Risk aversion under preference uncertainty

We show that if an agent is uncertain about the precise form of his utility function, his actual relative risk aversion may depend on wealth even if he knows his utility function lies in the class of constant relative risk aversion (CRRA) utility functions. We illustrate the consequences of this result for optimal asset allocation: poor agents that are uncertain about their risk aversion parameter invest less in risky assets than wealthy investors with identical risk aversion uncertainty.     

Derivative Pricing with Liquidity Risk: Theory and Evidence from the Credit Default Swap Market

We derive an equilibrium asset pricing model incorporating liquidity risk, derivatives, and short‐selling due to hedging of nontraded risk. We show that illiquid assets can have lower expected returns if the short‐sellers have more wealth, lower risk aversion, or shorter horizon. The pricing of liquidity risk is different for derivatives than for positive‐net‐supply assets, and depends on investors' net nontraded risk exposure. We estimate this model for the credit default swap market. We find strong evidence for an expected liquidity premium earned by the credit protection seller. The effect of liquidity risk is significant but economically small.     

Risk Aversion Revisited

In order to supply additional empirical evidence of the effect of wealth on relative risk aversion, this study investigates households' demand for risky assets, using analysis of covariance techniques applied to the asset holdings of Canadian individual households. The extent and pattern of life-cycle effects are also examined. Results generally point to decreasing relative risk aversion when housing is either excluded from the definition of wealth or treated as a riskless asset. The investor's life-cycle plays a prominent role in portfolio selection behavior, with risk aversion increasing uniformly with age. Tax differentials do not seem to be an important element in investment decisions with respect to risk. When the sample and wealth definitions are censored in order to approximate those of previous empirical studies, their findings on relative risk aversion are generally corroborated.     

Saving and investing for early retirement: A theoretical analysis

We study optimal consumption and portfolio choice in a framework where investors adjust their labor supply through an irreversible choice of their retirement time. We show that investing for early retirement tends to increase savings and reduce an agent's effective relative risk aversion, thus increasing her stock market exposure. Contrary to common intuition, an investor might find it optimal to increase the proportion of financial wealth held in stocks as she ages and accumulates assets, even when her income and the investment opportunity set are constant. The model predicts a decrease in risk aversion following strong market gains like those observed in the nineties.     

Risk aversion measures: comparing attitudes and asset allocation

Households' reported willingness to take financial risk is compared to the riskiness of their portfolios, measured as risky assets to wealth. Overall, their portfolio allocations are reliable indicators of attitudes toward risk, demonstrating an understanding of their relative level of risk taking. Multivariate regression analysis using multiply imputed data from the 1989 Survey of Consumer Finances indicates that households generally exhibit decreasing relative risk aversion. Further, investment in risky assets is significantly related to socioeconomic factors, attitude toward risk taking, desire to leave an estate and expectations about the adequacy of Social Security and pension income.     

MEASURING RISK AVERSION: ALLOCATION,LEVERAGE, AND ACCUMULATION

The risk-asset ratio that measures Arrow-Pratt relative risk aversion reflects a multidimensional risk behavior. The risk-asset ratio is decomposed into the product of ratios that measure portfolio allocation between riskless and risk assets, use of financial leverage, and accumulation of wealth in marketable form. The three dimensions are less sensitive to the definition of wealth than is the composite risk-asset ratio. Constant relative risk aversion can be characterized by offsetting changes in the three dimensions as wealth changes.     

Gender differences in defined contribution pension decisions

This paper considers gender differences in allocation of household wealth to defined contribution pensions. Using data from the 1989 Survey of Consumer Finances, we estimate the coefficient of relative risk aversion based on the allocation of wealth into defined contribution pensions. Unlike previous studies, we consider the problem in the context of the household’s overall portfolio. We find that women exhibit greater relative risk aversion in their allocation of wealth into defined contribution pension assets.     

The Dynamics of Financially Constrained Arbitrage

We develop a model in which financially constrained arbitrageurs exploit price discrepancies across segmented markets. We show that the dynamics of arbitrage capital are self‐correcting: following a shock that depletes capital, returns increase, which allows capital to be gradually replenished. Spreads increase more for trades with volatile fundamentals or more time to convergence. Arbitrageurs cut their positions more in those trades, except when volatility concerns the hedgeable component. Financial constraints yield a positive cross‐sectional relationship between spreads/returns and betas with respect to arbitrage capital. Diversification of arbitrageurs across markets induces contagion, but generally lowers arbitrageurs' risk and price volatility.     

Recovering copulas from limited information and an application to asset allocation

This paper proposes an entropy-based method to construct a new class of copulas - the most entropic canonical copulas (MECC). Our empirical study focuses on an investment problem for an investor with a constant relative risk aversion (CRRA) utility function allocating wealth between the Dow Jones Large-Cap and Small-Cap indices, of which the contemporaneous dependence can be modeled by the MECC or other commonly-used copulas. Both the theoretical analysis of the method and the empirical study indicate the potential for enormous statistical and economic gains as a result of using the MECC.     

Twin Picks: Disentangling the Determinants of Risk‐Taking in Household Portfolios

This paper investigates risk‐taking in the liquid portfolios held by a large panel of Swedish twins. We document that the portfolio share invested in risky assets is an increasing and concave function of financial wealth, leading to different risk sensitivities across investors. Human capital, which we estimate directly from individual labor income, also affects risk‐taking positively, while internal habit and expenditure commitments tend to reduce it. Our microfindings lend strong support to decreasing relative risk aversion and habit formation preferences. Furthermore, heterogeneous risk sensitivities across investors help reconcile individual preferences with representative‐agent models.     

What is the impact of wealth shocks on asset allocation?

I test the assumption of constant relative risk aversion using U.S. macroeconomic data and analyse the role of wealth shocks in generating transitory changes in asset portfolio composition. I show that the risky asset share exhibits cyclical behavior and it is significantly (and positively) affected by unexpected variation in wealth. Therefore, the empirical evidence suggests that risk aversion is counter-cyclical. I also find that the portfolio share of housing wealth falls when the agent is faced with a positive wealth shock, i.e. housing is a hedge against unfavorable wealth fluctuations. Finally, considering a variety of wealth definitions, the results show that: (i) wealth effects are stronger for direct holdings of risky assets than for indirect holdings, which highlights that investors do not typically trade some assets such as pension or mutual funds; (ii) although significant, wealth effects on asset allocation are mainly temporary as agents quickly rebalance the asset portfolio composition (i.e. there is weak evidence of inertia or slow adjustment in asset allocation); and (iii) changes in expected returns partially explain the variation in risky asset allocation.     

Mean-Variance Asset Liability Management with State-Dependent Risk Aversion

This article investigates the asset liability management problem with state-dependent risk aversion under the mean-variance criterion. The investor allocates the wealth among multiple assets including a risk-free asset and multiple risky assets governed by a system of geometric Brownian motion stochastic differential equations, and the investor faces the risk of paying uncontrollable random liabilities. The state-dependent risk aversion is taken into account in our model, linking the risk aversion to the current wealth held by the investor. An extended Hamilton-Jacobi-Bellman system is established for the optimization of asset liability management, and by solving the extended Hamilton-Jacobi-Bellman system, the analytical closed-form expressions for the time-inconsistent optimal investment strategies and the optimal value function are derived. Finally, numerical examples are presented to illustrate our results.     

Relative risk aversion once more: An analysis of Japanese households' financial asset holding pattern

It is widely accepted that as the total assets increse, households tend to diversify their portfolios. In other words, absolute risk aversion is decreasing. On the other hand, the proportion of risky assets may increase or decrease depending on whether relative risk aversion (RRA) is decreasing or increasing, and its direction is still left open as an empirical question. This study examines the constancy of RRA from Japanese individual households' financial asset holding data collected in 1984. Constant RRA implies that the proportion of risky assets in one's portfolio is constant regardless of the amount of total assets. A casual observation of household portfolio holding pattern suggests that this implication is clearly violated by the data, because there are substantial proportion of households which do not hold any risky assets. Zero-holding, however, may be interpreted as a result of fixed transaction cost incurred by individual investors when they hold risky assets. Then, we pose a question, ‘Do investors hold constant proportion of risky assets, when they decide to hold them?’ In order to explain a substantial number of zero risky asset holders in the sample, we propose a portfolio selection model with a transaction cost, and estimate the model using a variant of Heckman's two-step method. In estimation we control for individual investors' socioeconomic characteristics, as well as income and total assets. The construction of the model imposes nonlinear restrictions on the two estimators, from which we can test the specification of the model. The estimation results suggest that there is a statistically significant decreasing tendency linked to total assets but that its rate of change tapers off as total assets increase. Our results are consistent with the previous studies which tended to support constant RRA for the higher asset holders, and complement previous studies in explaining lower asset holders' investment behavior.     

Heterogeneous Background Risks and Portfolio Choice: Evidence from Micro‐level Data

We construct a set of household‐level background risk variables to capture the covariance structure of three nonfinancial assets and two financial assets. These risks are in general statistically significant and economically important for a household's stock market participation and stockholdings. A one‐standard‐deviation increase in background risks reduces the participation probability by 11% and the stockholdings‐to‐wealth ratio by 4%. The volatilities of labor income, housing value, and business income reduce a household's participation and stockholdings. A household with labor income highly correlated with stock (bond) returns is less (more) likely to invest in stock.     

Volatility Risk Premium,Risk Aversion,and the Cross‐Section of Stock Returns

We test if innovations in investor risk aversion are a priced factor in the stock market. Using 25 portfolios sorted on book‐to‐market and size as test assets, our new factor together with the market factor explains 64% of the variation in average returns compared to 60% for the Fama‐French model. The new factor is generally significant with an estimated risk premium close to its time series mean also when industry portfolios and portfolios sorted on previous returns are augmented to the test assets.     

Interpreting Factor Models

We argue that tests of reduced‐form factor models and horse races between “characteristics” and “covariances” cannot discriminate between alternative models of investor beliefs. Since asset returns have substantial commonality, absence of near‐arbitrage opportunities implies that the stochastic discount factor can be represented as a function of a few dominant sources of return variation. As long as some arbitrageurs are present, this conclusion applies even in an economy in which all cross‐sectional variation in expected returns is caused by sentiment. Sentiment‐investor demand results in substantial mispricing only if arbitrageurs are exposed to factor risk when taking the other side of these trades.     

Dynamic portfolio choice without cash

We consider the dynamic mean–variance portfolio choice without cash under a game theoretic framework. The mean–variance criterion is investigated in the situation where an investor allocates the wealth among risky assets while keeping no cash in a bank account. The problem is solved explicitly up to solutions of ordinary differential equations by applying the extended Hamilton–Jacobi–Bellman equation system. Given a constant risk aversion coefficient, the optimal allocation without a risk-free asset depends linearly on the current wealth, while that with a risk-free asset turns out to be independent of the current wealth. We also study the minimum-variance criterion, which can be viewed as an extension of the mean–variance model when the risk aversion coefficient tends to infinity. Calibration exercises demonstrate that for large investments, the mean–variance model without cash yields the highest certainty equivalent return for both short-term and long-term investments. Furthermore, the mean–variance portfolio choices with and without cash yield almost the same Sharpe ratio for an investment with large initial wealth.     

Increasing return response to changes in risk

Risk aversion theory is based on an individual's choice among risky assets with expected utility in its foundation. It is about investor behavior (i.e., investor choice), under normal circumstances, toward assets with various levels of risk. A positive and marginally diminishing relationship between risk and return exists. This study is about investor behavior related to their response (not choice) to risk. We present an argument and supporting evidence that investors’ return response to risk is increasing with the level of risk. Thus, investor behavior is subject to change and the level of risk is a determinant of such change. We also explain the negative time‐series correlation between risk and return.     

First-Best Equilibrium in Insurance Markets With Transaction Costs and Heterogeneity

We investigate extensions of the classic Rothschild and Stiglitz (1976) (RS) model of adverse selection under asymmetric information. In RS, low‐risk customers are worse off owing to an externality created by high‐risk buyers in the market. We find critical changes in insurance buyers' behavior under the joint assumptions of transaction costs and buyer heterogeneity with respect to either risk aversion or wealth. Combining transaction costs and heterogeneity, we find a separating equilibrium in which neither high‐risk nor low‐risk individuals are penalized due to information asymmetry.