found.
20 The multiple regression model used in this study is:
𝑝𝑟𝑖𝑠𝑘𝑦𝑖 = 𝛽0+ 𝛽1𝑎𝑔𝑒𝑖 + 𝛽2𝑎𝑔𝑒𝑖2+ 𝛽3𝑔𝑒𝑛𝑖+ 𝛽4ℎ𝑜𝑢𝑖+ 𝛽5𝑓𝑖𝑛𝑖 + 𝛽6𝑝𝑒𝑛𝑖 + 𝛽7𝑚𝑎𝑟𝑖 + 𝛽8𝑒𝑚𝑝𝑖 + 𝛽8𝑐ℎ𝑖𝑖 + 𝛽9𝑐ℎ𝑖𝑖2 + 𝛽10𝑖𝑛𝑐𝑖+ 𝛽11𝑛𝑤𝑖 + 𝛽12𝑒𝑡ℎ𝑖 + 𝛽13𝑒𝑑𝑐𝑖+ 𝜀𝑖
(14)
Where 𝜀𝑖 is the error term.
Because of the complexity of the data used, and the use of the program “scfcombo”, no tests could be made on the coefficients and the regression results to see if there is any sign of endogeneity or heteroskedasticity. I have used the methods described earlier in this section to try to correct for any problem that could occur when analyzing this complex data.
The error term is normally assumed to be normally distributed with zero conditional mean, 𝐸[𝜀|𝑥𝑖] = 0, have a constant conditional variance, 𝑣𝑎𝑟[𝜀|𝑥𝑖] = 𝜎2, and be independent. But because of the complexity of the data, the assumption that the error term has a constant conditional variance is often violated when using cross-sectional data because of the individual heterogeneity. To account for this, the 999 bootstrap replicates and sampling weights for each replicate is used to incorporate these problems in the estimators (Pence, 2006).
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6. Results
The model presented in the method section is estimated using a regression analysis with the OLS method. This section presents the results given by the regression analysis regarding what characteristics in households that correlates with the proportion of risky assets held in the household portfolio. In table 4 below, the results of the regression analysis are presented. The adjusted R-squared for the model analyzed is 38,76%, which indicates that there are additional factors that can further explain the proportion of risky assets held than what is included in this model. Since the RII technique is used, the total number of observations in the regression analysis is 5 927.
Table 5. Regression statistics.
OLS Coefficients
Age 0,001 (0,001)
Age2 0,000 (0,000)
Gender: Female -0,034*** (0,009)
Owns principal residence: Yes -0,077*** (0,008)
Willing to take financial risk: Yes 0,055*** (0,017)
Pension exists: Yes 0,024*** (0,008)
Marital status: Married/Living with partner -0,050*** (0,009)
Employment: Working in some way 0,056*** (0,009)
Children -0,013 (0,008)
Children squared 0,003 (0,002)
Income percentile groups
20-39,9 0,018 (0,011)
40-59,9 0,018 (0,011)
60-79,9 0,050*** (0,013)
80-89,9 0,050*** (0,017)
90-100 0,027 (0,018)
Net worth percentile group
25-49,9 0,121*** (0,009)
50-74,9 0,257*** (0,014)
75-89,9 0,421*** (0,015)
90-100 0,640*** (0,019)
Ethnicity
Black/African American -0,025** (0,010)
Hispanic -0,068*** (0,011)
Other -0,042*** (0,015)
Education level
High school diploma/GED 0,004 (0,013)
Some college but no degree 0,011 (0,012)
22
Associate degree or bachelor’s degree 0,039*** (0,013)
Master's degree 0,054*** (0,017)
Doctorate or professional school degree 0,050*** (0,019)
Constant 0,031 (0,033)
Adjusted R-squared 0,3876
Number of observations 5 927
Standard errors within parenthesis
***p<0,01 **p<0,05 *p<0,1
From the regression statistics we can see that 18 of the 27 estimates are significantly different from zero. This means that the majority of these characteristics correlates with the proportion of risky assets that the household has in their investment portfolio.
The characteristic that has the highest correlation with the dependent variable is net worth, where the results show that the proportion of risky assets increases significantly the larger the net worth is. For the income variable, only the income percentile groups between 60-79,9 and 80-89,9 are significantly different from zero, compared to the reference group “0-20”, and the two significant groups have the same correlating increasing effect on the proportion of risky assets held.
The age estimate, including age-squared, is shown to be insignificant, which is
inconsistent with previous studies that has been reviewed. In previous studies the results have shown that age has a significant correlation with risk tolerance, most of the results have shown a positive correlation where risk aversion increases with age. The fact that age is shown to be insignificant in this study is therefore considered surprising. This could be due to the fact that it is the head of the household that is the respondent in the study, and therefore it does not take into consideration the age of the spouse in a household where the head of the household is married.
The presence of children in the household is shown to not have a significant correlation on the dependent variable. If the head of the household is a female, the coefficient are negatively correlated with the dependent variable, compared to the reference group
“Male”, which is consistent with the previous research stating that women are more risk averse than men. If the head of the household is willing to take financial risk, the
proportion of risky assets held correlates positively with the variable coefficient, when compared to the reference group that is not willing to take financial risk. This result is
23
expected since the variable measures the households risk tolerance. If either the head of the household or the spouse has any existing pension, the correlation with the
proportion of risky assets is positive. If any principal residence is owned, the correlation with the dependent variable is negative, compared to the reference group that does not own a principal residence. The same results can be seen when the head of the household is married or living with partner, compared to the reference group “Not married nor living with partner”. When the head of the household is working in some way, the proportion of risky assets held should increase, compared to the reference group “Not working”.
When compared to the reference group, “white non-Hispanic”, all other ethnicity groups show a significant negative correlation with the proportion of risky assets held, where Hispanic show the largest negative correlation. If the head of the household has an associate degree, a bachelor’s degree, or higher, the proportion of risky assets held is significantly positively correlated with the coefficients compared to the reference group
“no high school diploma/GED”.
All of the estimates that are shown to be statistically significant, are significant on a 1%
level, except for the estimate for black/African American which is significant on a 5%
level. The significant coefficients show that there is an economic significance for these characteristics that can be explained by economic theory, the effect of the estimates is not negligible. The estimates are all in line with economic theory, and the vast majority of the results from the regression analysis are expected, except for the results for age which are shown to be insignificantly correlated with the dependent variable.
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7. Discussion
This studies purpose is to examine the relationship between different characteristics of households and the proportion of risky assets that is held by the household. The regression analysis shows that in total the majority of the characteristics studied has a significant effect on the proportion of risky assets held, except for age and the number of children in the household. The fact that age is not significant differs from the results from previous studies of the age effect on risk tolerance. The result in this study shows that age does not correlate with the proportion of risky assets that is held by the
household, whereas previous studies (see for example Pålsson (1996) and Wang and Hanna (1997)) indicates that age should correlate with the dependent variable, typically positively correlated. An explanation to why the previous studies differs in the results could be due to the fact that different data have been used covering other time periods.
Riley and Chow (1992) used U.S. data from the Survey of Income and Program Participation (SIPP) and Pålsson (1996) used Swedish data. Even though Wang and Hanna (1997) used SCF data, they used panel data for the years 1983-89, which differs from the data used in this study. The fact that the results in this study differs from previous studies indicates that this relationship needs further research to establish the correlation between the variables.
The factor that correlates highest with the proportion of risky assets is net worth. The results show that the proportion of risky assets held correlates significantly, and relatively high, with greater net worth. This is consistent with economic theory and previous studies (see for example Cohn et al. (1975) and Jianakopolos and Bernasek (1998)) that has been made. When net worth is large, the amount that can be afforded to lose when investing in risky assets increases, hence the household can afford to take on more risk when investing. A similar analysis can be made for income. However, only two of the income categories, 60-79,90 and 80-89,89, had a significant positive correlation with the dependent variable. If the study would include data for the same households for several years, it would be possible to study the income effect deeper and examine if an increase or decrease in the household’s income would have any effect on the proportion of risky assets held.
25
The estimate for the financial risk the household is willing to take shows a positive correlation with the dependent variable. This is expected since when investing in risky assets, a financial risk is taken. Therefore, a household that expresses a willingness to take on a financial risk is assumed to invest in risky assets. The fact that the proportion of risky assets increase if the head of the household is working in some way is also as expected since working indicates a stabile income which indicates a greater financial stability than if the head of the household was not working. Therefore, it is possible for the household to invest a larger amount of wealth in risky assets.
Similarly, the estimate for any existing pension also shows a positive correlation with the dependent variable. This can be explained by the secure income that the household has when retiring. If the household has any existing pension, it is willing to take on more financial risk with their assets by investing a larger proportion in risky assets.
The estimate for marriage shows that if the head of the household is marred or living with partner, the proportion of risky assets held would decrease. It could be that married couples are more conservative since there are two people that, assumedly, makes the investment decision together. Fratantoni (1998) achieved the same result, indicating that married couples has less investments in risky assets. The results estimated for
homeownerships is likewise consistent with the results found in Fratantoni’s study, if a primary residence is owned, the proportion of risky assets held increases. This could be explained by the increased need for liquid assets if anything would happen to the house.
The estimates for ethnicity show that ethnicity correlates with the proportion of risky assets held, it shows that Hispanic households invest less in risky assets than the other groups. White couples invest more in risky assets than other ethnicity groups. This is consistent with previous research and not surprising. As mentioned by Yao, Gutter and Hanna (2005), individuals that are foreign born may experience a language barrier which may result in foreign born individuals not having access to financial information in the same agree as those not experiencing language barriers. The results indicate that households included in these ethnicity groups could be relevant to reach out to for information and education about investments so that these households are not left behind and risk the loss of expected return that an investment in risky assets may give.
26
When examining education, the results of the estimates show that the proportion of risky assets held is significant positively correlated to education when the head of the household has an associate- or bachelor’s degree or higher. This is expected results since it is assumed that a well-educated individual has greater financial knowledge than an individual that does not have any education, and that an individual with education is more exposed to financial information than uneducated individuals are.
27
8. Conclusion and ideas for further work
In this paper I have studied how different characteristics of a household are correlated to the proportion of risky assets that is held by the household. The majority of the results show no surprising effect and are consistent with previous research. The study shows that a larger proportion of risky assets held are correlated with a household that has a relatively large income, large net worth, owns a primary residence, and where the head of the household is male, not married nor living with a partner, working in some way, willing to take on a financial risk, white or non-Hispanic, and has an education level of associate- or bachelor’s degree or higher. Age and number of children in the household is not shown to have a significant effect on the proportion of risky assets held in the household.
The study is limited by the complex data and the cross-section data by the SCF. The investment decisions are expected to change over the lifecycle of the household, it would therefore be of great interest to be able to study the same households over several years to see how, for example increased income, or more children in the household, effects the investment in risky assets. The SCF has for two periods previously re- interviewed the same households under two to three waves, where the latest panel survey is from the years 2007 and 2009.
Since different studies uses different measures of wealth, the results may differ depending on how the study defines wealth. This study has used the household’s total wealth but excluded the value of the primary residence, which has been discussed in the data section. It is possible that the results would be different if the definition of wealth would be different. It would therefore be useful to study how different definitions of wealth affects the results.
Since this model only explain 39% of which characteristics that explain the proportion of assets invested in risky assets of American households, further research needs to be made on this subject. Further studies could involve other demographic, socioeconomic and psychological factors to be able to understand the investment decisions made by households. It would be of interest to examine whether the area that the households live in have an effect on the proportion of financial assets invested in risky assets, could it be
28
that those who live in the city invest more in risky assets than those who lives on the countryside? The SCF data does not include any information of where the household lives with the purpose to protect their privacy. To be able to compare the investment behavior in different countries and see if it differs between countries, the same survey could be done in multiple countries to be able to tell if households have different levels of risk-aversion depending on where they live.
The results of this study provide information about what characteristics in a household that affects the household’s investment allocations. When studying the area of
household investment decisions, important information about financial behavior and knowledge may be found. To educate household’s in financial planning and
investments, the information from this study, and similar studies, may be taken in regard. There are many different characteristics and factors that affect household’s investment decisions, but the characteristics studied in this paper is some of the major and well-studied characteristics that is easy to find about the households. The area of household’s investment choices is of great interest within financial economics and needs further studies to provide households with useful and important investment and financial knowledge.
29
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