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.     

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.     

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 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.     

Consumption-portfolio optimization with recursive utility in incomplete markets

In an incomplete market, we study the optimal consumption-portfolio decision of an investor with recursive preferences of Epstein?CZin type. Applying a classical dynamic programming approach, we formulate the associated Hamilton?CJacobi?CBellman equation and provide a suitable verification theorem. The proof of this verification theorem is complicated by the fact that the Epstein?CZin aggregator is non-Lipschitz, so standard verification results (e.g. in Duffie and Epstein, Econometrica 60, 393?C394, 1992) are not applicable. We provide new explicit solutions to the Bellman equation with Epstein?CZin preferences in an incomplete market for non-unit elasticity of intertemporal substitution (EIS) and apply our verification result to prove that they solve the consumption-investment problem. We also compare our exact solutions to the Campbell?CShiller approximation and assess its accuracy.     

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.     

Synamic banking: a reconsideration

Financially intermediated and stock market consumption-investmentallocations, with and without governmental interventions, arecompared in a welfare sense in overlapping generation economieswith (and without) shocks to agents' intertemporal preferences.We first show that, in economies with preference shocks, governmentalinterventions subject to the same information requirements asthose imposed on financial intermediaries, lead to stock marketallocations that are not inferior to those attained under financialintermediation. Second, we argue that the necessary interventionsare qualitatively no different from those required to implementstationary optimal allocations in OLG models without shocksto agents' intertemporal consumption preferences.     

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.     

Time preference and capital asset pricing models

Results of the theory of individual optimal consumption-investment choice under uncertainty are extended to a class of intertemporally dependent preferences for consumption streams. These results are then used to show that with intertemporally dependent preferences, which are more realistic than the separable time-additive preference structure, Merton's (1973) multi-beta intertemporal capital asset pricing model is still valid, but it can no longer be collapsed to Breeden's (1979) single consumption-beta model.     

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.     

Consumption–investment optimization with Epstein–Zin utility in incomplete markets

In a market with stochastic investment opportunities, we study an optimal consumption–investment problem for an agent with recursive utility of Epstein–Zin type. Focusing on the empirically relevant specification where both risk aversion and elasticity of intertemporal substitution are in excess of one, we characterize optimal consumption and investment strategies via backward stochastic differential equations. The superdifferential of indirect utility is also obtained, meeting demands from applications in which Epstein–Zin utilities were used to resolve several asset pricing puzzles. The empirically relevant utility specification introduces difficulties to the optimization problem due to the fact that the Epstein–Zin aggregator is neither Lipschitz nor jointly concave in all its variables.     

Comparative Ambiguity Aversion in Intertemporal Decisions

This article examines the effects of ambiguity aversion on intertemporal decisions when there is ambiguity about a future state. Compared to the existing literature, we allow for a three-way separation between intertemporal substitution, risk aversion, and ambiguity aversion. Holding risk preferences, beliefs, and time preferences fixed, we explore how a change in ambiguity aversion increases the strength of the current willingness to pay. We apply our results to saving, self-protection, and self-insurance problems.     

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.     

An intertemporal equilibrium beta pricing model

This article develops an intertemporal, discrete-time, competitiveequilibrium version of the arbitrage pricing theory, (APT) andexplores the econometric implications of this model under variousrestrictions on investor preferences and on the dynamic behaviourof dividends. We describe conditions under which the econometrictechnique typically used for estimating and testing the APTcan be shown to be consistent with our economic model. We relateour intertemporal version of the APT to the static APT and toMerton's intertemporal capital asset pricing model.     

Intertemporal price discrimination with two products

We study the two‐product monopoly profit maximization problem for a seller who can commit to a dynamic pricing strategy. We show that if consumers' valuations are not strongly ordered, then optimality for the seller can require intertemporal price discrimination: the seller offers a choice between supplying a complete bundle now, or delaying the supply of a component of that bundle until a later date. For general valuations, we establish a sufficient condition for such dynamic pricing to be more profitable than mixed bundling. So we show that the established no‐discrimination‐across‐time result does not extend to two‐product sellers under standard taste distributions.     

Convex duality in optimal investment and contingent claim valuation in illiquid markets

This paper develops duality theory for optimal investment and contingent claim valuation in markets where traded assets may be subject to nonlinear trading costs and portfolio constraints. Under fairly general conditions, the dual expressions decompose into three terms, corresponding to the agent’s risk preferences, trading costs and portfolio constraints, respectively. The dual representations are shown to be valid when the market model satisfies an appropriate generalization of the no-arbitrage condition and the agent’s utility function satisfies an appropriate generalization of asymptotic elasticity conditions. When applied to classical liquid market models or models with bid–ask spreads, we recover well-known pricing formulas in terms of martingale measures and consistent price systems. Building on the general theory of convex stochastic optimization, we also obtain optimality conditions in terms of an extended notion of a “shadow price”. The results are illustrated by establishing the existence of solutions and optimality conditions for the nonlinear market models recently proposed in the literature. Our results allow significant extensions including nondifferentiable trading costs which arise, e.g., in modern limit order markets where the marginal price curve is necessarily discontinuous.     

Optimal liquidation under stochastic liquidity

We solve explicitly a two-dimensional singular control problem of finite fuel type for an infinite time horizon. The problem stems from the optimal liquidation of an asset position in a financial market with multiplicative and transient price impact. Liquidity is stochastic in that the volume effect process, which determines the intertemporal resilience of the market in the spirit of Predoiu et al. (SIAM J. Financ. Math. 2:183–212, 2011), is taken to be stochastic, being driven by its own random noise. The optimal control is obtained as the local time of a diffusion process reflected at a non-constant free boundary. To solve the HJB variational inequality and prove optimality, we need a combination of probabilistic arguments and calculus of variations methods, involving Laplace transforms of inverse local times for diffusions reflected at elastic boundaries.     

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.     

Optimal consumption and investment with Epstein–Zin recursive utility

We study continuous-time optimal consumption and investment with Epstein–Zin recursive preferences in incomplete markets. We develop a novel approach that rigorously constructs the solution of the associated Hamilton–Jacobi–Bellman equation by a fixed point argument and makes it possible to compute both the indirect utility and, more importantly, optimal strategies. Based on these results, we also establish a fast and accurate method for numerical computations. Our setting is not restricted to affine asset price dynamics; we only require boundedness of the underlying model coefficients.     

What Drives Consumption Booms?

Consumption booms have been common in both industrial and developingcountries, and several explanations have been offered for theiroccurrence. These include economywide wealth effects associatedwith favorable movements in the terms of trade or euphoric expectationstriggered by macroeconomic reforms, Ricardian effects associatedwith fiscal stabilization, lending booms following financialliberalization, and a variety of distortions in intertemporalrelative prices. Using a large cross-country sample of booms,this article assesses how widely applicable these explanationsare. The key finding is that wealth effects linked to favorablemovements in the terms of trade and anticipated improvementsin macroeconomic performance seem to have been more importantempirically than explanations relying primarily on fiscal phenomenaor distortions in intertemporal relative prices.