Investment horizon and portfolio choice of private investors

International Review of Financial Analysis 20 (2011) 68–75

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International Review of Financial Analysis

Investment horizon and portfolio choice of private investors☆ Yulia V. Veld-Merkoulova ⁎ Division of Accounting and Finance, Stirling Management School, University of Stirling, FK9 4LA, UK

a r t i c l e

i n f o

Article history: Received 5 July 2010 Received in revised form 22 December 2010 Accepted 14 February 2011 JEL classification: G11 Keywords: Investment horizon Household finance Portfolio choice Financial planning

a b s t r a c t I empirically investigate the impact of age and self-reported planning horizon on asset allocation decisions of individual investors. I find that age and investment horizon play different roles in determining investors' risky portfolios. When I consider total risky investments, including real estate, the share of risky assets declines with age. Planning horizon tends to influence only investments in financial risky assets, such as stocks, options, and mutual funds. A longer planning horizon leads to an increasing share of risky financial investments. Finally, less risk-averse investors and individuals with lower rate of time preference invest significantly more in stocks and other risky financial assets. © 2011 Elsevier Inc. All rights reserved.

1. Introduction The question of how much of their wealth investors should allocate in risky assets is highly debatable. An issue that remains open is the importance of investors’ time horizons for their asset allocation decisions.1 In this paper I address this question by empirically investigating the impact of age and self-reported planning horizon on asset allocation decisions for a broad cross-section of the population. Theoretically, Samuelson (1969) shows that investors with constant relative risk aversion should invest a constant proportion of their wealth in equity. In the case of decreasing relative risk aversion, a decreasing investment horizon leads to a lower optimal stock investment (Thorley 1995). Cocco, Gomes, and Maenhout's (2005) lifecycle model also predicts that in the presence of nontradable labor income, the optimal share of equities should decrease over an inves-

☆ I would like to thank an anonymous referee, Rob Engle, Alan Huang, Ranjini Jha, Natalia Kotchetova, Mohamed Sherif, Chris Veld, Christine Wiedman, YiLin Wu, seminar participants at Heriot-Watt University, University of Waterloo, University of Dundee, and participants at the 2008 AFFI Meeting, 2008 Scottish BAA Meeting, 2008 Financial Management Association Meeting, 7th National Taiwan University conference, 2009 BAA Meeting and 2010 Society for Financial Econometrics Annual Meeting for their helpful comments and suggestions. I also thank Sandra Sizer for editorial assistance. In this paper use is made of data of the DNB Household Survey. The financial support of the Dutch Science Organization (NWO; A laboratory for the use of household financial decisions), the 2009 Eurofonds-Fundclass Academic Award for the best European paper on retail investors, and of the Carnegie Trust for the Universities of Scotland is gratefully acknowledged. ⁎ Tel.: +44 1786 466417. E-mail address: [email protected]. 1 Viceira (2001), Letendre and Smith (2001), and Angerer and Lam (2009) analyze the impact of labor income on the optimal share of risky assets in household portfolios. 1057-5219/$ – see front matter © 2011 Elsevier Inc. All rights reserved. doi:10.1016/j.irfa.2011.02.005

tor's life. Bhandari and Deaves (2008) show that younger pension plan members report a preference for holding higher equity shares in their portfolio, and Cardak and Wilkins (2009) find that Australian households with longer savings horizon (measured on a scale from zero to five) tend to invest more in risky financial assets. The second problem I dealt within this paper is the low participation of households in the markets for financial risky assets, found in a number of previous studies (see Campbell (2006) for extensive overview). An important point in reconciling this non-participation puzzle with the possibility of investors still making rational decisions is the fact that a typical household invests in two types of risky assets: equity and real estate. The real estate part is often overlooked in empirical studies, while the total household investment in these two categories is much larger than the financial risky asset holdings alone. The high volatility of the housing market prices supports the treatment of the owner-occupied housing as a risky asset rather than viewing it as a relatively safe investment. For example, during the peak of the recent financial crisis, the US home prices (as measured by the S&P/Case-Shiller Index) have decreased by 28.63% in the short period between January 2007 and January 2009.2 In addition, the interest rate risk associated with the mortgages can significantly increase the overall riskiness of the portfolios that contain real estate.3 The returns on the stock and housing markets have either a weak correlation or none at all: Quan and Titman (1999) find that for all 14 2

Source: http://www.standardandpoors.com. I am grateful to Rob Engle for this suggestion. Overall, both the riskiness of the real estate and the risk associated with the mortgages favor using total risky assets (including owner-occupied housing) in calculating a proxy for the share of risky assets in the investors' portfolios. 3

Y.V. Veld-Merkoulova / International Review of Financial Analysis 20 (2011) 68–75

countries in their sample, a correlation of real estate values with stock market is not statistically significant, with the coefficient of correlation for the U.S. market equal to 0.001. Theoretically, Flavin and Yamashita (2002), Cocco (2004), Yao and Zhang (2005), and Pelizzon and Weber (2009) show that households' optimal equity portfolios should be affected by the presence of owner-occupied housing. Although many studies suggest an optimal theoretical solution to the individual asset allocation problem, the relation between time horizon and asset allocation has not yet been empirically explored. The purpose of this paper is to empirically investigate the effects of the planning horizon and investor's age on the portfolio allocation decisions of individuals. In my study, I explicitly take into account the real estate investments, including owner-occupied housing, as an important category of risky assets. I deal with the issue of the impact of housing investment on the financial decisions of individuals by separately considering both total risky asset allocation and investment in financial risky assets. My main finding is that the age of an investor determines the share of total risky assets (including real estate) in his or her portfolio, supporting the life-cycle model of Cocco et al. (2005). However, it is the actual planning horizon that dictates how much will be invested in risky financial assets, primarily stocks. In addition, I find that investors' attitudes towards risk and time matter only in their financial asset allocation decisions. Total asset allocation, including real estate, is not affected by investors' aversion to risk and time preferences. However, the less risk-averse investors, and those respondents who are more prepared to sacrifice current gains for future benefit, invest a significantly larger share of their liquid financial wealth in stocks and other risky financial assets. I also show that even after taking investors' attitudes into account, age and planning horizon remain important factors in asset allocation. My finding that investors apply relevant factors, such as their investment horizon, life-cycle position and risk attitudes, in different ways to the equity and housing components of their total portfolios is in line with the behavioral portfolio theory of Shefrin and Statman (2000). This theory suggests that various layers of investment portfolios are treated independently and serve to achieve different investment goals. The rest of the paper is organized as follows. In Section 2 I discuss the database and the survey questions used for the analysis. In Section 3 I introduce main hypotheses and explain how variables are constructed. In Section 4 I present the main model estimation results and explore how individual attitudes towards risk and rate of time preferences can affect the results. Section 5 concludes.

2. Data I obtain the data on the investors' horizon from the questions submitted in November 2003 to the panel of Dutch households, run by CentERdata, which is a survey research institute specializing in online surveys. I match these questions with the extensive data on the household assets, liabilities, income, and demographic characteristics from the closest in time (2004) wave of the Dutch National Bank (DNB) household survey that is also organized by CentERdata. CentERdata is based at Tilburg University in the Netherlands. Information on CentERdata and the CentERpanel is available at http:// www.centerdata.nl. The survey is generally done via the Internet, but having a personal computer with an Internet connection is not a selection criterion. Households that do not have access to the Internet are provided with a so-called NetBox with which the household can establish a connection to the Internet via a telephone line and a television set. Panel recruiting is done by telephone, and is independent of whether or not households have Internet access. The panel is representative of the Dutch population with respect to a number of important demographic characteristics. In other words, the

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average panel member has the same experiences and knowledge as the average person living in the Netherlands. The members of the panel are interviewed by businesses and university researchers each week on a number of issues, most of which deal with financial matters. This panel is used extensively for economic, finance, and marketing research. Among economic and finance studies using this panel are, for example, Bellemare, Krause, Kröger, and Zhang (2005) on the effect of information feedback versus the effect of investment flexibility in myopic loss aversion; Das and Donkers (1999) on subjective income uncertainty; Dong, Robinson, and Veld (2005), who study preferences of individual investors on dividend payments; Guiso, Sapienza, and Zingales (2008), who investigate the relation between trust and stock market participation; and Veld and Veld-Merkoulova (2008), who look at individual risk perceptions. The answers of respondents on the length of their investment horizon were matched with the detailed data on their assets from the Dutch National Bank survey. This resulted in 617 valid observations. Excluding the outliers with highest and lowest 5% of assets (below €3,500 and above €670,000) reduces the total number of observations to 555.4 Table 1 presents summary statistics of the detailed breakdown of respondents’ assets and liabilities, together with their demographic characteristics. The mean total value of the assets in the sample is €225,113, with the mean value of owner-occupied housing responsible for €180,557. The mean value of debt is €66,382, and mostly comprises mortgage debt. Therefore, the average net worth (difference between values of total assets and total debt) is €158,731. Given the large share of real estate in total investors’ portfolio, other categories of investments are relatively less important. The mean total investment in stocks, mutual and growth funds and options combined is €6,162, with more than half of this amount in mutual funds. 3. Hypotheses and variable description 3.1. Main hypotheses I test two main hypotheses, both of which have been proposed in the literature and are commonly used in the financial planning practice. Hypothesis 1 is related to the common financial advice to invest relatively more in risky assets at a younger age. It is consistent with the Cocco et al. (2005) life-cycle model, which predicts that the optimal share of risky investments should decrease with age. On the other hand, Frijns, Koellen, and Lehnert (2008) experimental setting results suggest that older investors have a stronger preference for risky assets. Since I study two different forms of risky assets (including and excluding real estate), which can play different roles in investors’ decision-making in line with the behavioral portfolio theory of Shefrin and Statman (2000), I put forward two forms of hypothesis 1: Hypothesis 1A. The share of wealth allocated to total risky assets is negatively related to age. Hypothesis 1B. The share of wealth allocated to financial risky assets is negatively related to age. The second hypothesis is based on Thorley's (1995) finding that for investors with decreasing relative risk aversion, the optimal share of wealth allocated to the risky assets increases with investment horizon. Similarly to the previous hypothesis, I distinguish between Hypotheses 2A and 2B, depending on the definition of risky assets. 4 In their study of U.S. households, Shum and Faig (2006) exclude between 33% and 40% of their sample based on various net worth and income-based screens. Heaton and Lucas (2000) impose a minimum of $10,000 of financial net worth.

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Table 1 Summary statistics of personal and financial characteristics of respondents. This table presents detailed breakdown of assets and liabilities of the 555 respondents included in the study, as well as summary statistics of the respondents' answers to the risk attitudes and present-future tradeoff questions. All asset, debt, and income amounts are in euros. Horizon is calculated as the time in years until the first major capital requirement planned by a respondent (such as retirement, house purchase or child's college education). Answers to the risk attitudes and present-future tradeoff questions are on the scale from one to seven, where one indicates “Totally disagree” and seven indicates “Totally agree.” Panel A. Descriptive statistics Variable

Mean

Median

Standard deviation

Assets, total including: Checking accounts Employer-sponsored savings plans Savings or deposit accounts Deposit books Savings certificates Single-premium annuity insurance policies Savings or endowment insurance policies Growth funds Mutual funds Bonds Stocks Options Investment real estate Loans to family and friends Owner-occupied house Second house Mortgage-related savings and investments Equity in partnerships, private business or large shareholdings Other assets

€225113.0

€220974.0

€150961.5

Minimum €3621.0

Maximum €658504.9

3047.8 1918.65 15342.8 372.1 104.1 4372.6 3299.6 813.8 3572.1 868.5 2708.8 67.4 2036.7 639.6 180556.8 1848.6 2849.0 445.3 248.5

1700.0 22.50 6011.0 0 0 0 0 0 0 0 0 0 0 0 189000.0 0 0 0 0

5948.9 4914.2 24947.6 3140.0 1277.6 15721.9 11560.2 6372.6 15735.6 6484.3 16716.7 667.7 18816.1 5110.7 130544.0 14039.6 8220.4 3094.5 2242.4

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

€66381.8

€45000.0

€91886.4

0

507.3 589.1 7.5 34.9 438.5 245.0 21.9 666.7 393.8 63309.1 168.0 158731.2 192049.6 184442.2 7243.9 71.7 10.5 37863.3 5.7 50.0 0.26 0.14

0 0 0 0 0 0 0 0 0 43000.0 0 139127.6 195000.0 190000.0 0 87.4 0 35360.0 3.0 50.0 0 0

4884.3 2856.5 127.7 414.9 3567.3 2044.6 203.1 9082.0 4735.6 89394.2 3406.4 147908.3 138768.5 134145.7 25026.6 34.2 20.9 23691.0 7.2 13.9 0.44 0.35

0 0 0 0 0 0 0 0 0 0 0 -1113888 0 0 0 0 0 -1360.0 0 22.0 0 0

Question

Mean

Median

Standard deviation

Number of observations

A. Risk attitudes questions R1. If I think an investment will be profitable, I am prepared to borrow money to make this investment R2. I want to be certain that my investments are safe R3. I get more and more convinced that I should take greater financial risks to improve my financial position

2.26 5.61 2.81

2 6 2

1.56 1.15 1.66

517 517 517

3.74 3.46 3.61 3.75

4 3 4 4

1.49 1.55 1.64 1.44

525 525 525 525

Debt, total including: Private loans Extended lines of credit Debts on hire-purchase contracts, based on payment by installments and equity-based loans Debts with mail-order firms, shops and other retailers Loans from family and friends Study loans Credit card debt Other loans Mortgages on investment real estate Mortgages on owner-occupied house Mortgages on second house Net worth Risky assets Real estate Liquid risky assets Share of risky assets in total assets (%) Share of liquid risky assets in liquid (non-real estate) assets (%) Income Horizon (years) Age Gender (0 = male, 1 = female) Education (1 = university degree, 0 = no university degree)

80000.0 73449.0 241491.0 52164.0 22246.0 195952.0 106000.0 117195.7 205952.0 110000.0 328900.0 10190.0 250000.0 100000.0 600000.0 180000.0 97069.6 30000.0 35406.0 €1302925 97562.0 30000.0 2550.0 7500.0 60000.0 30000.0 3200.0 178000.0 79411.0 1296750.0 79000.0 658169.2 635500.0 620000.0 328900.0 100.0 97.5 325035.0 60.0 84.0 1 1

Panel B. Respondents' attitudes to risk and tradeoff between present and future

B. Tradeoff between present and future questions T1. I often work on things that will only pay off in a couple of years T2. I am only concerned about the present because I trust that things will work themselves out in the future T3. With everything I do, I am only concerned about the immediate consequences (say a period of a couple of days or weeks) T4. I think there is no need to sacrifice things now for problems that lie in the future, because it will always be possible to solve these future problems later

Hypothesis 2A. The share of wealth allocated to total risky assets is positively related to the planning horizon. Hypothesis 2B. The share of wealth allocated to financial risky assets is positively related to the planning horizon.

Hypotheses 1 and 2 are closely related and are not mutually exclusive. For example, since the age-related time to retirement is often seen as a proxy for investment horizon, Thorley's (1995) result is also consistent with the financial planning advice in practice. To study these hypotheses, I estimate a censored model with the proportion of risky

Y.V. Veld-Merkoulova / International Review of Financial Analysis 20 (2011) 68–75

assets as the dependent variable, and age, horizon, and investors’ demographic characteristics as explanatory variables. 3.2. Variables 3.2.1. Share of risky assets Since the main issue in this study is what determines risky asset allocation for the private investors, I use two proxies for risky asset share in the portfolio, the share of risky assets in total assets, and the share of liquid risky assets in liquid total assets. “Total assets” here includes all financial, real estate, and private business assets owned by individuals. “Risky assets” are defined as total investment in mutual funds, stocks, options, real estate, and private business equity combined. “Liquid total assets” are assets excluding real estate, and “liquid risky assets” include investment in mutual funds, stocks, and options. Such a division makes it possible to take into account investment in the two most important classes of risky assets: financial assets and real estate. 3.2.2. Age and investment horizon The two main variables I use to test Hypotheses 1 and 2 are the age of the respondents and their investment horizon. To measure investment horizon, respondents are asked what is the most important goal, for which they save or invest (examples include an addition to pension, early retirement, a major purchase, such house, boat or a car, children's education, leaving an inheritance or no specific goal), and how many years they plan or expect it would take until this event will take place. The investment horizon is then defined as the self-reported time expected until such a savings or investment goal. If a respondent indicates two or three main goals he or she is saving for, the time to reach the nearest of these goals is taken as a proxy for investment horizon. 3.2.3. Background characteristics of investors I also include several control variables to isolate the effects of age and horizon on financial decisions. These control variables comprise respondents' gender, education (dummy equal to one when a respondent holds university degree, and zero otherwise), income, and net worth. I calculate net worth as the difference between total assets (including real estate) and total debt (including mortgage debt). 3.2.4. Risk attitudes and time preferences Apart from the household wealth and planning horizon, personal preferences might play an important role in individuals' deciding how much of their portfolio to hold in stocks and other risky assets. The DNB survey I use in this study includes several questions that are intended to reveal respondents’ attitudes towards financial risk. Another set of questions measures how well the respondents are prepared to sacrifice present wealth to achieve future gains. I use the information contained in these questions to control for the individual risk attitudes and their planning and savings behavior. Three of these questions concern risk attitudes. These questions are summarized in Panel B of Table 1 as questions R1 to R3 (grouped as risk attitudes questions). In these questions, respondents are asked to give a grade from one (“Totally disagree”) to seven (“Totally agree”) to statements such as “I want to be certain that my investments are safe” (question R2). The remaining four questions (labeled in Table 1 as T1 to T4 for present/future tradeoff questions) measure how well the respondents are prepared to sacrifice present wealth to achieve future gains, and may be considered as a proxy for their degree of time preference. In these questions, respondents also gave a grade from one to seven to questions like “I often work on things that will only pay off in a couple of years” (question T1). There are 517 responses to each of the three risk-aversion questions, and 525 responses to each of the four present/future tradeoff

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questions. Most respondents tend to be on the risk-averse side, with, for example, a mean value of 5.61 (median of six) on a scale of one to seven (where seven indicates “Totally agree”) of the response to the question R2 “I want to be certain that my investments are safe”. For the time tradeoff, the replies are distributed more towards the middle of the scale. For example, question T3 (“With everything I do, I am only concerned about the immediate consequences (say a period of a couple of days or weeks)”) has a mean response of 3.61 and median of four. Three out of four questions in this group have medians of four on the scale of one to seven. Table 2 presents correlations between the answers to these seven questions. From this table, we can see that the answers to the three risk attitudes questions are highly correlated. The absolute values of the correlation coefficients for this group range from 0.26 to 0.40, all highly statistically significant. The signs of these coefficients are also in line with the design of the questions and with our expectations. For questions R1,“If I think an investment will be profitable, I am prepared to borrow money to make this investment”, and R3, “I get more and more convinced that I should take greater financial risks to improve my financial position”, in which a higher degree of agreeing with the statement suggests less aversion to risk, the estimated correlation coefficient is positive. Question R2 (“I want to be certain that my investments are safe”) will receive a higher score from the more risk averse investors; consequently, it is negatively correlated with both question R1 and R3. In the group of the rate of time preference questions, variable T1 has high values for individuals who like to invest for the future and who do not have very high discount rate. (The statement reads: “I often work on things that will only pay off in a couple of years.”) Variables T2 to T4 have the opposite meaning, so we would expect them to be positively correlated with each other and negatively correlated with variable T1. The estimated correlation coefficients are in line with these expectations, with exception of not statistically significant correlation between variables T1 and T3 of 0.02. Overall, the correlation analysis supports the validity of the risk attitudes and time preference questions, and their use as controls for the individual preferences. 3.2.5. Factor analysis results The high correlations between the seven risk- and time-preference questions obviously preclude their use as explanatory variables in a same regression. To simultaneously exploit the information contained in these questions in one regression, I must reduce the dimensionality of the matrix of individual answers. Thus, I use factor analysis, which should uncover the underlying preference structure. Table 2 Correlation between risk and time preference measures. This table presents Spearman rank-order correlations between the respondents’ answers to the risk attitudes and present-future tradeoff questions (R1 to R3, and T1 to T4, correspondingly). t-statistics are in parentheses. *** is significant at the 0.01 level. ** is significant at the 0.05 level. * is significant at the 0.10 level. R1 R1 R2 R3 T1 T2 T3 T4

1 −0.26⁎⁎⁎ (− 6.12) 0.40⁎⁎⁎ (9.97) 0.05 (1.07) 0.10⁎⁎ (2.35) 0.06 (1.25) 0.03 (0.79)

R2

R3

T1

T2

T3

T4

1 −0.26⁎⁎⁎ (− 6.17) 0.01 (0.26) −0.09⁎⁎ (− 2.06) −0.02 (− 0.41) 0.07 (1.56)

1 0.08⁎ (1.87) 0.03 (0.63) 0.04 (0.88) 0.03 (0.68)

1 −0.56⁎⁎⁎ (− 15.37) 0.02 (0.48) −0.21⁎⁎⁎

0.26⁎⁎⁎ (6.23) 0.36⁎⁎⁎

(− 4.83)

(8.82)

1 1 0.08⁎ (1.91)

1

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Y.V. Veld-Merkoulova / International Review of Financial Analysis 20 (2011) 68–75

By using factor analysis in this case I assume that answers to all seven preference questions (observable variables) represent a function of a smaller number of latent (unobservable) factors that describe individual preferences. Formally, this relation can be described as follows: Xi −μ = LFi + εi ;

ð1Þ

Table 4 Risky asset allocation. Mean and median values of risky asset shares are classified by the values of control/explanatory variables. Panel A presents the share of total risky assets, including real estate, in respondents' total assets. Panel B reports the share of financial risky assets in total financial assets. Total number of observations is 555 for all categories. The column titled “Test statistic” presents t-statistics for the differences in means and van der Waerden test values for the differences in medians. P-values are in parentheses. Categories

where for each individual i, Xi is a vector of observable answers to questions R1 to R3 and T1 to T4, μ is the vector of variable means, L is a so-called factor loading matrix of coefficients, Fi is a vector of common factors, and εi is a vector of unique factors. To estimate the model, I impose the following restrictions: E(Fi) = 0, E(εi) = 0, E(Fiεi) = 0, E(FiF’i) = I, and E(εiεi) is a diagonal matrix. After estimating factor loading coefficients, I compute the estimates of the (unobservable) common factors. These results together with the diagnostic statistics are presented in Table 3. I identify two main factors by using principal components analysis. Factor one (further referred to as “Risk tolerance”) is highly correlated with the answers to questions R1 to R3. Higher values of this factor indicate that the respondent displays more tolerance to risk. Factor two (“Time preference”) is strongly related to questions T1 to T4. Higher values of this factor indicate that a respondent has a relatively higher rate of time preference. In other words, he places greater values on present benefits relative to future benefits. These factors are further used in asset allocation regressions as substitutes for the answers to individual questions. 4. Model description and estimation results 4.1. Univariate results In Table 4 I present the results of the univariate analysis of the risky asset allocation. I classify the mean and median measures of risky asset shares by the values of explanatory and control variables, with results of t-test for the mean and the Van der Waerden test for the median. Panel A of Table 4 focuses on the total share of risky assets, including real estate assets. The results of both mean and median tests show that respondents with higher incomes have a higher share of risky assets, with a mean of 80.17% and a median of 89.11%. The lower income half of investors have on average only 63.34% of their money invested in risky assets (with a median of 84.16%). The difference between these two groups is highly significant, both economically and statistically. In line with Papke's (1998) results, gender does not seem to play a role in the risky asset allocation. Both males and females invest similar proportions in risky assets (72.50% for men and 69.61% for women). Therefore, I do not reject the null hypothesis that both means and medians are the same for males and females. Table 3 Results of factor analysis. This table reports the results of factor model estimation on variables R1 to R3 and T1 to T4. These variables are the respondents' scores (from one to seven) given to the risk and time tradeoff attitude questions. Factor loadings matrix Variable

R1 R2 R3 T1 T2 T3 T4

Factor Factor 1 (“Time preference”)

Factor 2 (“Risk tolerance”)

Communality

Uniqueness

0.108 −0.064 0.043 −0.608 0.772 0.208 0.414

0.477 −0.316 0.495 0.194 0.014 0.087 −0.010

0.239 0.104 0.247 0.408 0.595 0.051 0.171

0.761 0.896 0.753 0.592 0.405 0.949 0.829

Mean Test statistic

Median Test statistic

Number of observations

Panel A. Share of risky assets High income Low income Male Female University degree No university degree High net worth Low net worth Planning horizon of 3 years or less Planning horizon over 3 years Age under 50 years Age 50 years and over

in total 80.17 63.34 72.50 69.61 67.25 72.48 85.98 57.55 70.78

assets 5.98 (0.00) 0.88 (0.38) 1.26 (0.21) 10.76 (0.00) 0.70

89.11 84.16 87.84 86.20 84.13 87.62 89.37 82.84 86.97

9.80 (0.00) 0.43 (0.51) 3.32 (0.07) 40.26 (0.00) 0.92

277 278 408 147 79 476 277 278 291

72.80

(0.49)

88.14

(0.34)

264

72.13 71.35

0.27 (0.79)

87.74 86.70

0.31 (0.58)

277 278

Panel B. Share of liquid risky High income Low income Male Female University degree No university degree High net worth Low net worth Planning horizon of 3 years or less Planning horizon over 3 years Age under 50 years Age 50 years and over

assets in 12.82 8.10 11.02 8.88 14.00 9.87 10.48 10.43 9.88

liquid total 2.68 (0.01) 1.07 (0.29) 1.63 (0.10) 0.02 (0.98) 0.68

assets 0 0 0 0 0 0 0 0 0

17.34 (0.00) 7.49 (0.01) 7.74 (0.01) 6.33 (0.01) 6.24

277 278 408 147 79 476 277 278 291

11.09

(0.50)

0

(0.01)

264

10.48 10.43

0.03 (0.98)

0 0

5.09 (0.02)

277 278

There is also a difference in investment behavior based on the education level of the respondents. Those with a university degree tend to invest less in risky assets, although the difference is only statistically significant for the medians. Median risky investment share is lower by 3.49% for the better-educated respondents. Net worth has an even more pronounced effect on the investment in risky assets than does respondents’ income. The mean risky asset share for the higher net-worth half of the investors is 85.98%, while for the lower net-worth half, this number is only 57.55%. Both mean and median differences are highly significant. This finding supports the Wachter and Yogo (2010) life-cycle model, which predicts that portfolio share in risky assets should increase in wealth. Finally, without controlling for the other factors, both age and the self-reported planning horizon do not have any significant effect on the observed risky asset allocation. Panel B of Table 4 completely excludes nonfinancial (real estate) assets from consideration, and focuses on the share of liquid (mostly financial) risky assets in liquid total assets of the investors. This measure is quite often used in the studies on individual asset allocation. By considering these variables separately, I can also see relative importance of real estate as a category of risky assets. After excluding real estate, my results are similar to those in Panel A.5 Investors with higher incomes invest significantly more in risky assets.

5 Large proportion of observations equal to zero in this sample means that the distribution of the share of liquid risky assets is far from normal (this is confirmed by the Jarque-Bera statistics equal to 12,865.04). In this case, a non-parametric test, such as van der Waerden test, provides a better test for the significance of the differences between the subgroups than a t-test.

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Table 5 Individual risk and time preferences factors and risky asset allocation. This table reports the results of censored logistic model estimation for 517 observations. The risky assets shares are used as the dependent variables. “Time preference” and “Risk tolerance” are the factor scores derived from the respondents’ scores given to the risk and time tradeoff attitude questions. Z-statistics are in parentheses. ⁎⁎⁎ is significant at the 0.01 level. ⁎⁎ is significant at the 0.05 level. ⁎ is significant at the 0.10 level. Dependent variable Share of risky assets in total assets

Share of liquid risky assets in liquid total assets

(1)

(2)

(3)

(4)

(5)

(6)

(7)

Constant

79.67⁎⁎⁎ (10.79) 1.45⁎⁎

120.49⁎⁎⁎ (6.23) 1.67⁎⁎⁎

67.03⁎⁎⁎ (14.35) 1.42⁎⁎

−43.74⁎⁎⁎ (− 3.69) 1.56⁎

−9.23 (− 0.31) 1.71⁎⁎

−36.35⁎⁎⁎ (− 5.04) 1.57⁎

(2.48) 9.21⁎⁎⁎ (7.26) 1.35 (0.39) −10.39⁎⁎ (− 2.41) −0.13 (− 0.61)

(2.81) 9.82⁎⁎⁎ (7.56) 1.73 (0.50) −12.29⁎⁎⁎ (− 2.82) 0.25 (0.60) −0.0105 (− 0.90) −2.29⁎⁎⁎

(2.42) 8.94⁎⁎⁎ (7.10) 1.45 (0.42) −9.97⁎⁎

(1.90) 4.74⁎⁎⁎ (2.78) −0.44 (− 0.08) 2.92 (0.48) 0.77⁎⁎

(2.07) 4.75⁎⁎⁎ (2.77) −0.41 (− 0.07) 2.08 (0.34) 0.11 (0.18) 0.022 (1.41) −1.16 (− 0.94) 0.012 (1.04) −9.42⁎⁎⁎ (− 3.24) 15.24⁎⁎⁎ (4.32) −1069.14 61.32⁎⁎⁎

(1.94) 4.40⁎⁎⁎ (2.63) −0.56 (− 0.10) 3.16 (0.52)

Income*10-4 Net worth*10-5 Female University education Horizon Horizon squared

−0.46⁎⁎⁎ (− 3.53)

Age Age squared Time preference Risk tolerance Log likelihood Log likelihood ratio

−1.95 (− 1.08) 1.80 (0.79) −2294.70 71.70⁎⁎⁎

(− 2.31)

(2.40) −0.0042 (− 0.72)

(− 2.89) 0.0177⁎⁎ (2.36) −2.23 (− 1.22) 1.66 (0.72) −2291.81 77.48⁎⁎⁎

−0.0038⁎⁎⁎ (− 3.23) −1.69 (− 0.93) 2.14 (0.93) −2295.94 69.22⁎⁎⁎

Males and higher net-worth individuals invest more in risky financial assets than do females and lower net-worth respondents. Median investment in liquid risky assets is higher for the respondents with longer planning horizon and those whose age is under 50. This finding supports Hypotheses 1B and 2B. These findings are also partially in line with Ackert, Church, and Englis (2002), who show that the proportion of equity holdings in a financial portfolio is higher for males and increases with net worth. However, in their sample, age is not a significant factor for portfolio asset allocation. The only difference between these results and those in the previous panel is that respondents with a university degree invest a higher proportion of their financial assets in risky assets. Although interesting in themselves, the univariate results do not show the complete picture. Obviously, all these variables affect the final asset allocation decision jointly. In addition, it should be taken into account that the risky asset allocation variable that we observe is censored at zero. Therefore, the full model must correct for both factors. 4.2. Model description and empirical results The large proportion of zero risky holdings in the sample suggests censored regression as the best underlying model for such data. I adopt a censored logistic regression, as it best fits empirical properties of the data. I denote the observable share of risky assets in an individual portfolio i as yi. Then y⁎i is the corresponding latent variable, not censored at 0, and y⁎i is related to yi in the following way: yi =

(  0 if yi ≤0 

ð2Þ



yi if yi N 0

I estimate the model (for the latent variable y⁎i ) in the following form: Share of Risky Assetsi = α0 + a1 Incomei + α2 NetWorthi + α3 Horizoni + α4 Agei + + α5 Educationi + α6 Genderi + α7 Time Preferencei + α8 Risk Tolerancei + εi ; Eðεi Þ = 0:

ð3Þ

0.15 (0.78)

−8.76⁎⁎⁎ (− 3.02) 15.86⁎⁎⁎ (4.45) −1070.80 58.02⁎⁎⁎

0.02448⁎⁎⁎ (3.19)

0.00125 (0.71) −9.19⁎⁎⁎ (− 3.18) 15.41⁎⁎⁎ (4.38) −1069.59 60.44⁎⁎⁎

As is common with censored models, the explanatory variables will affect both the probability of risky assets being positive and the share of risky assets:     EðyjxÞ = Probðy N 0jxÞ × E y jx; y N 0

ð4Þ

The marginal effects in this model can be interpreted in a way similar to the Tobit model (see Greene (1999) for the general result). Agarwal, Driscoll, Gabaix, and Laibson (2009) find evidence of non-linear relation between age and performance in various financial markets. It is reasonable to assume that the relation between age, horizon and investments in risky assets is also not always linear. I include quadratic terms to take this possible non-linearity into account. However, in many cases I do not find non-linear patterns for either age or horizon variables. Therefore, I also present results of the regression specifications that exclude non-linear terms. Table 5 presents the main results of the paper. In Table 5, the censored regression is estimated for six different specifications of the model (columns 2 to 7). In the first three regressions in Table 5, the dependent variable is the share of risky assets in total assets. This variable comprises all risky assets held by individuals, including real estate assets such as owner-occupied housing. Column 2 includes age and horizon variables in the linear form only, column 3 has quadratic terms added, and column 4 contains only quadratic terms for these variables.6 With regard to the control variables, all of them have the same effect on the investors’ share of risky assets, regardless of the chosen regression specification. I find a strong positive relation between investors’ income and share of risky assets. The same holds for net 6 Since age and planning horizon are often closely correlated (for many respondents close to retirement, the planning horizon is equal to the retirement age minus their current age), including these variables in the same regression might introduce multicollinearity and disturb the results. For this reason, I have also estimated these regressions with only age and only horizon variables included. The results in these regressions are very similar to the ones presented in Table 5. The results are also robust to various specifications of the model, with or without the risk tolerance and time preferences variables.

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worth. In line with the results presented in Table 4, gender plays no role in asset allocation, and individuals with a university degree tend to invest relatively less in risky assets. The two variables that I hypothesize as having an important impact on the asset allocation are investment horizon and age of the investors. However, I find that coefficients for the horizon are not statistically significant in any of the regressions. This lack of significance suggests that the decision on how much to invest in risky assets, including real estate assets, does not depend on the planning horizon of the individual, but rather on her financial situation. A likely explanation for this finding is that higher wealth leads to more expensive owner-occupied housing, which constitutes a large portion of the total risky investments of most households. The regressions in columns 2 to 4 of Table 5 indicate that this decision is not affected by the planning horizon. However, the age variable does have a significant negative impact on the risky asset allocation. As an individual's age increases, the proportion of her risky assets decreases. This finding is consistent with Hypothesis 1A. However, since I have shown that the time horizon plays no role in asset allocation, here, age is unlikely to merely be a proxy for the investor's horizon. One possible explanation for this result is that real estate investments, which are a major component of the risky part of the portfolio, increase in value less rapidly over an investor's life cycle than do the accumulated savings from labor income. None of the variables that measure investors' risk attitudes and time preferences is statistically significant in these regressions. From Table 5 it appears that the overall asset allocation decisions are based primarily on the wealth and age of the investors, with the risky share increasing in income and net worth, and decreasing in investor's age. Neither risk tolerance nor time preference factors affect the total share of risky assets. Overall, I conclude that the total risky asset allocation is primarily dictated by the investor's wealth and his/her stage in the life cycle, rather than by their investment horizon or risk tolerance and rate of time preference. Although previous studies do not consider real estate as part of the risky portfolio, it is a well-established fact that investors' risk aversion leads to a significantly lower share of equity in the portfolio. For example, Shum and Faig (2006) find that self-reported risk attitude has negative impact on portfolio equity shares in all four of the U.S. Surveys of Consumer Finances that they study. In order to make the results more comparable, I further calculate the dependent variable as ratio of risky financial assets to total financial assets in the households' portfolio. This variable is comparable to earlier studies and can help explain whether the different results obtained in previous regressions are caused by the including real estate in the definition of risky assets or by using a different sample. Columns 5 to 7 of Table 5 present the results of the same models estimated with the ratio of liquid risky assets to total liquid assets as the dependent variable. Most of the explanatory variables that I discuss earlier in this paper have the same impact on the share of risky financial assets. Consistent with the results in Table 4, Panel B, income has a less profound impact on the risky asset investments, although it is still positive and significant (at 5% to 10% level). Neither gender nor education seems to play any role at all. Higher net worth leads to the higher share of liquid risky assets, in line with the expected effects of decreasing risk aversion. Age is not significant in any of the regressions, indicating that once the real estate investments are excluded, individuals do not consider age a factor in selecting their financial portfolio. The coefficient for horizon is now positive and statistically significant. A longer investment horizon leads to higher risky assets holdings (significant at 1% to 5% level). Interestingly, the quadratic term appears to have even more impact on the share of risky financial investments than the linear one, suggesting that relatively short

horizons lead to very low levels of risky investments and that the increase in investment horizon is particularly important for investors with already long horizons. This suggests that with an increase in investors' horizon, their investments in risky financial assets grow at a much faster rate. Overall, the results in this table support Hypothesis 2B, but not Hypothesis 1B. Based on these results, it should be emphasized that age does not seem to be a good proxy for investment horizon in the individual financial decisions. Finally, the investors' preference variables now appear to play a much more important role in asset allocation decisions. The risk tolerance factor has the expected positive sign and is highly statistically significant. This result is consistent with previous studies, suggesting that the inclusion of real estate investments and not a different sample is the factor that caused the risk tolerance variable to lack significance in the regressions for the total risky assets. Investors who are less averse to risk tend to invest higher proportion of their liquid assets in risky securities. The time preference factor also affects the share of risky financial assets in these regressions. The estimation results show that those investors who display a high preference for having things today, rather than in the future, tend to invest significantly lower share of their wealth in risky assets. This evidence might reflect the common perception of shares as long-term investments, but I note that this preference does not substitute for the investment horizon. Investors still display a strong positive relation between their investment horizons and the share of risky assets. To conclude, both risk tolerance and the time preference factor appear to strongly influence the choice of financial asset allocation. Investors who are more risk tolerant invest significantly more in risky financial assets, such as shares and options. The proportion of risky assets is also higher for the investors who display a lower degree of preference for immediate payoff. Thus, if we consider the financial assets, which represent the investments that are far less driven by the investors’ life cycle and in which investors can exercise a lot of flexibility, both the investment horizon and individual preferences appear to be important for asset allocation. 5. Conclusions The goal of this study is to investigate how age, investment horizon, income, and the investor's background influence his or her decision to invest in risky assets. There are two main points that I make in this study. First, I distinguish between investors' age and their actual self-reported planning horizon. Second, I include real estate assets, such as owner-occupied housing, in the universe of risky investments. My main result is that age plays a different role from that of the investment horizon in determining investors' risky portfolio. Age is an important factor when I take into account total risky investments, including real estate. In line with my expectations, the share of risky assets tends to decline with age. However, the investment planning horizon is the factor that drives investments in financial risky assets, such as stocks, options and mutual funds. A longer investment horizon leads to an increasing share of risky financial investments, independently from investors' age. The differential results for the portfolios that include real estate and the financial-assets-only portfolios are consistent with the behavioral portfolio theory of Shefrin and Statman (2000). The behavioral portfolio theory suggests that investors “layer” their portfolios, with the bottom layers designed to protect from poverty and the top layers constructed to maximize the chances of achieving greater wealth. The investors in my sample can be seen as using their owner-occupied housing in order to provide the long-term protection, consistent with the predictions of the life-cycle models. At the same time, the stocks in the financial portfolios are acquired to reach the shorter-term goals and to provide the investors an opportunity for

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getting rich, which is not generally available for the well-diversified investors (Statman, 2004). I also find that the portfolio share invested in stocks and other risky financial instruments decreases with the risk aversion of the respondents and with their rate of time preference. However, after controlling for the individual preferences, age and horizon remain two important determinants of investment decisions. The results of this study show that personal financial planning should differentiate between the actual planning horizon and its crude proxy (age) when making decisions concerning financial investments.

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