Wealth,Information Acquisition,and Portfolio Choice
Joe¨l Peress
INSEAD
I solve(with an approximation)a Grossman-Stiglitz economy under general prefer-
ences,thus allowing for wealth effects.Because information generates increasing returns,decreasing absolute risk aversion,in conjunction with the availability of costly information,is sufficient to explain why wealthier households invest a larger fraction of their wealth in risky assets.One no longer needs to resort to decreasing relative risk aversion,an empirically questionable assumption.Furthermore,I show how to distinguish empirically between these two explanations.Finally,I find that the availability of costly information exacerbates wealth inequalities.
The effect of wealth on households’demand for risky assets has long been studied,starting with the works of Cohn et al.(1975)and Friend and Blume(1975).They document that the fraction of wealth households invest in stocks increases with their wealth.Several recent studies using different datasets and estimation techniques confirm their observation.1 One common explanation for the observed patte
rn of portfolio shares is that relative risk aversion decreases with ,Cohn et al.(1975)]. Moreover,some ,Morin and Suarez(1983)]use portfolio data to elicit households’preferences and conclude from the observation of shares that relative risk aversion is decreasing.However,abstracting from portfolio data,there is not much evidence in favor of decreasing relative risk aversion.Several studies reject this hypothesis using data that contains information about attitudes toward risk such as farm data,survey data,or experimental data.2Here,I suggest an alternative explanation for I am particularly grateful to my dissertation advisors Lars Peter Hansen(chairman),Pierre-Andre´Chiappori,and Pietro Veronesi for their guidance and support.I would like to acknowledge helpful comments from Antonio Bernardo,Bernard Dumas,Luigi Guiso,Harald Hau,John Heaton,Josef Perktold,Joao Rato,Guy Saidenberg,Jose´Scheinkman,Olivier Vigneron,Robert Verrecchia,Annette Vissing-Jørgensen,and seminar participants at the University of Chicago,the EFA meeting in London, Delta,Crest,Essec,HEC,INSEAD,London School of Economics,Banca d’Italia,AFFI meeting in Namur,and the SED meeting in Stockholm.I thank the University of Chicago,the French government, and the European Commission for their financial support.Address correspondence to Joe¨l Peress, INSEAD,Department of Finance,Boulevard de Constance,77305Fontainebleau Cedex,France,or e-mail:joel.peress@insead.edu.
1These studies estimate the elasticity of portfolio shares with respect to wealth to be around0.1,where portfolio shares refer to the fraction of financial wealth invested in risky assets,both directly and indirectly,conditional on holding some risky assets.I review the evidence in detail in Section1.
2In addition,Arrow(1971)makes a theoretical argument in favor of increasing relative risk aversion.The empirical studies are reviewed in Section1.Section6also rules out alternative explanations for portfolio shares based on fixed entry costs and psychological biases.
The Review of Financial Studies Vol.17,No.3ª2004The Society for Financial Studies;all rights reserved. DOI:10.1093/rfs/hhg056Advance Access publication October15,2003
The Review of Financial Studies/v17n32004
the observed pattern of portfolio shares and wealth.This explanation only requires absolute risk aversion to be decreasing with wealth,an assump-tion that is supported by all empirical studies.(In particular,the model reconciles the common assumption that relative risk aversion is constant with the observed pattern of portfolio shares.)
In addition to decreasing absolute risk aversion,the explanation offered in this article relies on the possibility to acquire,at a cost,information about stocks.Though they are not directly observable,there is evidence that differences in information do matter to investors’decisions and that these differences are related to households’measurable characteristics such as wealth.Several surveys in Europe and the United States document the importance of information for stock ownership.3For example, Alessie,Hochguertel,and Van Soest(2002)use data from a Dutch survey that includes a measure of interest in financial matters and find that this variable has a significant and positive effect on portfolio shares.More-over,Donkers and Van Soest(1999)show that this financial interest variable is strongly positively correlated to income.In the same spirit, Lewellen,Lease,and Schlarbaum(1977)report that the money spent by investors on financial periodicals,investment research services,and professional counseling increases with both income and education.On another front,research in accounting shows that small trades react less to earnings news than large trades do,suggesting that wealthier investors (i.e.,investors who place large orders)process the news and adjust their orders faster than poorer investors.4
This article explains the cross-sectional pattern of stockholdings and wealth by endogenous differences in information.For that purpose,I model explicitly how investors acquire information.I sho
w that though they do not have lower relative risk aversion,wealthier investors hold a larger fraction of their wealth in stocks.5The reason is that the value of information increases with the amount to be invested,whereas its cost does not.This implies that agents with more to invest acquire more information.Consequently they purchase even more stocks and hold a larger portfolio share.Thus they do so not because they are relatively less 3For Europe,see Alessie,Hochguertel and Van Soest(2002),Borsch-Supan and Eymann(2002),Guiso and Jappelli(2002).For the United States,see King and Leape(1987).
4See Cready(1988)and Lee(1992).In addition,some articles argue that costly information processing explains some puzzling phenomena in finance such as the‘‘home equity bias’’[French and Poterba(1991), Kang and Stulz(1994),Coval and Moskowitz(1999)]and the‘‘weekend effect’’[Miller(1988)and Lakonishok and Maberly(1990)]and others provide evidence on the role of financial education and social interactions for stock ownership[Bernheim and Garret(1996),Chiteji and Stafford(1999), Weisbenner(1999),Bernheim,Garret,and Maki(2001),Huberman(2001),Duflo and Saez(2002)].
5Therefore one should be cautious when infering the determinants of relative risk aversion from portfolio shares.What looks like decreasing relative risk aversion(increasing portfolio shares)may in f
act be the result of decreasing absolute risk aversion combined with information purchase.This applies not only to wealth,as the article shows,but also to other determinants of risk aversion such as age or education. 880
absolute relativeWealth,Information Acquisition,and Portfolio Choice
risk averse,but because the stock is less risky to them.Importantly,this result does not rely on any form of increasing returns to scale embedded in technology or preferences:it is obtained in spite of a strictly convex informa-tion acquisition cost and prevails when relative risk aversion is increasing.
The model builds on Grossman and Stiglitz(1980)and Verrecchia (1982).In Grossman and Stiglitz(1980),traders may purchase private information about the payoff of a stock,which they use to trade competi-tively in the market.Their information gets revealed by the equilibrium price,but only partially because there is some noise in the system.In Verrecchia(1982),traders are allowed to choose continuously the preci-sion of their private signal.A key assumption of these rational expecta-tions models with asymmetric information is that agents have constant absolute risk aversion utility(CARA or exponential).Hence these models ignore the role of wealth,though it is an important determinant of stock-holdings.To capture wealth effects,I solve the model under general preferences.
6A closed-form solution is derived by making a small risk approximation.The point of the article is that,as long as absolute risk aversion decreases with wealth,there will be increasing returns to acquir-ing private information even though it gets revealed by public signals.7 Finally,I study the link between wealth inequality and stock prices. Because information generates increasing returns,the demand for stocks is a convex function of wealth.Hence the more unequal the distribution of wealth,the higher the stock price.Conversely,wealthier investors achieve a higher expected return,a higher variance,and a higher Sharpe ratio on their portfolio.Consequently,the distribution of final wealth as measured by expected wealth or by certainty equivalent is more unequal than the distribution of initial wealth.This fact also suggests a simple way of discriminating the information model from the decreasing relative risk aversion model:in the former,the Sharpe ratio on an agent’s portfolio increases with her wealth,whereas in the latter,it is constant.Using a comprehensive dataset on Swedish households,Massa and Simonov (2003)report that Sharpe ratios increase with financial wealth,in accor-dance with the information model.More research is needed to confirm these results.
The remainder of the article is organized as follows.Section1reviews the evidence on the relations between wealth,portfolio shares,relative risk aversion,and information acquisition.Section2describes the economy. Section3defines the equilibrium concept.Section4solves the model:the 6However,it sho
uld be noted that the model presented here is static and hence does not capture hedging demands.This important feature of portfolio choice is considered in dynamic models with CARA preferences.
7The idea of increasing returns to information is not new,but to my knowledge,it has not been modeled in a setup where private information gets partially revealed by public signals,as in the stock market[Wilson (1975)and Arrow(1987)].
881
The Review of Financial Studies/v17n32004
equilibrium is characterized and the relation between wealth and portfolio shares is described.Section5studies the effect of information acquisition on wealth and return inequality.Finally,Section6addresses some empiri-cal issues:I calibrate the model to U.S.data,show how to discriminate the information acquisition model from the decreasing risk aversion model using micro data,and finally,discuss alternative explanations based on fixed entry costs and psychological biases.Section7concludes and suggests some applications.Proofs and robustness checks are in the appendix. 1.Evidence
In this section I review the evidence on the relations between wealth, portfolio shares,relative risk aversion,and information acquisition.
1.1Wealth and portfolio shares
This article is motivated by the observation that the share of wealth households invest in stocks increases with their wealth,so let me now be more precise about how portfolio shares are measured.First,stocks refer to equity that is held both directly and indirectly through mutual funds.
Second,depending on how housing is treated(whether it is excluded, included as a riskless asset,included as a risky asset,priced at market value,or priced at owner’s equity value),different studies reach different conclusions about the effect of wealth on portfolio shares of risky assets.
However,virtually all agree that the fraction of financial wealth invested in ,total wealth excluding housing,capitalized labor,private businesses,social security,and pension incomes)increases with financial wealth.Third,portfolio shares of stocks are computed conditional on owning some stocks.Accordingly,the purpose of this article is to explain the fraction of financial wealth households invest in risky assets,both directly and indirectly,conditional on being a stockholder.
Several recent articles estimate the elasticity of portfolio shares with respect to wealth to be around0.1.The ones mentioned below use differ-ent datasets and econometric techniques,but all conform with the three points made above and,in particular,separate the share choice from the participation decision.Vissing-Jørgensen(2002)uses the Panel Study of Income Dynamics and finds estimates of0.09,0.12,and0.10,depending on the specification of the model.8Bertaut and Starr-McCluer(2002)use several waves of the Survey of Consumer Finance and find estimates of
0.17,0.04,and0.06.Finally,Perraudin and Sørensen(2000)use the1983
Survey of Consumer Finance and find an estimate of0.09.Other articles 8For example,in Table2,Vissing-Jørgensen(2002)reports regression coefficients on wealth and wealth squared equal to0.0011andÀ0.00000149,which imply an elasticity of0.12using the average wealth of $74,810.
882
Wealth,Information Acquisition,and Portfolio Choice
report elasticities but differ either in their measures of wealth or do not condition on participation.9An often-cited explanation for the observed positive elasticity is that relative risk aversion is decreasing with wealth. As the next section shows,this hypothesis does not hold in the data.
1.2Wealth and relative risk aversion
In contrast to decreasing absolute risk aversion,there is not much support for decreasing relative risk aversion outside portfolio data.The evidence instead points to increasing or constant relative risk aversion in environ-ments where information cannot be acquired.10First,studies in agricultural economics use data on farmers who allocate their land across crops of different risks,the same way an investor allocates her wealth across securities.Saha,Shumway,and Talpaz(1994)and Bar-Shira,Just,and Zilberman(1997)find a clear pattern of decreasing absolute risk aversion and increasing relative risk aversion using different estimation techniques and datasets.
Second,surveys have been designed to elicit the respondents’risk aver-sion by asking questions about hypothetical lotteries.Barsky et al.(1997) offered the respondents of the Health and Retirement Study gambles involving new jobs and found that relative risk aversion rises and then falls with wealth.Similarly,Guiso and Paiella(2001)asked the respon-dents of the Bank of Italy Survey of Household Income and Wealth for the maximum price they would be willing to pay to participate in a lottery. The answers show that absolute risk aversion is a decreasing function of wealth,while relative risk aversion is an increasing function.Furthermore, when portfolio shares of risky assets are regressed on the measure of risk aversion,wealth,and other demographic variables,the coefficient on
risk aversion is significantly negative and the coefficient on wealth is signifi-cantly positive,suggesting that wealth plays a role not captured by risk aversion.11
Finally,experimental studies provide some interesting insights on risk aversion.Gordon,Paradis,and Rorke(1972),Binswanger(1981),and 9For example,King and Leape(1998)use net worth as their measure of wealth and Heaton and Lucas (2000)do not condition on stock ownership in their regressions of portfolio shares on financial wealth (Table IX).
10An exception is Ogaki and Zhang(2001),but this study focuses on households close to their subsistence level.
11Studies in other fields strengthen the case against decreasing relative risk aversion.Szpiro(1986)uses aggregate data on property and liability insurance in the United States from1951to1975and finds that relative risk-aversion is constant.Wolf and Pohlman(1983)examine the bids of a U.S.bond dealer who gets most of his income from a fixed share of the profits he generates.Combining this information with the dealer’s returns forecasts,they find that absolute risk aversion is decreasing and that relative risk aversion is constant or slightly increasing.Aı¨t-Sahalia and Lo(2000)and Jackwerth(2000)use options prices to estimate the risk-neutral and subjective distri
butions of the S&P500index(a measure of aggregate wealth)from which they infer a representative investor’s risk aversion.They find that relative risk aversion is a nonmonotonic function of wealth.
883

版权声明：本站内容均来自互联网，仅供演示用，请勿用于商业和其他非法用途。如果侵犯了您的权益请与我们联系QQ:729038198，我们将在24小时内删除。