Behavioral biases and portfolio choice M. Massa and A. Simonov Insead and Stockholm School of Economics.∗ May 2004.
Abstract We investigate the way investors react to prior gains/losses. We use a new and unique dataset with detailed information on investors’ various components of wealth, income, demographic characteristics and portfolio holdings identified at the stock level. We test the theory of loss aversion against the alternative provided by standard utility theory and the house-money effect. We show that, on a yearly horizon, investors do not behave according to loss aversion and more in line with standard utility theory or the housemoney effect. We also show that investors do not suffer from the mental accounting bias. Investors consider wealth in its entirety and risk taking in the financial market is affected by gains/losses in overall wealth, financial wealth and real estate wealth. Keywords: Behavioral finance, portfolio investment, loss aversion. JEL classification: G11, G14 .
∗
Corresponding author: M. Massa, Finance Department, INSEAD, Boulevard de Constance, 77305 Fontainebleau Cedex, France. Tel: (33)1 60 72 44 81 Fax: (33)1 60 72 40 45. Email:
[email protected]. We thank for helpful comments O.Bondarenko, F.DeJong, B.Dumas, H.Hau, P.Hillion, R.Jaganathan, M.Lettau, P.Maenhout, M. Huang, S. Mullanaithen, T. Odean, J.Peress, R. Shiller, P.Sodini, M.Suominen, A. Subrahmanyan, B. Swaminathan, R. Thaler, L.Tepla, P.Veronesi, M.Weber and the participants of the Summer Financial Markets Symposium at Gerzensee and the NBER Behavioral Finance meeting Fall 2002. We are grateful to Sven-Ivan Sundqvist for numerous helpful discussions and for providing us with the data. Andrei Simonov acknowledges financial support from the Stockholm Institute for Financial Research and Jan Wallander och Tom Hedelius Stiftelse. We thank for precious financial support Inquire Europe. All the remaining errors are ours.
1
Behavioral Biases and Portfolio Choice
Abstract We investigate the way investors react to prior gains/losses. We use a new and unique dataset with detailed information on investors’ various components of wealth, income, demographic characteristics and portfolio holdings identiÞed at the stock level. We test the theory of loss aversion against the alternative provided by standard utility theory and the house-money effect. We show that, on a yearly horizon, investors do not behave according to loss aversion and more in line with standard utility theory or the house-money effect. We also show that investors do not suffer from the mental accounting bias. Investors consider wealth in its entirety and risk taking in the Þnancial market is affected by gains/losses in overall wealth, Þnancial wealth and real estate wealth.
JEL classiÞcation: G11, G14. Keywords: Behavioral Þnance, portfolio investment, loss aversion.
1
Introduction
Behavioral motivations have been advocated as a main driving force in portfolio choice. Maybe the most relevant manifestation of this bias is the way investors react to prior gains and losses. While it seems clear that investor behavior is affected by prior outcomes and by the changes in wealth as opposed to the mere level of it, the "direction" of this reaction is uncertain. The main theory in behavioral Þnance - "loss aversion" - posits that prior losses increase risk taking. This runs counter to alternative behavioral explanations - "house money effect" and standard utility theory (with decreasing risk aversion) - that assume that prior losses decrease risk taking. The very deÞnition of gain/loss is also not clear. The portfolio decision of the investor may be a function of prior gains/losses on his overall assets (Þnancial and non-Þnancial assets) or just on a subset of them (Þnancial assets or speciÞc portfolios). In the latter case, investors would suffer from narrow framing. Efforts to empirically address these issues have been hindered by the limitation of the data that has made it impossible to test the different behavioral theories one against the other. We bridge this gap by using a new and unique dataset. Given the richness of the data - that contains basically any information on the holdings, wealth, broken down into all of its components, income and demographic characteristics of the a highly representative sample of the Swedish population - we are able to properly control for most components of the investor’s decision. In particular, we test loss aversion against the alternative hypotheses - house-money effect and standard utility theory with decreasing risk aversion - by directly inspecting investor reactions to different deÞnitions of gains and losses (i.e., overall wealth, paper Þnancial gains and losses and realized Þnancial capital gains and losses). We also investigate the issue of narrow framing and mental accounting by considering how gains and losses in a category of wealth (e.g., real estate) affect changes in holdings in other categories (e.g., Þnancial assets). Our evidence fails to support either loss-aversion or narrow framing, pointing in the direction of the house-money effect or standard utility theory. That is, investors change their holdings of risky assets as a function of both Þnancial and real estate gains. Prior gains increase risk taking, while prior losses reduce it. An important contribution of our study is that we are able to properly control for most of the other determinants affecting the investor’s decision that may have confounding effects on 1
the tests. In particular, the use of a full panoply of control variables (measures of income and wealth, contemporaneous gain/loss variables, borrowing constraints, demographic variables, momentum variables, and geographic and macroeconomic variables) allows us to move closer to a designed experiment, and to exploit the advantages of Þeld data, while addressing the main criticisms to its use when compared to experimental studies. The remainder of the paper is articulated as follows. In Section 2, we describe the problem we study and in Section 3, we lay-out the empirical restrictions we will test. In Sections 4 and 5, we describe the datasets and the variables used. In Section 6, we empirically test the restrictions and report the main Þndings. A brief conclusion will follow.
2
The problem
We focus on one salient moment of investor behavior - risk-taking - and study the relationship between risk taking and prior gains and losses. Behavioral theory argues that prior gains induce a different behavior from prior losses. The standard behavioral work-horse is the "Loss aversion theory". This theory hypothesizes that prior losses increase risk-taking, while prior gains reduce it. This induces investors to gamble and "to seek risk when faced with possible losses, and to avoid risk when a certain gain is possible" (Tversky and Kahneman, 1979, Benartzi and Thaler, 1995). Loss aversion is based on the psychological grounding that a decline in utility arising out of the realization of losses relative to gains induces investors not to sell losing stocks rather than winning ones. Empirical evidence of this, in the form of the "disposition effect", has been found by Odean (1998) and Barber and Odean (2000). They have shown that investors tend to "hold on to the losers and sell the winners". The alternatives to this theory are either the "house-money theory" or standard utility theory with decreasing risk aversion. The house-money theory posits that prior gains, by providing investors with a "cushion" that makes future losses less painful, in fact increase risk-taking. In particular, Thaler and Johnson (1990) show that "while a prior gain can increase subjects willingness to accept gambles, ...prior losses sensitize people to subsequent losses of similar magnitude." Barberis, Huang and Santos (2001) use this behavioral Þnding in order to explain the size of the equity premium and patterns in stock volatility. They argue that "previous capital gains reduce investors’ sensitivity to risk...while previous losses, by making any new loss more painful, increase risk aversion". Standard utility theory, in the case of utility characterized by decreasing risk aversion, 2
posits that previous losses, by reducing wealth, increase risk aversion, while previous gains, by increasing wealth, reduce risk aversion.1 Therefore, both the house-money effect theory and standard utility theory in the presence of decreasing risk aversion represent our alternative to loss-aversion. All these theories are vague about the deÞnition of ”gains” and ”losses” - i.e., whether they apply to the overall investor wealth or to a limited subset of it (i.e., Þnancial wealth, real estate, single stocks). This theory can be deÞned as ”mental accounting” or ”narrow framing”. For example, Barberis and Huang (2000) have suggested that investors apply mental accounting to stock holdings and react separately to gains and losses for different stocks. While experimental literature has provided ample evidence of the conditions under which loss aversion and the house-money effect take place (Shefrin and Statman, 1985, Tversky and Kanheman, 1981, Weber and Camerer, 1998), these alternative theories have never been simultaneously tested using Þeld data. Indeed, given that the implications of these theories are often very highly correlated, separate partial tests may fail to provide proper identiÞcation that avoids spurious correlation. In fact, these theories deliver a set of easily testable crossrestrictions. Loss aversion postulates a positive correlation between risk-taking and prior losses. The house-money effect (or standard utility theory), on the other hand, postulates a negative correlation between risk-taking and prior losses. Joint tests can exploit these cross-restrictions to effectively distinguish the theories. The main obstacle to the implementation of these tests has, up to now, been the lack of good-quality data on the overall wealth of the investors for a representative sample of investors in the market. Detailed information on the overall wealth of the investor is required not only to deÞne the variables needed to carry out the tests (i.e., gains and losses, risktaking), but also to construct proper control variables for all the other factors affecting investor behavior. Indeed, the main criticism that empirical studies based on Þeld data face is the "ceteris paribus" condition or spurious correlation. The use of information limited to a subset of the entire stock-portfolio with no control for the other sources of wealth or income of the investor (i.e., labor income, entrepreneurial income) may be problematic. For example, if a change in wealth of the investor is due to 1 Empirically, there is not much evidence in favor of decreasing relative risk aversion. The evidence points toward increasing or constant risk aversion. For example, Guiso et al. (2002) Þnd increasing risk aversion using survey data on hypothetical gambles. So do studies using farm data.
3
income shocks or real estate capital gains, a test of investor behavior based only on changes in portfolio holdings and stock market gains/losses would not be able to distinguish loss aversion from standard wealth effects. Moreover, the lack of data on real estate wealth may be very worrisome. Changes in wealth due to real estate capital gains/losses may swing investor behavior, regardless of the Þnancial capital gains/losses. Genesove and Mayer (2001) shed some light on this topic by analyzing loss aversion and seller behavior in the housing market.2 This would affect any behavioral study focused only on Þnancial holdings. Data constraints have induced the literature to focus only on a subset of investor’s wealth and to limit itself to a particular subset of investors. For example, Barber and Odean (2000, 2001, 2002) and Odean (1998, 1999) study the stock-trading behavior of a subset of investors who have an account with a big discount broker. Only Grinblatt and Kelloarji (2000, 2001a, 2001b) use a dataset that contains, for the Þrst time, the entire stock portfolio of the investors. However, they focus on issues such as geographical preferences and momentum trading, without considering the overall dimension of the portfolio problem (wealth, real estate, non-Þnancial income). Recently, Brown et al. (2002), using Australian data, show that loss-aversion is a short-term phenomenon, predictor of short-term behavior, while the housemoney effect mostly applies to long run behavior. However, similarly, the analysis is based just on stock holdings and does not account for the wealth of the investor in its entirety. The availability of a unique dataset with detailed information on investor wealth, income and asset holdings allows us to bring the alternative theories to the data. We are able to run a direct horse race, after controlling for investor’s other income and wealth shocks. Our study therefore complements the ones done at higher frequency (Barber and Odean, 2000, 2001, 2002 and Odean 1998, 1999).
3
Our approach
We assess the relative merit of the different theories by focusing on risk taking and investor characteristics. The standard formulation assumes that risk-taking is a function of prior gains/losses. Let us consider a simpliÞed reduced form that relates risk-taking to prior gains and losses: RTit = β 1 Git−1 + γ 1 Lit−1 + δ 1 Cit ,
(1)
2 However, while they are the Þrst ones to use real estate data to test behavioral theories, they do not consider the other aspects of the investor’s wealth problem.
4
where, for each ith investor, RT it is the amount of risk-taking, deÞned as the change of the investment in risky assets of the investor in the period [t, t-1], Git−1 and Lit−1 are, respectively, prior gains and losses and Cit is a vector of control variables.3 It contains all the alternative factors that alternative theories have found to affect the portfolio choice of the ith investor (e.g., labor income risk, level of wealth, demographic characteristics,...). It is worth noting that loss aversion, house-money effect or standard utility do not prevent the existence of a "view" in the portfolio choice.4 Therefore, we include control variables that account for the standard portfolio choice in the presence of risky non-Þnancial income (i.e., correlation of Þnancial and non-Þnancial income, volatility and conditional value of non-Þnancial income). Moreover, we also include variables that proxy for the degree of informativeness and sophistication of the investors. These variables allow us to control for the investor’s view and to focus directly on the impact of the biases. Equation 1 nests the alternative theories. H1: Loss aversion would require that: β 1 < 0, γ 1 > 0.
(2)
The house-money effect or standard utility theory would require that: β 1 > 0, γ 1 < 0.
(3)
That is, we expect that investors react to prior losses (gains) by taking more (less) risk in the case of loss aversion and by taking less (more) risk in the case of the house-money effect. Equations 2 and 3 provide the set of restrictions we will be testing. If we consider a more limited deÞnitions of wealth, we can rewrite equation 1 as: re re re RTitf = β f1 Gfit−1 + γ f1 Lfit−1 + β re 1 Git−1 + γ 1 Lit−1 + δ 1 Cit ,
(4)
where, for each ith investor, the superscripts f and re represent respectively capital gains/losses in Þnancial assets and real estate. H2: Mental accounting would require that: re β f1 6= 0, γ f1 6= 0, β re 1 6= 0, γ 1 6= 0.
(5)
That is, investors categorize different sources of wealth in different accounts and gains/losses in a particular account only affect the risk taking in the speciÞc account. 3 4
We separately consider gains and losses so as to investigate the relative importance of each of them. We thank M. Huang for suggesting this point.
5
4
Data description and variable construction
We use data from different sources. The data contain information on both sides of the market: the investors as well as the companies. For each investor, we have detailed information of his individual holdings of stocks (broken down at the stock level), mutual funds, bank accounts, real estate and other types of wealth. We also have available information on the income proÞle of the investor provided by the Þscal authorities, as well as his demographic and family characteristics. This information has been matched at the individual level, so that, for each investor, we have available all the investment and income information. For each stock, we have detailed information on the company as well as stock market data (price, volume and volatility). We also use aggregated data on Swedish macroeconomic conditions and on the indexes of the real estate market. Let us see the sources in more detail.
4.1
Individual stockholding
We use the data on individual shareholders collected by Värdepappererscentralen (VPC), the Security Register Center. The data contain both stockholding held directly and on the street name, including holdings of US-listed ADRs. In addition, SIS Ägarservice AB collects information on ultimate owners of shares held via trusts, foreign holding companies and the like (for details see Sundin and Sundquist, 2002). Our data cover the period 1995-1999. Overall, the records provide information about the owners of 98% of the market capitalization of publicly traded Swedish companies. For the median company, we have information about 97.9% of the equity, and in the worst case we have information on 81.6% of market capitalization of the company. The data provided by SIS Ägarservice AB were linked by Statistics Sweden with the LINDA dataset described below.
4.2
LINDA
LINDA (Longitudinal INdividual DAtaset for Sweden) is a register-based longitudinal data set and is a joint endeavor between the Department of Economics at Uppsala University, The National Social Insurance Board (RFV), Statistics Sweden, and the Ministries of Finance and Labor. It consists of a large panel of individuals, and their household members, which is representative for the population during 1960 to 1999. For each year, information on all
6
family members of the sampled individuals are added to the data set. Apart from being a panel which is representative of the population in general, the sampling procedure ensures that the data are representative for each year. Moreover, the same family is traced over time. This provides a real time series dimension in general missing in surveys based on different cohorts polled over time. The variables available include individual background variables (sex, age, marital status, country of birth, citizenship, year of immigration, place of residence detailed at the parish level, education, profession, employment status), housing information (type and size of housing, owner, rental and occupation status, one-family or several-family dwelling, year of construction, housing taxation value) and tax and wealth information. In particular, the income and wealth tax registers include information on labor income, capital gains and losses, business income and losses, pension contributions, taxes paid and taxable wealth. A detailed description of the dataset is provided by Edin and Fredriksson, (2000) and is available on the web site http://linda.nek.uu.se/. The tax part deserves more detailed discussion. In Sweden, in addition to usual income taxation, there also exists a wealth tax which is paid by every investor with a net worth in excess of 900,000 SEK (about US$90,000). The taxable wealth includes tax-accessed value of real estate, market value of publicly listed securities, balance of bank accounts and fair value of valuable possessions (including jewelry, cars, antiques, etc.). For the purpose of this paper, we compute the current market value of housing using the tax-accessed value provided by LINDA. We evaluate it at current prices by using the average ratio of market value to tax-accessed value that is provided for each year and county by the Swedish Office of Statistics.5 There is no estimate of market value of privately held companies. However, the data contains an indicator variable for owners of privately held companies and entrepreneurs who Þle their business tax return along with their personal tax return. For the privately held unlimited liability companies the value of the assets is included in the tax return. For the privately held limited liability companies that are not listed the value of assets held is in general missing. However, the size of the group is rather small (1.74%-1.91% of the sample depending on a year) and is unlikely to affect our estimates in a signiÞcant way. Moreover, for the members of the wealthiest 5,000 families, we have been able to reconstruct their 5 It may lack precision for summer houses if they are located in a county different from the one in which the household is residing, as no information about the location of summer houses is provided.
7
values and to correctly impute it by using information from SIS Ägarservice AB (Sundin and Sundquist, 2002). The combined LINDA/Shareholding dataset covers the period 1995-1999. In addition, we also use data from LINDA for the period 1991-1994. The overall sample we use contains 1,487,602 observations. In Table 1 we report some descriptive statistics. In particular, Panel A contains the general demographic characteristics (number of households, members in household, adults in household, age of the oldest member of household, percentage of the sample with secondary and higher education). Panels B and C report, respectively, the age and gender distribution of the sample and their wealth and income characteristics, deÞned in terms of wealth, real estate, labor and entrepreneurial income.
4.3
Firm-level information and other data
In order to derive information on individual security returns (including dividends) and to track the overall market index (SIX Index), we use the SIX Trust Database. For information on the various Þrm-level characteristics, we use the Market Manager Partners Databases. These two databases are the equivalent of, respectively, CRSP and COMPUSTAT for the US. In addition, Market Manager Partners Databases contain information at the plant level, including location of the plant (detailed at the level of municipality). We use the set of Swedish residential real estate indices provided by Englund. The indices were computed at the county level and are based on resale value of the properties.6 The consumer conÞdence index is provided by Statistics Sweden. Geographical coordinates are supplied by Swedish Postal Service and contain latitude and longitude of Swedish Postal Offices (on 3-digit level).
4.4
Control Variables
Given the importance of properly controlling for spurious correlation, we consider a panoply of control variables. The availability of these control variables makes the results unique as it allows us to control for the aforementioned issues of spurious correlation. We consider the following sets of control variables: measures of income and wealth, contemporaneous gain/loss variables, borrowing constraints, demographic variables, momentum variables, and geographic and macroeconomic variables. 6
The methodology of construction of the indices is described in Englund, Quigley and Redfearn (1998).
8
The measures of income include the variance of labor and entrepreneurial income of the investor and the correlation between them and Þnancial and real estate income. In order to make the results comparable with the standard literature on portfolio choice in the presence of non-Þnancial income risk, we construct measures of the permanent non-Þnancial income following the approach of Carrol and Samwick (1997) and Vissing-Jørgensen (2002). We consider as non-Þnancial income: labor income and entrepreneurial income. In the Appendix, we provide a detailed description of the procedure. As an additional robustness check, we replicate our results by using the actual levels of non-Þnancial income, their volatilities and the correlation of Þnancial and non-Þnancial income, deÞned as in Heaton and Lucas (2002a). This replaces the measures of permanent income, volatility of income and their correlation with portfolio returns that had been constructed according to the Carrol and Samwick (1997) methodology we described earlier. Given that the results are consistent, we will report only those based on the Carrol and Samwick methodology.7 The contemporaneous gain/loss variables are the contemporaneous capital gains/losses and the contemporaneous changes in overall wealth. We also include the mean and variance of the investor’s portfolio return in the year and Þnancial and real estate capital gains and losses. These are the ones reported for tax purposes on stocks, bonds, mutual funds and real estate. The measures of wealth include the overall level of wealth of the investor and its breakdown into its components. Overall wealth is deÞned as the sum of Þnancial and real estate wealth. We consider two types of borrowing constraints. The Þrst one is the ratio of investor debt to total income and the second one is the ratio of investor debt to total wealth. Both of them are constructed at the investor level at time t. Also, we include a variable that accounts for the number of positions (type of assets) held by the investors. The momentum variables include the return and the volatility of the portfolio of the investor in the previous 12 months and the return and the volatility of the market in the previous 12 months. These variables are meant to control for the possibility that the change in wealth is merely due to momentum, that is, consecutive increases in value in the stock market or in the value of the holdings. The demographic variables include: the profession of the investor, his level of education, 7
The results are available upon request from the authors.
9
broken down into high-school and university level. We also include the age of the oldest member of the family of the investor and its value squared. This latter variable is consistent with standard results (Guiso and Jappelli, 2002, Vissing-Jørgensen, 2002) which Þnd a nonlinear relationship between age and the degree of stock market participation. We also include a dummy that takes the value of 1 if the investor lives in the capital and 0 otherwise and the investor’s immigration status. The latter takes the value 0 if all the members of the household are native Swedes, and 1 if at least one member of the household immigrated.8 Furthermore, we construct a variable to proxy for the ability of the investor in his occupation. This is based on the difference between his income and the average income of his profession. The assumption is that the higher the income of the investor relative to the average income of the other investors in the same area, the higher his ability should be. Finally, the geographic and macroeconomic variables include an Index of Consumer ConÞdence and a set of dummies that account for the regional location of the investor as well as the industry in which he works. We consider 8 geographical areas and 10 industries.9
5
Econometric issues
Before addressing the econometric issues, let us describe the samples we use. We investigate how the reaction to prior gains/losses varies for different levels of wealth and degrees of liquidity of the portfolio of the investor. Both wealth and liquidity are a good proxy for the degree of informativeness of the investor. We therefore consider four different samples: the overall sample and two sub-samples constructed on the basis of either the wealth or the liquidity of the investor’s overall portfolio. In particular, we deÞne as high-wealth investors all the investors who, in the previous year, paid the wealth tax. We deÞne as low-wealth investors all the others. The high-wealth investors represent approximately 8% of the overall sample. Then, we split the high-wealth investors into two categories: illiquid and liquid. In order to do this, we rank all the high-wealth investors in terms of the ratio of illiquid assets (i.e., real estate) over total wealth. Illiquid investors are those who, in the previous year, belonged to the top quintile, while liquid investors are those who, in the previous year, 8
We also tried two alternative speciÞcations. In the Þrst one, we used the sum of the immigration statuses of the members of the household. That is, if two members of the household are immigrants, the variable takes value 2. In a second speciÞcation, we used the inverse of the number of years since the oldest immigrant in the household arrived in Sweden. These two alternative speciÞcations deliver results that are qualitatively analogous to those reported. These results are available upon request from the authors. 9 Geographical area deÞnitions are based on the NUTS2 classiÞcation for Sweden. An additional dummy for public sector workers is added to the industrial classiÞcation of households.
10
belonged to the bottom quintile. The biggest econometric issue is generated by the selection bias due to the fact that only a minority of the households enters the stock market. The fact that we do not observe the investment decision of investors who do not participate in the Þnancial market and the fact that such a participation is endogenous makes the standard estimates biased. To address this issue, we follow the standard theoretical (Calvet et al., 2002) and empirical literature (Vissing-Jørgensen, 2002). We use the Heckman (1979) two-stage procedure and separately estimate what induces the investor to enter the stock market and what inßuences his choices of assets. The decision to enter the market for the ith investor can be represented as: Pit = α0 + β0 Xit + ε1,it ,
(6)
where Pit is a dummy that takes the value of 1 if the investor participates in the Þnancial market and zero otherwise, and Xit is a vector of variables that affect the probability of entry. We include among them all the control variables deÞned before. The probability that the investor enters the Þnancial market is modeled as a normal c.d.f. In order to estimate this model, we need to consider a bigger dataset based on the whole sample universe: i.e., both the households who hold Þnancial assets and the households who do not. The expanded dataset includes the totality of the households tracked over time over each of the sample years 1995 through 1999, regardless of whether they invested in the stock market. It totals 1,487,602 households tracked over time. From the equation 6 we can construct a variables (λit , or "Heckman’s lambda") that we use to control for the problem of omission of variables due to self-selection. Given that equation 6 is just an auxiliary regression only needed for the proper estimation of the second stage, but out of the scope of this paper, we will not discuss the results.10 Restriction H1 The empirical analogue of the risk-taking decision, that corresponds to equation 1 and restrictions 2 and 3, for the ith investor’s and conditional on market participation, is: RTit = α1 + β 1 Gt−1 + γ 1 Lt−1 + θ1 λit + µ1 RTit−1 + δ 1 Cijt + ε1,it ,
(7)
where λit is the vector that controls for selection bias and Cijt is the vector of control variables. The variable that proxies for risk-taking (RT i ) is the percentage change of the investment 10
They are available upon request from the authors.
11
in risky assets of the investor in the period ([t, t − 1]) by the ith investor. The vector of control variables is similar to the ones used in the Þrst stage (i.e., equation 6). However, some variables that are in the Þrst stage are not included in the second stage. This is done in order to have the identiÞcation restriction of the Heckman speciÞcation.11 The lagged dependent variable is added for robustness and in line with the existing empirical literature on portfolio choice (Vissing-Jørgensen, 2002). Gt−1 and Lt−1 are, respectively, the prior gains and losses, normalized on the level of the investor’s wealth. We now describe how we deÞne gains and losses. We proceed in three steps: the speciÞcation of the horizon over which they have taken place, the correct identiÞcation of the measure of gains/losses and the construction of proxies for them. In terms of the speciÞcation of the horizon, we try to be consistent with the standard literature. Therefore, we follow Benartzi and Thaler (1995), Barberis, Huang and Santos (2001) and Barberis and Huang (2001) and consider the unit of measure equal to one year. The rationale of this choice is that "we Þle taxes once a year and receive our most comprehensive mutual fund reports every year; moreover, institutional investors scrutinize their money managers’ performance most carefully on an annual basis" (Benartzi and Thaler, 1995). Moreover, this horizon allows us to operate at a frequency where we can properly account for all the other sources of income and changes in wealth of the investor. Our study, therefore, complements the seminal ones done at higher frequency by Barber and Odean (2000, 2001, 2002) and Odean (1998, 1999) which focus on transaction data and short-term behavior. The second step is the proper identiÞcation of the measure of gains and losses. This requires us to spell out the "reference point". That is, the reference price to which the new value (either of the asset in the portfolio in the case of paper gains/losses or of the asset sold in the case of realized gains/losses) is compared. This represents the historical benchmark level. The identiÞcation is not easy as, "for some investors, it may represent an average of recent stock prices. For others, it may be the speciÞc stock price at salient moments in the past, such as the end of the year" (Barberis, Huang and Santos, 2000). Barberis, Huang and Santos (2001) consider as reference point the status quo, scaled up by the risk-free rate. More operationally, Odean (1998) considers the "average purchase price". We think that the purchase price is indeed the best candidate to represent the status 11
These variables include the set of time and industry dummies as well as the correlations between the market portfolio and investors’ sources of non-Þnancial income (i.e., labor income, entrepreneurial income and real estate).
12
quo as each investor directly deÞne gains and losses in terms of the original purchase price. We therefore use as a reference point the price at which the asset has been purchased. Unlike Odean, we do not need to reconstruct it on the basis of previous trades, as it is provided to us directly in the data. This induces us to focus mostly on realized gains/losses. We also consider paper gains/losses. However, given that the deÞnition of paper gains/losses requires strong assumptions in terms of investment horizon and reinvestment strategy, we use an alternative approach where we consider both realized gains/losses and the overall change in wealth, inclusive of both Þnancial and real estate realized and paper gains/losses. This allows us to indirectly account for them without being forced to make assumptions. This approach also presents the additional advantage of allowing us to test whether investors just react to the overall gains/losses or to a subset of them. We also experimented with the direct inclusion of paper gains/losses, and the results
12
are qualitatively similar to those reported.
The third step is the construction of the proxies of gains/losses. We consider three measures: the change in overall wealth (ΠW t = W ealtht /W ealtht−1 − 1), the realized Þnancial capital gains and losses (ΠF t = (F inancial Capital Gains-F inancial Capital Lossest )/W ealtht−1 )) and the realized real estate capital gains and losses (ΠRt = (RealEstate Capital Gains-RealEstate Capital Lossest )/W ealtht−1 )). The changes are standardized by the level of wealth to make them homogenous across investors. The literature (Benartzi and Thaler, 1995 and Barberis, Huang and Santos, 2001) considers just the changes in the value of the investor’s Þnancial wealth. As a robustness check, and in order to study the differential impact of gains/losses related to different sources of wealth, we also consider real estate and overall wealth. It is worth pointing out that a change in wealth is a less precise measure of gains/losses, as it also contains the saving decisions of the investor. In order to account for this, we include among the explanatory variables the main moments (mean, variance and correlation with Þnancial and real estate income) of the other sources of income. Provided that the saving/income ratio of the investor does not change wildly over time, this should control for it. Descriptive statistics about the different proxies for gains and losses are reported in Table 2. Panel A, reports the mean and median values for the different classes, as well as their 12
Not reported, but available upon request from the authors.
13
standard deviation and inter-quartile range (I.Q.R.). We consider raw gains and risk-adjusted gains, i.e., net of risk. Risk is constructed as the standard deviation of the returns of the assets held, weighted according to their holdings. Table 2, Panels B and C, reports the tests of differences between classes of investors. We compare the high-wealth investors with the low-wealth ones and the liquid investors with the illiquid ones. Given the characteristics of the distribution of the investors, we consider three different tests: t-tests, Wilcoxon test and Kolmogorov-Smirnov test. In the case where the classes are deÞned in terms of wealth (Panel B), all the tests consistently show that high-wealth investors have higher gains than the lowwealth ones. Also, in the case where the classiÞcation is based on the degree of liquidity of the overall portfolio (Panel C), liquid investors seem to have higher gains than the illiquid ones.13 SpeciÞcation 7 allows us to directly identify the variables that affects investor’s choice. However, as we pointed out before, loss aversion or the house-money effect do not prevent the existence of a "view" in the portfolio choice. Therefore, speciÞcation 7 contains control variables that account for the standard portfolio choice in the presence of risky non-Þnancial income (i.e., correlation of Þnancial and non-Þnancial income, volatility and conditional value of non-Þnancial income) and for the degree of informativeness and sophistication of the investors. These variables allow us to control for the investor’s view and to focus directly on the impact of the biases. One possible objection to this approach is that gains/losses merely proxy for either serial correlation or momentum in the stock market or in the returns of the stocks held in the portfolio. Alternatively, they may proxy for investor’s trend-chasing behavior. In order to address this issue, we include among the control variables "momentum variables" (i.e., investors’ portfolio and market returns and volatility in the previous 12 and 24 months). Moreover, we also experimented with a speciÞcation based on "unexpected" gains/losses, that is, the unpredictable components in the regression of gains/losses on past gains/losses, market and momentum variables. The results (not reported) are consistent with the reported ones. We consider a dynamic speciÞcation in order to account for possible feedback effects14 13
If we use the tests based on the median (i.e., Wilcoxon and Kolmogorov-Smirnov), the more liquid investors always make more proÞts than the less liquid ones do. If we consider the t-test, however, it appears that there is no signiÞcant difference for the gains deÞned in terms of overall wealth, while the less liquid investors make more real estate capital gains. Given the skewness of the distribution of the investors, we consider the median-based tests to be more reliable. 14 At the aggregate level, market participation as well as portfolio choice are a function of asset returns.
14
from past values of the dependent variable. Given that the hedging variables, as well as the parameter λit , have been generated on the basis of a previous estimation, we need to properly account for the bias induced by the "generated regressors". This problem is exacerbated by the existence of the lagged dependent variable. The endogeneity issues further complicates the task of Þnding proper instrumental variables, as only strictly exogenous variables or predetermined ones can be used in the case in which the variables are predetermined. We therefore follow the standard literature (Arellano, 1990, Arellano and Bond, 1991 and Kiviet, 1995) and the previous applications to Þnance (Vissing-Jørgensen, 2002) and use an instrumental variable estimation, with instruments based on a combination of strictly exogenous variables (i.e., demographic variables) and the lagged values of the potential endogenous variables. SpeciÞcation 7 is estimated by using two-stage least squares with consistent variance-covariance matrix. We use data disaggregated at the individual investor level as well as disaggregated at the household level. The results do not differ from those based on households, so we will report only the latter. The signiÞcance of the estimate of θ 2 provides a test the null of no sample selection bias. In all the speciÞcations we Þnd a high degree of signiÞcance of λit , which suggests that self-selection is indeed important in the sample.
6
Empirical findings
We start by comparing the alternative behavioral theories in terms of reaction to prior gains/losses. We recall from equation 7, that the risk-taking decision, conditional on market participation, can be represented as: RTit = α1 + β 1 Gt−1 + γ 1 Lt−1 + θ1 λit + µ1 RTit−1 + δ 1 Cijt + ε1,it ,
(8)
The results are reported in Table 3. Panel A contains the result for the full-ßedged speciÞcation, while Panels B and C contain the robustness checks based on alternative speciÞcations (without contemporaneous proÞts, without demographic variables). We report the results of the speciÞcation with the Heckman correction. We will discuss the results of the fully-ßedged speciÞcation (Panel A) and leave the others as robustness checks. There are three main Þndings that are worth discussing. First, the results strongly reject the loss-aversion story, as investors react to prior positive (negative) changes in wealth by Asset returns are, themselves, a function of market demand. Given that we are effectively considering the demand of all the investors in the economy, we expect it to affect stock returns and therefore future demand.
15
increasing (reducing) risk-taking. This holds for different classes of investors and for changes in overall wealth, as well as for Þnancial and real estate capital gains. In particular, for the entire sample, a 1% increase in the overall wealth in the prior year increases risk-taking in the stock market by 0.26%, while a 1% reduction of wealth decreases risk-taking by a mere 0.05%. The same holds for the case of gains and losses. On average, a realized gain in the prior year equal to 1% of the investor’s (overall) wealth increases risk-taking in the stock market by 0.17%, while a realized loss in the prior year equal to 1% of the investor’s (overall) wealth reduces risk-taking in the stock market by 0.79%. Second, the investors who react more strongly are the high-wealth investors and the liquid ones, that is those we deÞne as "informed". This holds, regardless of the speciÞcation. In particular, high-wealth investors react more than low-wealth investors, both in the case of prior gains and losses (the coefficients are, respectively, 4.17 vs. 2.18 in the case of prior gains and -5.06 vs. -0.33 in the case of prior losses) and in the case of prior changes in wealth (the coefficients are, respectively, 0.33 vs. 0.19 in the case of prior positive changes in wealth and -0.15 vs. -0.12 in the case of prior negative changes in wealth). Analogously, liquid wealth investors react more than illiquid investors, both in the case of prior gains and losses (respectively, 2.82 vs. 0.97 in the case of prior gains and -2.99 vs. -2.51 in the case of prior losses) and in the case of prior changes in wealth (respectively, 0.34 vs. 0.27 in the case of prior positive changes in wealth and a statistically signiÞcant -0.53 vs. a non-signiÞcant 0.003 in the case of prior negative changes in wealth). The third observation is the asymmetry in the reaction to positive and negative changes. In particular, liquid investors react more strongly to prior losses than to prior gains, as well as to prior negative changes in wealth than to prior positive changes in wealth. Low-wealth investors, on the other hand, react more strongly to prior gains than to prior losses, as well as to prior positive changes in wealth than to prior negative changes in wealth. The fact that liquid investors react more strongly to losses than to gains can be explained by the fact that they have a higher fraction of their wealth invested in Þnancial assets. This makes losses very painful and the reaction stronger. The fact that for the low-wealth investors, the reaction is disproportionately stronger for gains than for losses, suggests instead that there may be borrowing constraints. In fact, in the case of low-wealth investors, our measures of borrowing constraints (i.e., debt-to-wealth ratio and debt-to-total income ratio) display a signiÞcant negative correlation with the investment
16
in risky assets. In the case of the high-wealth investors, however, borrowing constraints seem to affect only the illiquid investors, presumably the ones more exposed to mortgages given their higher investment in real estate. The liquid investors are not affected by borrowing constraints. Interestingly, the illiquid investors do not seem to be affected by either Þnancial gains or Þnancial losses. They have most of their wealth invested in real estate, and this may explain this lower reaction. In the case of the liquid investors, instead, the reaction to Þnancial gains and losses is stronger and approximately identical (i.e., the coefficients are 2.81 in the case of gains and 2.99 in the case of losses). If we now consider the test of mental accounting, we see that both Þnancial gain/losses and real estate gain/losses affect overall risk taking in the stock market. On average, a realized real estate gain in the prior year equal to 1% of the investor’s (overall) wealth increases risktaking in the stock market by 0.31%, while a realized real estate loss in the prior year equal to 1% of the investor’s (overall) wealth reduces risk-taking in the stock market by 0.18%. At a disaggregated level, this holds for both high-wealth and low-wealth investors.15 The reaction to gains is less strong than the one to losses, for all classes with the exception of the illiquid ones. In particular, the reaction to prior real estate gains ranges between 1.7% to 11.5%, while the reaction to prior real estate losses ranges between 0.49% to 0.90%. These feedback from real estate to Þnancial market are consistent with a wealth effect due to the real estate (Case, Quigley and Shiller, 2001). It is important to stress that these results hold after controlling for other wealth and income effects as well as momentum. That is, they are not due to momentum trading behavior or to spurious correlation with portfolio or stock market appreciation. It is worth noting that these results employ data at a lower frequency that the previous Þndings based on transaction data (Odean, 1998 and Barber and Odean, 1999). These results consistent with recent Þndings (Jackson, 2002) who show that, for Australian data, the disposition effect fades away after approximately 200 days. This suggests that maybe loss aversion is a better predictor of short term behavior, while house-money effect (or standard utility theory) mostly applies to long run behavior. 15 This feedback from real estate to Þnancial market is consistent with a real estate wealth effect (Shiller, Case and Quigley, 2001).
17
7
Conclusion
We focus on the determinants of portfolio choice, by directly comparing and testing the theory of loss aversion against the alternative provided by the house-money effect and standard utility theory. We provide evidence showing that investors do not react to prior gains/losses as postulated by loss-aversion by more in line with either the house-money effect or standard utility theory. That is, previous gains increase investor risk-taking, while previous losses reduce it. We do not Þnd evidence of mental accounting as investors consider wealth in its entirety and risk taking in the Þnancial market is affected by gains/losses in overall wealth, Þnancial wealth and real estate wealth.
8
Appendix: Construction of income-related variables
Here, we brießy describe the methodology we follow to construct proxies for permanent non-Þnancial income, its volatility and its correlation to Þnancial and real estate income. We follow the approach of Carrol and Samwick (1997) and Vissing-Jørgensen (2002). We consider as non-Þnancial income: labor income and entrepreneurial income. In particular, we deÞne the conditional moments of the long-term investor’s non-Þnancial income: E(Yit |Yit−1 , Xit−1 ) and V ar(Yit |Yit−1 , Xit−1 ),
(9)
where Yit is the non-Þnancial income of investor i at time t and Xit−1 are the variables that can be used to predict income next period. We assume that non-Þnancial income follows: ln ω it = pit + εit ,
(10)
where, pit = git + pit−1 + η it , εit ∼ N(0, σ2εi ), ηit ∼ N(0, σ2ηi ), and cov(εit , εis ) = 0, cov(η it , ηis ) = 0, for each t 6= s and cov(εit , ηis ) = 0 for each t, s. The variable p it represents the permanent income component of non-Þnancial income. It has a drift term (g it ) that is known and based on the information available at t − 1. This allows us to write: ln ω it − ln ω it−1 = pit − pit−1 + εit − εit−1 = git + εit − εit−1 + ηit or ln ω it = ln ω it−1 + git + ηit + εit − εit−1 .
18
(11) (12)
This implies:
E(ωit |ω i,t−1 , Xi,t−1 ) = ω i,t−1 Git exp{0.5Jit }
V ar(ω |ω 2 it i,t−1 , Xi,t−1 ) = Jit = (ωi,t−1 Git ) exp(Jit ){exp(Jit ) − 1},
(13)
where Git = exp(git ), Jit = σ2ηi + 2σ2εi and Xi,t−1 is the set of variables usable to predict git . In order to estimate E(Yit |Yi,t−1 , Xi,t−1 ) and V ar(Yit |Yi,t−1 , Xi,t−1 ), we use income data for the period 1990-1999, with a 5-year rolling window, based on the previous 5 years of data. Following Carrol and Samwick (1997) and Vissing-Jørgensen (2002a) methodology, we regress ln Yit − ln Yit−1 on the set of explanatory variables Xi,t−1 and use the predicted values of such a regression as an estimate of git and the residuals as an estimate of η it + εit − εit−1 .16
We then use the sample variance to construct σ2ηi + 2σ2εi . To control for measurement and
estimation errors, we use instrumental variables. We also construct a measure of the conditional correlation between shocks to log nonÞnancial income (η it + εit − εit−1 ) and the log gross stock returns (i.e., ln(1 + Rt )). This correlation is denoted as Corr(Yit , Rt ), where Rt is the return on the Þnancial assets. We consider two Þnancial returns (Rt ), the return on the market portfolio (Rmt ) and the return on the portfolio of the investor (Rport,t ). Following Vissing-Jørgensen (2002a), given the potential inaccuracy of estimates based on few observations, we calculate the correlation over the entire sample. These variables are our measures of the investor’s non-Þnancial income, its variance and its correlation to his portfolio.
References [1] Arellano, M., 1990, Testing for Autocorrelation in Dynamic Random Effects Models. Review of Economic Studies, 57 127-134. [2] Arellano, M. and Bond, S.R., 1991, Some Tests of SpeciÞcation for Panel Data. Monte Carlo Evidence and an Application to Employment Equations, Review of Economic Studies, 58, 277297. [3] Barber, B. M.and Odean, T., 2000, Trading Is Hazardous to Your Wealth: The Common Stock Investment Performance of Individual Investors, Journal of Finance, 55, 773-806. [4] Barber, B. M. and Odean, T., 2001, Boys Will Be Boys: Gender, OverconÞdence, and Common Stock Investment, Quarterly Journal of Economics, 116, 261-292. 16 The set of variables contained in Xi,t−1 are: demographic variables (secondary education, higher education, age, age squared, marriage status, size of the household, number of adults belonging to the household), changes in the demographic variables, industry dummies for the company the investor is working for (e.g., oil industry), dummies for the type of profession of the investor (e.g., doctor), immigration status.
19
[5] Barber, B. M. and Odean, T. 2002, Online Investors: Do the Slow Die First?, Review of Financial Studies, 15, 455-487. [6] Barberis, N., Huang, M., and Santos, T., 2001, Prospect Theory and Asset Prices, Quarterly Journal of Economics, 116, pp. 1-53. [7] Barberis, N. and Huang, M., 2001, Mental Accounting, Loss Aversion, and Individual Stock Returns, Journal of Finance, 56, 4, pp. 1247-92. [8] Barry, C.B. and Brown, S.J., 1984, Anomalies in Security Returns and the SpeciÞcation of the Market Model, Journal of Finance, 39, 807-815. [9] Barry, C.B. and Brown, S.J., 1985, Differential Information and Security Market Equilibrium, Journal of Financial and Quantitative Analysis, 20, 407-422. [10] Benartzi, S. and Thaler, R., 1995, Myopic Loss Aversion and the Equity Premium Puzzle, Quarterly Journal of Economics, 110, 73-92. [11] Benartzi, S., 2001, Excessive Extrapolation and the Allocation of 401(k) Accounts to Company Stock, Journal of Finance, 56, 1747-1764. [12] Benartzi, S. and Thaler, R., 2001, Naive DiversiÞcation Strategies in DeÞned Contribution Saving Plans, American Economic Review, 91, 79-98. [13] Brown, P., Chappel, N., da Silva Rosa, R. and Walter, T., 2002, The Reach of the Disposition Effect: Large Sample Evidence Across Investor Classes, Mimeo. [14] Brennan, M.J., 1997, The Role of Learning in Dynamic Portfolio Decisions, European Finance Review, 1, 295-306. [15] Calvet, L., Gonzalez-Eiras and Sodini, P., 2002, "Financial Innovation, Stock Market Participation and Asset prices", SSE/WFI Working Paper 464. [16] Campbell, J.C., 2000, Asset Pricing at the Millennium, The Journal of Finance, 40, 1515-1567. [17] Carroll, C. D. and Samwick, A. A., 1997, The Nature of Precautionary Wealth, Journal of Monetary Economics, 40, 41-71. [18] Carroll, C.D. and Kimball, M.S., 2001, Liquidity Constraints and Precautionary Saving, NBER Working Paper 8496. [19] Edin, P.A., and Fredriksson, P., 2000, LINDA: Longitudinal Individual Data for Sweden 19601997, Uppsala University Working Paper. [20] Englund, P., Quigley, J.M., and Redfearn, C., 1998, Improved Price Indexes for Real Estate: Measuring the Course of Swedish Housing Prices, Journal of Urban Economics 44, 171-196. [21] Feenberg, D. R. and Poterba, J. M., 2000, The Income and Tax Share of Very High-Income Households, 1960-1995, American Economic Review, 90, 264-270 . [22] Genesove, D. and Mayer, C., 2001, Loss Aversion and Seller Behavior: Evidence from the Housing Market, Quarterly Journal of Economics, 116, 1233-1260. [23] Grinblatt, M. and Keloharju„ 2000, The Investment Behavior and Performance of Various Investor Types: A Study of Finland’s Unique Data Set, Journal of Financial Economics, 55, 43-67.
20
[24] Grinblatt, M. and Keloharju, M., 2001, How Distance, Language, and Culture Inßuence Stockholdings and Trades, Journal of Finance, 56, 1053-1073. [25] Grinblatt, M. and Keloharju, M., 2001, What Makes Investors Trade?, Journal of Finance, 56, 589-616. [26] Guiso, L. and Jappelli, T., 2002, Household Portfolios in Italy, in Households Portfolios, edited by Guiso, Jappelli and Haliassos, MIT Press, 250-289. [27] Heaton, J. and Lucas, D., 2000, Portfolio Choice and Asset Prices: The Importance of Entrepreneurial Risk, Journal of Finance, 55, 1163-1198. [28] Heaton, J. and Lucas, D., 2000, Portfolio Choice in the Presence of Background Risk, Economic Journal, 110, 1-26. [29] Heckman, J., 1979, Sample Selection Bias as a SpeciÞcation Error, Econometrica 47, 153-161. [30] Kiviet, J.F., 1995, On Bias, Inconsistency and Efficiency of Various Estimators in Dynamic Panel Data Models. Journal of Econometrics 68, 53-78. [31] Odean, T., 1998, Are Investors Reluctant to Realize Their Losses?, Journal of Finance, 53, 17751798. [32] Odean, T., 1999, Do Investors Trade Too Much?, American Economic Review, 89, 1279-1298 [33] Peress, J., 2002, Wealth, Information Acquisition and Portfolio Choice, Mimeo. [34] Poterba, J. M. and Samwick, A.A., 1997, Household Portfolio Allocation Over the Life Cycle, NBER Working Paper: 6185. [35] Shefrin, H. and Statman, M., 1985, The Disposition to Sell Winners Too Early and Ride Losers Too Long: Theory and Evidence, Journal of Finance, 40, 777-791. [36] Shiller, R., Case, K. and Quigley, J., 2001, Stock Market Wealth, Housing Market Wealth, Spending and Consumption," Berkeley Program on Housing and Urban Policy, Working Paper W01-004, Berkeley. [37] Sundin A. and Sundqvist, S.I., 2002, "Owners and Power in Sweden’s Listed Companies," SIS Ägarservice AB, 1986-2002. [38] Tversky, A. and Kahneman, D., 1979, Prospect Theory: an Analysis of Decision Under Risk, Econometrica, Vol. 47, 263-293. [39] Tversky, A. and Kahneman, D., 1986, Rational Choice and the Framing of Decisions, Journal of Business, 59. [40] Vissing-Jørgensen, A., 2002, Towards an Explanation of Household Portfolio Choice Heterogeneity: Non-Financial Income and Participation Cost Structures, Mimeo. [41] Vissing-Jørgensen, A., 2002, Limited Stock Market Participation and the Equity Premium Puzzle, Mimeo. [42] Yitzhaki, S., 1987, The Reationship between Return and Income, The Quarterly Journal of Economics, 78-95. [43] Weber, M. and Camerer, C.F., 1998, The Disposition Effect in Securities Trading: An Experimental Analysis, Journal of Economic Behavior & Organization, 33, p167-185.
21
Table 1: Descriptive Statistics of the sample This table contains the descriptive statistics of the sample. Panel A reports the general demographic characteristics (number of households for each year, members in household, adults in the household, age of the oldest member of the household, percentage of the sample with secondary and higher education). Panel B reports the age and gender distribution of the sample. We report Mean, Median, Standard Deviation, Inter-Quartile Range (IQR) and Maximum value. They have been calculated over the whole sample (i.e., across-investors and time). Panel C reports the percentage of the households paying wealth tax, having labor income, having entrepreneurial income and having real estate wealth. The column “Representation in the sample” reports the fraction of households in the sample who pay wealth tax, earn labor or entrepreneurial income or hold real estate wealth. The other columns report statistics (Mean, Median, Standard Deviation, IQR, Maximum) of, respectively, the value of wealth, labor and entrepreneurial income (gross yearly income) and real estate. All monetary values are in Swedish Krones. Panel A: General demographic characteristics Variable Number of households # of members in household # of adults in household Age of oldest household member % with secondary education % with higher education
Mean
Median
Std.Dev.
IQR
Maximum
292,901 2.67 1.77 49.28 43.5% 31.4%
291,913 2.00 2.00 47 43.5% 31.2%
647 1.51 0.69 17 0.6% 1.4%
686 3.00 1.00 24 0.5% 1.4%
293,320 16.00 9.00 107 44.3% 33.7%
Panel B: Age and gender distribution of the sample Age 0-19 20-29 30-39 40-49 50-59 60+ Total
Males 18.2% 4.8% 7.1% 7.4% 5.9% 6.6% 49.9%
Females 17.2% 4.9% 8.2% 7.4% 5.3% 7.2% 50.2%
Age of oldest household member 0.5% 10.7% 21.7% 23.6% 17.9% 25.8% 100%
Panel C: Wealth and income characteristics of households Variable
Representation in the sample Wealth-tax Payers 7.9% Labor Income Earners 100.0% Entrepreneurial Income Earners 9.8% Real Estate Holders 54.6%
Mean
Median
359,592
102,700
321,489
287,722
237,526
276,190
43,445,271
88,114
43,268
172,565
111,726
7,320,000
449,400
387,000
348,736
340,000
78,140,000
22
Std.Dev.
I. Q. R.
Maximum
2,648,521 353,400 1,023,147,857
Table 2: Descriptive statistics of gain measures. This table reports the descriptive statistics for three measures of gains: wealth-based, securities’ gains/losses based and real estate capital gains and losses-based. The first measure is defined as ΠWt=(Wealtht/Wealtht-1-1) and capital gains/losses are defined as ΠF,R t=(CAPITAL GAINStCAPITAL LOSSESt)/ Wealtht-1, where capital gains are those for securities (real estate) correspondingly. We report statistics for both raw measures and risk-adjusted measures. Panel B reports the results of t-test, Wilcoxon and Kolmogorov-Smirnov tests of equality for high-wealth vs. low-wealth households. Panel C reports the results of t-test, Wilcoxon and KolmogorovSmirnov tests of equality for liquid vs. illiquid high-wealth households.
Panel A: Descriptive statistics Low-wealth Median StdDev
Variable
Mean
ΠF t ΠR t ΠWt
0.007 0.018 0.094
0.000 0.000 0.050
0.033 0.083 0.415
ΠF t ΠR t ΠWt
0.037 0.161 0.792
0.000 0.000 0.214
0.236 0.921 4.228
I.Q.R. Mean Raw Gains 0.000 0.008 0.003 0.026 0.162 0.123 Risk-adjusted Gains 0.002 0.069 0.014 0.350 0.750 1.556
Wealthy Median StdDev
I.Q.R.
0.000 0.002 0.087
0.029 0.067 0.259
0.000 0.024 0.204
0.000 0.016 0.519
0.335 0.981 3.840
0.002 0.258 2.188
Panel B: Tests of differences between high- and low-wealth households t-test Variable
t-Value
ΠF t ΠR t ΠWt
4.25 16.16 13.65
ΠF t ΠR t ΠWt
15.96 29.99 29.36
Wilcoxon Test Prob>|t| Z Prob>|Z| Raw Gains
