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.     

Robust consumption and portfolio choice for time varying investment opportunities

This paper examines a continuous-time intertemporal consumption and portfolio choice problem for an investor with recursive preferences. The investor worries about model misspecification and seeks robust decision rules. The expected excess return of a risky asset follows a mean-reverting process. I find that whether the concern about model misspecification decreases the total demand for equities largely depends on risk aversion and the attitude toward intertemporal substitution. When the elasticity of intertemporal substitution is about 1 and risk aversion is moderate, the aversion to model uncertainty increases the proportion of wealth invested in equities. The calibration analysis based on detection-error probabilities shows that the quantitative effect of robustness is almost negligible.     

Optimal savings distortions with recursive preferences

This paper derives an intertemporal optimality condition for economies with private information, focusing on a class of recursive preferences. By comparing it to the situation where agents can freely save in a risk-free asset market, we derive the optimal savings distortions necessary for constrained optimality. Our recursive preferences are homogeneous and satisfy a balanced-growth condition, while allowing us to separate the role of risk aversion and intertemporal elasticity of substitution. We perform some quantitative exercises that disentangle the respective roles played by these two parameters in optimal distortions and the implied welfare gains.     

Generalized Disappointment Aversion and Asset Prices

We characterize generalized disappointment aversion (GDA) risk preferences that can overweight lower‐tail outcomes relative to expected utility. We show in an endowment economy that recursive utility with GDA risk preferences generates effective risk aversion that is countercyclical. This feature comes from endogenous variation in the probability of disappointment in the representative agent's intertemporal consumption‐saving problem that underlies the asset pricing model. The variation in effective risk aversion produces a large equity premium and a risk‐free rate that is procyclical and has low volatility in an economy with a simple autoregressive endowment‐growth process.     

Is stochastic volatility relevant for dynamic portfolio choice under ambiguity?

Literature on dynamic portfolio choice has been finding that volatility risk has low impact on portfolio choice. For example, using long-run US data, Chacko and Viceira [2005. “Dynamic Consumption and Portfolio Choice with Stochastic Volatility in Incomplete Markets.” The Review of Financial Studies 18 (4): 1369–1402] found that intertemporal hedging demand (required by investors for protection against adverse changes in volatility) is empirically small even for highly risk-averse investors. We want to assess if this continues to be true in the presence of ambiguity. Adopting robust control and perturbation theory techniques, we study the problem of a long-horizon investor with recursive preferences that faces ambiguity about the stochastic processes that generate the investment opportunity set. We find that ambiguity impacts portfolio choice, with the relevant channel being the return process. Ambiguity about the volatility process is only relevant if, through a specific correlation structure, it also induces ambiguity about the return process. Using the same long-run US data, we find that ambiguity about the return process may be empirically relevant, much more than ambiguity about the volatility process. Anyway, intertemporal hedging demand is still very low: investors are essentially focused on the short-term risk–return characteristics of the risky asset.     

Endogenous Life‐Cycle Housing Investment and Portfolio Allocation

This paper develops a life‐cycle portfolio allocation model to address the effects of housing investment on the portfolio allocation of households. The model employs a comprehensive housing investment structure, Epstein–Zin recursive preferences, and a stock market entry cost. Furthermore, rather than resorting to calibration we estimate the value of the relative risk aversion and elasticity of intertemporal substitution. The model shows that housing investment has a strong crowding out effect on investment in risky assets throughout the life‐cycle. We further find that the effect of the presence of housing investment on households portfolio allocation is larger than the effect of having EZ recursive preferences.     

Asset pricing under quantile utility maximization

“Focus on the downside, and the upside will take care of itself” is a famous quote among professional investors. By considering an agent who follows this advice, we reproduce the first and second moments of stock returns, risk-free rate and consumption growth. The agent's behavior toward risk is analogous to a relative risk aversion of about 3 under expected utility, the elasticity of intertemporal substitution is about 0.5 and the time discount factor is below 1. In particular, the proposed model separates time and risk preferences in an innovative way.     

Robust multivariate portfolio choice with stochastic covariance in the presence of ambiguity

This paper provides the optimal multivariate intertemporal portfolio for an ambiguity averse investor, who has access to stocks and derivative markets, in closed form. The stock prices follow stochastic covariance processes and the investor can have different levels of uncertainty about the diffusion parts of the stocks and the covariance structure. We find strong evidence that the optimal exposures to stock and covariance risks are significantly affected by ambiguity aversion. Welfare analyses show that investors who ignore model uncertainty incur large losses, larger than those suffered under the embedded one-dimensional cases. We further confirm large welfare losses from not trading in derivatives as well as ignoring intertemporal hedging, we study the impact of ambiguity in that regard and justify the importance of including these factors in the scope of portfolio optimization. Conditions are provided for a well-behaved solution in general, together with verification theorems for the incomplete market case.     

Robust portfolio choice with uncertainty about jump and diffusion risk

We analyze the portfolio planning problem of an ambiguity averse investor. The stock follows a jump-diffusion process. We find that there are pronounced differences between ambiguity aversion with respect to diffusion risk and jump risk. Ignoring ambiguity with respect to jump risk causes larger losses in an incomplete market, whereas ignoring ambiguity with respect to diffusion risk is more severe in a complete market. For a deterministic jump size we show that the loss from market incompleteness is always increasing in the level of ambiguity aversion with respect to one risk factor and decreasing in the level of ambiguity aversion with respect to the other risk factor.     

Risk aversion, intertemporal substitution, and the aggregate investment-uncertainty relationship

We analyze the role of risk aversion and intertemporal substitution in a simple dynamic general equilibrium model of investment and savings. Our main finding is that risk aversion cannot by itself explain a negative relationship between aggregate investment and aggregate uncertainty, as the effect of increased uncertainty on investment also depends on the intertemporal elasticity of substitution. In particular, the relationship between aggregate investment and aggregate uncertainty is positive even if agents are very risk averse, as long as the elasticity of intertemporal substitution is low. A negative investment-uncertainty relationship requires that the relative risk aversion and the elasticity of intertemporal substitution are both relatively high or both relatively low. We also show that the implications of our model are consistent with the available empirical evidence.     

The independence axiom and asset returns

This paper integrates models of atemporal risk preference that relax the independence axiom into a recursive intertemporal asset-pricing framework. The resulting models are amenable to empirical analysis using market data and standard Euler equation methods. We are thereby able to provide the first nonlaboratory-based evidence regarding the usefulness of several new theories of risk preference for addressing standard problems in dynamic economics. Using both stock and bond returns data, we find that a model incorporating risk preferences that exhibit first-order risk aversion accounts for significantly more of the mean and autocorrelation properties of the data than models that exhibit only second-order risk aversion. Unlike the latter class of models which require parameter estimates that are outside of the admissible parameter space, e.g., negative rates of time preference, the model with first-order risk aversion generates point estimates that are economically meaningful. We also examine the relationship between first-order risk aversion and models that employ exogenous stochastic switching processes for consumption growth.     

The term structure of interest rates in a DSGE model with recursive preferences

A dynamic stochastic general equilibrium (DSGE) model in which households have Epstein and Zin recursive preferences is solved with perturbation. The parameters governing preferences and technology are estimated by maximum likelihood using macroeconomic data and the term structure of interest rates. The estimates imply a large risk aversion, an elasticity of intertemporal substitution higher than one, and substantial adjustment costs. Furthermore, the paper identifies the tensions within the model by estimating it on subsets of these data. The analysis concludes by pointing out potential extensions that may improve the model's fit.     

Can ambiguity aversion solve the equity premium puzzle? Survey evidence from international data

Ambiguity aversion has been suggested as a potential explanation for the equity premium puzzle in recent theoretical models. To test this hypothesis, we measure the amount of ambiguity aversion in a large-scale international survey. A comparison to the average equity premia in these countries demonstrates that ambiguity aversion does, indeed, have a significant influence on the amount of equity risk premium, even when controlling for macroeconomic parameters. Finally, we connect differences in ambiguity aversion to differences in uncertainty avoidance, one of Hofstede’s cultural dimensions.     

Dynamic Consumption and Portfolio Choice with Stochastic Volatility in Incomplete Markets

This paper examines the optimal consumption and portfolio-choiceproblem of long-horizon investors who have access to a risklessasset with constant return and a risky asset ("stocks") withconstant expected return and time-varying precision—thereciprocal of volatility. Markets are incomplete, and investorshave recursive preferences defined over intermediate consumption.The paper obtains a solution to this problem which is exactfor investors with unit elasticity of intertemporal substitutionof consumption and approximate otherwise. The optimal portfoliodemand for stocks includes an intertemporal hedging componentthat is negative when investors have coefficients of relativerisk aversion larger than one, and the instantaneous correlationbetween volatility and stock returns is negative, as typicallyestimated from stock return data. Our estimates of the jointprocess for stock returns and precision (or volatility) usingU.S. data confirm this finding. But we also find that stockreturn volatility does not appear to be variable and persistentenough to generate large intertemporal hedging demands.     

Asset pricing in production economies with extrapolative expectations

Introducing extrapolative bias into a standard production-based model with recursive preferences reconciles salient stylized facts about business cycles (low consumption volatility, high investment volatility relative to output) and financial markets (high equity premium, volatile stock returns, low and smooth risk-free rate) with plausible levels of risk aversion and intertemporal elasticity of substitution. Furthermore, the model captures return predictability based upon dividend yield, Q, and investment. Intuitively, extrapolative bias increases the variation in the wealth–consumption ratio, which is heavily priced under recursive preferences; adjustment costs decrease the covariance between marginal utility and asset returns. Empirical support for key implications of the model is also provided.     

Optimal investments for risk- and ambiguity-averse preferences: a duality approach

Ambiguity, also called Knightian or model uncertainty, is a key feature in financial modeling. A recent paper by Maccheroni et al. (preprint, 2004) characterizes investor preferences under aversion against both risk and ambiguity. Their result shows that these preferences can be numerically represented in terms of convex risk measures. In this paper we study the corresponding problem of optimal investment over a given time horizon, using a duality approach and building upon the results by Kramkov and Schachermayer (Ann. Appl. Probab. 9, 904–950, 1999; Ann. Appl. Probab. 13, 1504–1516, 2003). Supported by Deutsche Forschungsgemeinschaft through the SFB 649 “Economic Risk”.     

Risk aversion in the expected and the nonexpected utility functions

If asset returns are i.i.d. over time, the preference parameter in the time additive von Neumann-Morgenstern expected utility is the risk aversion coefficient in the Epstein-Zin nonexpected utility. By distinguishing between risk aversion and intertemporal substitution, this article provides an explanation about the observed discrepancy in the empirical estimates of the risk aversion coefficient.     

Multivariate risk aversion and intertemporal substitution

Researchers often assume that preferences over uncertain consumption streams are representable by $$E\left[ {\left( {{1 \mathord{\left/ {\vphantom {1 \gamma }} \right. \kern-\nulldelimiterspace} \gamma }} \right)\sum\limits_{t = 0}^x {\delta ^t \tilde c_t^\gamma } } \right]$$ , where \(\tilde c_t \) , is (random) period t consumption. It is moreover often asserted that estimates of γ cannot be unambiguously interpreted, since the quantity 1 ? γ measures both relative risk aversion and the reciprocal of the elasticity of substitution. Clearly, this ambiguity arises only if 1 ? γ indeed measures risk aversion. Although changes in γ cannot reflect changes in risk aversion according to standard definitions of comparative multivariate risk aversion, we show that γ is rationalizable as a risk aversion measure provided that the “acceptance set” of sure prospects is restricted. We also show, however, that there is essentially no relationship between changes in γ and optimal consumption, even in a simple two period model; this finding casts doubt upon the interpretation of γ as a risk aversion measure.