Growth uncertainty,generalized disappointment aversion and production-based asset pricing

We study a production economy with regime switching in the conditional mean and volatility of productivity growth. The representative agent has generalized disappointment aversion (GDA) preferences. We show that volatility risk in productivity growth carries a positive and sizable risk premium in levered equity. Our model can endogenously generate long-run risks in the volatility of consumption growth observed in the data. We show that introducing leverage with a procyclical dividend process consistent with the data is critical for the GDA preferences to have a large impact on equity returns.     

Risk-adjusted option-implied moments

This paper provides a new way of converting risk-neutral moments into the corresponding physical moments, which are required for many applications. The main theoretical result is a new analytical representation of the expected payoffs of put and call options under the physical measure in terms of current option prices and a representative investor’s preferences. This representation is then used to derive analytical expressions for a variety of ex-ante physical return moments, showing explicitly how moment premiums depend on current option prices and preferences. As an empirical application of our theoretical results, we provide option-implied estimates of the representative stock market investor’s disappointment aversion using S&P 500 index option prices. We find that disappointment aversion has a procyclical pattern. It is high in times of high index levels and declines when the index falls. We confirm the view that investors with high risk aversion and disappointment aversion leave the stock market during times of turbulence and reenter it after a period of high returns.     

Commodity futures hedging,risk aversion and the hedging horizon

This paper examines the impact of management preferences on optimal futures hedging strategy and associated performance. Applying an expected utility hedging objective, the optimal futures hedge ratio is determined for a range of preferences on risk aversion, hedging horizon and expected returns. Empirical results reveal substantial hedge ratio variation across distinct management preferences and are supportive of the hedging policies of real firms. Hedging performance is further shown to be strongly dependent on underlying preferences. In particular, hedgers with high risk aversion and short horizon reduce hedge portfolio risk but achieve inferior utility in comparison to those with low aversion.     

Why stocks may disappoint

We provide a formal treatment of both static and dynamic portfolio choice using the Disappointment Aversion preferences of Gul (1991. Econometrica 59(3), 667–686), which imply asymmetric aversion to gains versus losses. Our dynamic formulation nests the standard CRRA asset allocation problem as a special case. Using realistic data generating processes, we find reasonable equity portfolio allocations for disappointment averse investors with utility functions exhibiting low curvature. Moderate variation in parameters can robustly generate substantial cross-sectional variation in portfolio holdings, including optimal non-participation in the stock market.     

Buffer stocks and precautionary savings with loss aversion

This paper reexamines buffer stocks and precautionary savings in the presence of loss aversion. We assume that agents are disappointment averse, as in Gul [Econometrica, 59 (1991) 667–686]. We show that the concavity of the marginal utility continues to determine precautionary saving, but its effect is of a second order magnitude (proportional to the square of the coefficient of variation) compared to the first order effect (proportional to the coefficient of variation) induced by loss aversion. We show that a stabilization fund that is rather small when agents are maximizing the conventional expected utility, turns out to be rather large with loss aversion.     

Age‐Dependent Increasing Risk Aversion and the Equity Premium Puzzle

We introduce a new preference structure—age‐dependent increasing risk aversion (IRA)—in a three‐period overlapping generations model with borrowing constraints, and examine the behavior of equity premium in this framework. We find that IRA preferences generate results that are more consistent with U.S. data for the equity premium, level of savings and portfolio shares, without assuming unreasonable levels of risk aversion. We find that the relative difference between the two risk aversions (how much more risk‐averse old agents are relative to the middle‐aged) matters more than the average risk aversion in the economy (how much more risk‐averse both cohorts are). Our findings are robust with respect to a number of model generalizations.     

Precautionary Saving and Consumption Smoothing across Time and Possibilities

This paper examines how aversion to risk and aversion to intertemporal substitution determine the strength of the precautionary saving motive in a two-period model with Selden/Kreps–Porteus preferences. For small risks, we derive a measure of the strength of the precautionary saving motive that generalizes the concept of "prudence" introduced by Kimball (1990b) . For large risks, we show that decreasing absolute risk aversion guarantees that the precautionary saving motive is stronger than risk aversion, regardless of the elasticity of intertemporal substitution. Holding risk preferences fixed, the extent to which the precautionary saving motive is stronger than risk aversion increases with the elasticity of intertemporal substitution. We derive sufficient conditions for a change in risk preferences alone to increase the strength of the precautionary saving motive and for the strength of the precautionary saving motive to decline with wealth. Within the class of constant elasticity of intertemporal substitution, constant-relative risk aversion utility functions, these conditions are also necessary.     

Cross-hedging with futures and options: The effects of disappointment aversion

This article examines the effect of disappointment aversion on cross-hedging decisions. We show that, when both futures and options markets are unbiased, disappointment aversion has no effect on the optimal hedge positions. In case that either market is biased, disappointment aversion induces the hedger to behave more conservatively. In addition, as the hedger becomes more disappointment averse, his action is more reserved. It is also found that disappointment aversion tends to depress the importance of the put options whereas the effect of risk aversion is not uniform. Analytical predictions are supplemented by numerical exercises.     

A Generalisation of the Mean-Variance Analysis

In this paper we consider a decision maker whose utility function has a kink at the reference point with different functions below and above this reference point. We also suppose that the decision maker generally distorts the objective probabilities. First we show that the expected utility function of this decision maker can be approximated by a function of mean and partial moments of distribution. This 'mean-partial moments' utility generalises not only mean-variance utility of Tobin and Markowitz, but also mean-semivariance utility of Markowitz. Then, in the spirit of Arrow and Pratt, we derive an expression for a risk premium when risk is small. Our analysis shows that a decision maker in this framework exhibits three types of aversions: aversion to loss, aversion to uncertainty in gains, and aversion to uncertainty in losses. Finally we present a solution to the optimal capital allocation problem and derive an expression for a portfolio performance measure which generalises the Sharpe and Sortino ratios. We demonstrate that in this framework the decision maker's skewness preferences have first-order impact on risk measurement even when the risk is small.     

Constant Absolute Risk Aversion Preferences and Constant Equilibrium Interest Rates

This paper constructs a general equilibrium model with endogenous stochastic production and establishes that the equilibrium interest rate can be constant in a closed production economy when the preferences are represented by constant absolute risk aversion utility functions. The results in this paper and their limitations are compared and contrasted with related contributions in the financial economics literature.     

Risk aversion with state-dependent preferences in the rank-dependent expected utility theory

We extend the analysis of risk aversion with state-dependent preferences to the rank-dependent expected utility theory. We find that in this extended theory, for two preference relations to be comparable in risk aversion not only do their reference sets need to coincide (a condition first introduced by Karni [1983, 1985] in the original expected utility framework), but they must also rank the prospective state-dependent outcomes in the same manner. We formalize this additional condition by introducing the concept of certainty sets. Under our condition of comparability, various results and characterizations of interpersonal comparison of risk aversion are obtained. The implications for a specific insurance problem are also discussed.     

Time-varying risk preferences and emerging market co-movements

This paper examines how shocks can transmit across international stock markets through the channel of time-varying investor risk preferences. We highlight the effects of this channel by comparing the conventional constant relative risk aversion utility function with the habit-formation utility function of Campbell and Cochrane (J. Pol. Econ. 107 (1999) 205). Calibrating our model with data from Argentina, Korea and Mexico, we find that in the presence of time-varying investor risk preferences, market integration generates a substantial increase in cross-country co-movements of stock returns.     

Bond Pricing with a Time‐Varying Price of Risk in an Estimated Medium‐Scale Bayesian DSGE Model

New Keynesian model in which households have Epstein–Zin preferences with time‐varying risk aversion and the central bank has a time‐varying inflation target can match the dynamics of nominal bond prices in the U.S. economy well. The model generates a large steady‐state term spread and its fitting errors for bond yields are comparable to those obtained from a nonstructural three‐factor model, and one‐third smaller than in models with a constant inflation target or risk aversion. Including data on interest rates has large effects on variance decompositions, making investment technology shocks much less important than found in other recent papers.     

Loss aversion,asymmetric market comovements,and the home bias

Loss aversion has been used to explain why a high equity premium might be consistent with plausible levels of risk aversion. The intuition is that the first-order-different utility impact of wealth gains and losses leads loss-averse investors to behave similarly to investors with high risk aversion. But if so, should those agents not perceive larger gains from international diversification than standard expected-utility investors with plausible levels of risk aversion? They might not, because comovements in international stock markets are asymmetric: correlations are higher in market downturns than in upturns. This asymmetry dampens the gains from diversification relatively more for loss-averse investors. We analyze the portfolio problem of such an investor who has to choose between home and foreign equities in the presence of asymmetric comovement in returns. Perhaps surprisingly, in the context of the home bias puzzle we find that loss-averse investors behave similarly to those with standard expected-utility preferences and plausible levels of risk aversion. We argue that preference specifications that appear to perform well with respect to the equity premium puzzle should be subjected to this “test”.     

Portfolio Choice and Life Insurance: The CRRA Case

We solve a portfolio choice problem that includes life insurance and labor income under constant relative risk aversion (CRRA) preferences. We focus on the correlation between the dynamics of human capital and financial capital and model the utility of the family as opposed to separating consumption and bequest. We simplify the underlying Hamilton–Jacobi–Bellman equation using a similarity reduction technique that leads to an efficient numerical solution. Households for whom shocks to human capital are negatively correlated with shocks to financial capital should own more life insurance with greater equity/stock exposure. Life insurance hedges human capital and is insensitive to the family's risk aversion, consistent with practitioner guidance.     

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.     

Risk aversion and skewness preference

Empirically, co-skewness of asset returns seems to explain a substantial part of the cross-sectional variation of mean return not explained by beta. This finding is typically interpreted in terms of a risk averse representative investor with a cubic utility function. This paper questions this interpretation. We show that the empirical tests fail to impose risk aversion and the implied utility function takes an inverse S-shape. Unfortunately, the first-order conditions are not sufficient to guarantee that the market portfolio is the global maximum for this utility function, and our results suggest that the market portfolio is more likely to represent the global minimum. In addition, if we do impose risk aversion, then co-skewness has minimal explanatory power.     

Market pricing of executive stock options and implied risk preferences

When managers get to trade in options received as compensation, their trading prices reveal several aspects of subjective option pricing and risk preferences. Two subjective pricing models are fitted to show that executive stock option prices incorporate a subjective discount. It depends positively on implied volatility and negatively on option moneyness. Further, risk preferences are estimated using the semiparametric model of Aït-Sahalia and Lo (2000). The results suggest that relative risk aversion is just above 1 for a certain stock price range. This level of risk aversion is low but reasonable, and it may be explained by the typical manager being wealthy and having low marginal utility. Related to risk aversion, it is found that marginal rate of substitution increases considerably in states with low stock prices.     

Portfolio choice with skewness preference and wealth-dependent risk aversion

This paper studies a dynamic portfolio choice problem for an investor with both wealth-dependent risk aversion and wealth-dependent skewness preferences. In a general economic setting, the solution is characterized in terms of a system of extended Hamilton-Jacobi-Bellman (EHJB) equations and the solution is given in closed form in some special cases. We demonstrate the effects of higher order risk preferences and state-dependent risk aversion on the optimal asset allocation decisions. We find that wealth-dependent risk aversion facilitates risk taking and the skewness preference leads to a more positively skewed portfolio in certain circumstances.