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We test whether relative risk aversion varies with wealth using the Panel Study of Income Dynamics data in the U.S. Our analytical results indicate the following implications. For each household, there are two channels through which the risky share responds to wealth fluctuations, the income channel and the habit channel. For across households, there are heterogeneous responses through both the habit channel and the income channel. Finally, two potential misspecification problems on time-varying relative risk aversion arise when both heterogeneous responses through the habit channel and the responses through the income channel are ignored. Our main empirical findings are to show the importance of the income channel and the heterogeneous responses, and to provide strong evidence of relative risk aversion varying with wealth, after correcting two misspecification problems.
We estimate risk aversion from investors' financial decisions in a person-to-person lending platform. We develop a method that obtains a risk aversion parameter from each portfolio choice. Since the same individuals invest repeatedly, we construct a panel dataset that we use to disentangle heterogeneity in attitudes towards risk across investors, from the elasticity of risk aversion to changes in wealth. We find that wealthier investors are more risk averse in the cross section, and that investors become more risk averse after a negative housing wealth shock. Thus, investors exhibit preferences consistent with decreasing relative risk aversion and habit formation.
Recent asset pricing models depart from the standard time-separable CRRA preferences - by introducing additive habit formation, for example - so that wealth shocks produce transitory variation in agents' relative risk aversion. We investigate whether there is micro-level evidence in support of this proposed (negative) relationship between wealth shocks and relative risk aversion. To this end, we analyze two decades of panel data on household asset allocation from the PSID and CEX surveys. Using a variety of specifications, we find that the share of financial assets that households invest in risky assets is unaffected by shocks to their wealth. We also find that following in- and outflows of financial wealth, and, in particular, capital gains and losses, households rebalance only very little. But even controlling for this inertia, wealth shocks do not have economically significant effects on household asset allocation. Our results suggest that wealth fluctuations do not generate time-varying risk aversion.
Modern literature departs from time-separable constant relative risk aversion preferences to explain asset pricing facts. This deviation typically implies that wealth shocks generate transitory variations in agents' relative risk aversion and, possibly, portfolio re-allocations over time.I empirically analyze this relationship using U.S. macroeconomic data and find evidence for time-variation in portfolio shares that is consistent with counter-cyclical risk aversion. These results suggest, therefore, that wealth-dependent, habit-formation or loss and disappointment aversion utility functions are a good description of preferences.Controlling for observed versus expected asset returns, I also show that: (i) wealth effects are significant (although temporary) and there is no evidence of inertia contrary to Brunnermeier and Nagel (2006); and (ii) the consumption-wealth ratio (Lettau and Ludvigson, 2001), the labor income risk (Julliard, 2004) and the labor income-consumption ratio (Santos and Veronesi, 2006) partially explain changes in the risky asset share.
The dissertation studies the role of housing in asset pricing and household asset allocation. Housing is unique in the sense that it is both an asset and a consumption good. In addition, any adjustment in housing consumption will incur a non-convex adjustment cost. This makes housing adjustment infrequent. Due to these unique characteristics, the role of housing in a household portfolio is quite different from financial assets such as stocks and bonds. The first chapter, "The Housing CCAPM with Adjustment Costs and Heterogeneous Agents" examines how the inclusion of housing consumption in the utility function can increase the volatility and countercyclicality of the stochastic discount factor and thus help explain a higher level of equity premium despite only moderate curvature of the utility function. The keys to better performance of the model are (i) existence of the adjustment cost (ii) non-separability between housing goods and nondurable goods in the utility function and (iii) low substitutability between housing consumption and nondurable consumption. It is also shown that the housing CCAPM performs better than a standard CCAPM in explaining the variation of cross-sectional risk premia. Chapter 2, "Implications of the Housing Market for Endogenous Risk Aversion" studies household portfolio choice in a partial equilibrium model with housing consumption, adjustment costs, and varying housing prices. It is shown that household relative risk aversion is dependent on their house value to wealth ratio. Therefore, by changing the household's house value to wealth ratio, variation in house prices can affect household stock holdings through a change in household risk aversion. In addition, the model has two specific implications for households. The first is that volatile house price dynamics leads to more frequent moving. The second is that household moving leads to higher relative risk aversion. In general equilibrium, these effects would imply that volatile housing prices can lead to a higher moving frequency and thus result in a higher level of aggregate risk aversion, which would increase the price of risk in the risky asset markets. We provide empirical evidence that there is a high correlation between housing price volatility and the price of risk. Chapter 3, "Implications of the Housing Model for Moving Frequency, Relative Risk Aversion and the Portfolio Share of Risky Assets" tests the implications of the household portfolio choice model developed in Chapter 2 using household level data from the Panel Study of Income Dynamics and finds that the empirical evidence is consistent with the model. Firstly, we use cross-sectional variation in state level house prices and household moving to study the relationship between the volatility of house prices and moving frequency. Secondly, we use household moving and portfolio data to study the effect of moving on risk aversion. In addition, Chapter 3 also studies the effect of becoming unemployed on household moving by solving a model with housing consumption, adjustment costs, and a stochastic labor income process. The result suggests that the overall effect of unemployment is to reduce the frequency of moving. In addition, a sudden shift to an unemployed status can increase household risk aversion. Thus in general equilibrium, we would expect that a higher unemployment rate will increase economy wide risk aversion, which will in turn decrease the demand for stocks and increase the risk premium required. This provides a new channel (through the change in risk aversion) for the unemployment rate to affect asset prices.
We use data from the PSID to investigate how households' portfolio allocations change in response to wealth fluctuations. Persistent habits, consumption commitments, and subsistence levels can generate time-varying risk aversion with the consequence that when the level of liquid wealth changes, the proportion a household invests in risky assets should also change in the same direction. In contrast, our analysis shows that the share of liquid assets that households invest in risky assets is not affected by wealth changes. Instead, one of the major drivers of households' portfolio allocation seems to be inertia: households rebalance only very slowly following inflows and outflows or capital gains and losses.
We use data from the PSID to investigate how households' portfolio allocations change in response to wealth fluctuations. Persistent habits, consumption commitments, and subsistence levels can generate time-varying risk aversion with the consequence that when the level of liquid wealth changes, the proportion a household invests in risky assets should also change in the same direction. In contrast, our analysis shows that the share of liquid assets that households invest in risky assets is not affected by wealth changes. Instead, one of the major drivers of households' portfolio allocation seems to be inertia: households rebalance only very slowly following inflows and outflows or capital gains and losses
Academic finance has had a remarkable impact on many financial services. Yet long-term investors have received curiously little guidance from academic financial economists. Mean-variance analysis, developed almost fifty years ago, has provided a basic paradigm for portfolio choice. This approach usefully emphasizes the ability of diversification to reduce risk, but it ignores several critically important factors. Most notably, the analysis is static; it assumes that investors care only about risks to wealth one period ahead. However, many investors—-both individuals and institutions such as charitable foundations or universities—-seek to finance a stream of consumption over a long lifetime. In addition, mean-variance analysis treats financial wealth in isolation from income. Long-term investors typically receive a stream of income and use it, along with financial wealth, to support their consumption. At the theoretical level, it is well understood that the solution to a long-term portfolio choice problem can be very different from the solution to a short-term problem. Long-term investors care about intertemporal shocks to investment opportunities and labor income as well as shocks to wealth itself, and they may use financial assets to hedge their intertemporal risks. This should be important in practice because there is a great deal of empirical evidence that investment opportunities—-both interest rates and risk premia on bonds and stocks—-vary through time. Yet this insight has had little influence on investment practice because it is hard to solve for optimal portfolios in intertemporal models. This book seeks to develop the intertemporal approach into an empirical paradigm that can compete with the standard mean-variance analysis. The book shows that long-term inflation-indexed bonds are the riskless asset for long-term investors, it explains the conditions under which stocks are safer assets for long-term than for short-term investors, and it shows how labor income influences portfolio choice. These results shed new light on the rules of thumb used by financial planners. The book explains recent advances in both analytical and numerical methods, and shows how they can be used to understand the portfolio choice problems of long-term investors.
We develop a life-cycle consumption and portfolio choice model in which households have nonhomothetic utility over two types of goods, basic and luxury. We calibrate the model to match the cross-sectional and life-cycle variation in the basic expenditure share in the Consumer Expenditure Survey. The model explains the degree to which the portfolio share in risky assets rises in wealth in the cross-section of households in the Survey of Consumer Finances. For a given household, the portfolio share can fall in response to an increase in wealth, even though the model implies decreasing relative risk aversion.