Epstein-Zin Utility Research Articles

The sensitivity of risk premiums to the elasticity of intertemporal substitution

AbstractThis paper incorporates reference‐dependent preferences into a consumption‐based asset pricing model featuring Epstein–Zin utility. Three relevant results emerge from this extension. First, agents prefer the late resolution of uncertainty in recursive utility. Second, the late resolution of uncertainty helps replicate the downward‐sloping term structure of market excess return. Third, the intertemporal substitution elasticity is more sensitive to asset prices through increasing precautionary saving motivations. A closed‐form solution for the proposed model largely explains (i) high, volatile, and countercyclical equity premiums; (ii) low risk‐free rates; and (iii) the downward‐sloping term structure of equity premiums and variance ratios.

Optimal consumption and portfolio selection with Epstein–Zin utility under general constraints

Optimal consumption and portfolio selection with Epstein–Zin utility under general constraints

Asset Allocation Strategy and Convergence with Epstein-Zin Utility function

In this paper, we study the optimal consumption and investment problems for an individual with the Epstein-Zin type utility. We employ the binomial tree model for dynamics of the risky asset and derive optimal policies. We show that the optimal policies converge to those in the continuous-time model of Schroder and Skiadas. The convergence rate of optimal policies is of the order of equal to the time interval between consecutive time points, and there is little difference in convergence rates between CRRA and Epstein-Zin utilities. We also show that the optimal consumption decreases as the elasticity of intertemporal substitution increases.

Quasi-hyperbolic discounting under recursive utility and consumption–investment decisions

This paper examines an Epstein–Zin recursive utility with quasi-hyperbolic discounting in continuous time. I directly define the utility process supporting the Hamilton–Jacobi–Bellman (HJB) equation in the literature and consider Merton's optimal consumption–investment problem for application. I show that a solution to the HJB equation is the value function. The numerical and mathematical analyses show that unlike in the constant relative risk aversion utility, present bias in the Epstein–Zin utility causes economically significant overconsumption, maintaining a plausible attitude toward risks. Additionally, the sophisticated agent's preproperation occurs if and only if the elasticity of intertemporal substitution is larger than one.

Valuation risk revalued

This paper shows the success of valuation risk—time‐preference shocks in Epstein–Zin utility—in resolving asset pricing puzzles rests sensitively on the way it is introduced. The specification used in the literature is at odds with several desirable properties of recursive preferences because the weights in the time‐aggregator do not sum to one. When we revise the specification in a simple asset pricing model the puzzles resurface. However, when estimating a sequence of increasingly rich models, we find valuation risk under the revised specification consistently improves the ability of the models to match asset price and cash‐flow dynamics.

Optimal Claiming of Social Security Benefits

Using a lifecycle framework with Epstein-Zin (1989) utility and a mixed-integer optimization approach, we compute the optimal age to claim Social Security benefits. Taking advantage of homogeneity, a sufficient statistic is the ratio of wealth to the primary insurance amount (PIA). If the investor's wealth to PIA ratio exceeds a certain threshold, individuals should defer Social Security for at least a year. The optimal threshold depends on mortality assumptions and an individual’s utility preferences, but is less sensitive to capital market assumptions. The threshold wealth to PIA ratio increases from 5.5 for men and 5.2 for women at age 62 to 11.1 for men and 10.4 for women at age 69. Below the threshold wealth to PIA ratio, individuals claim Social Security to raise consumption. Above this level, investors can afford to fund consumption out of wealth for at least one year, and then claim a higher benefit.

Gain/loss asymmetric stochastic differential utility

This study examines a gain/loss asymmetric utility in continuous time in which the investor discounts their utility gain by more than the utility loss. By employing the theory of stochastic differential utility, the model allows an endogenously time-varying subjective discount rate. In addition, the model can express various forms of utility functions including a version of the Epstein–Zin utility. Under the model, even if the state variables do not have any jump in their paths, the optimal consumption/wealth ratio and portfolio weight can change non-smoothly.

Quasi-Hyperbolic Discounting under Recursive Utility and Consumption-Investment Decisions

This paper examines an Epstein-Zin recursive utility with quasi-hyperbolic discounting in continuous time. I directly define the utility process and consider a Merton's optimal consumption-investment problem for application. I show that a solution to the Hamilton-Jacobi-Bellman equation is the value function. The numerical comparative statics and mathematical analysis shows that, unlike in the constant relative risk aversion utility, present bias in the Epstein-Zin utility causes economically significant overconsumption, maintaining a plausible attitude toward risks. Additionally, I show that the sophisticated agent's preproperation occurs if and only if his or her elasticity of intertemporal substitution in consumption is larger than one.

Unemployment-based Capital Asset Pricing Model

In this paper, we wish to examine how prospects of unemployment might change predictions of consumption based CAPM with regards to equity premium and term structure of interest. In particular, instead of agents having varied consumption growth, we study agents with probability of losing significant portion of their consumption. Thus, volatility of unemployment determines risk in the economy, rather than volatility of the consumption. Within framework of Epstein-Zin utility function, our model correctly predicts term structure premium and equity premium. In particular, the model predicts one-year risk-free rate of 1.71%, 30-year risk-free rate of 3.17% and equity rate of 7.33% given parameter of risk aversion of 1,2, EIS of 1,54, and time discount factor of 0.9578. Additionally, we study importance of third moments in our model and discover new pricing factor that is missing in current skewness models. Empirical tests under various conditions confirm statistical significance of our factor. Finally, we utilize our model to predict market changes based on shifts in term structure and then empirically verify model predictions. This paper demonstrates that standard C-based CAPM is more than enough to predict observed term structure and equity premium and no model modification is required if proper consumption variation statistics is used.

Epstein–Zin Utility, Asset Prices, and the Business Cycle Revisited

Abstract This paper discusses the advantages of Epstein and Zin (1989) (EZ) preferences when building dynamic stochastic general equilibrium (DSGE) models that are consistent with well-known stylized facts of both the business cycle and asset markets. To this end, we combine EZ preferences with several building blocks from the DSGE literature that has tried to solve the equity premium puzzle and to replicate characteristic statistics of the labor market. Our goal is to guide researchers in this area to useful modeling devices and to discuss EZ preferences vis-a-vis the standard time-additive expected utility function. EZ preferences separate the attitude toward risk from the attitude toward intertemporal substitution. We demonstrate that this additional degree of freedom allows us to closely match the empirical facts already in a frictionless production economy with endogenous labor supply. Our study follows Heer and Maußner (2013). We examine models that consider adjustment costs of capital accumulation, consumption habits, and frictions in the allocation of labor. Our empirical targets are estimated from German data.

Consumption and Portfolio Choice under Internal Multiplicative Habit Formation

This paper explores the optimal consumption and investment behavior of an individual who derives utility from the ratio between his consumption and an endogenous habit. We obtain closed-form policies under general utility functionals and stochastic investment opportunities by developing a nontrivial linearization to the budget constraint. This enables us to explicitly characterize how habit formation affects the marginal propensity to consume and optimal stock–bond investments. We also show that in a setting that combines habit formation with Epstein–Zin utility, consumption no longer grows at unrealistically high rates at high ages and investments in risky assets decrease.

Tractable Rare Disaster Probability and Options-Pricing

We derive an option-pricing formula from recursive preference and estimate rare disaster probability. The new options-pricing formula applies to far-out-of-the money put options on the stock market when disaster risk dominates, the size distribution of disasters follows a power law, and the economy has a representative agent with Epstein-Zin utility. The formula conforms with options data on the S&P 500 index from 1983-2018 and for analogous indices for other countries. The disaster probability, inferred from monthly fixed effects, is highly correlated across countries, peaks during the 2008-2009 financial crisis, and forecasts equity index returns and growth vulnerabilities in the economy.

Recursive utility and parameter uncertainty

We explore how the Epstein–Zin utility captures an agent's sensitivity to parameter uncertainty. Our main result is a closed-form representation of the Epstein–Zin utility for an i.i.d. consumption process with unknown parameter, as the discount factor approaches 1. Using this representation, and under the usual assumption about the relationship between risk aversion and the attitude towards time smoothing, we show that the agent is averse to parameter uncertainty.

Survival in speculative markets

In this paper, I consider an exchange economy with complete markets where agents have heterogeneous beliefs and, possibly, preferences, and investigate the Market Selection Hypothesis that speculation rewards the agent with the most accurate beliefs. First, on the methodological level, I derive the relative consumption dynamics as a function of agents' effective discount factors, related to consumption decisions across time, and agents' effective beliefs, related to consumption decisions across states. Sufficient conditions for agents' survival, either in isolation or in a group, depend on the relative size of effective discount factors and on the relative accuracy of effective beliefs. Then, I show that in economies where agents maximize an Epstein–Zin utility the Market Selection Hypothesis fails: there exist parametrizations where the agent with correct beliefs vanishes and parametrizations where beliefs heterogeneity persists in the long run. Results are robust to local changes of beliefs, risk preferences, and the aggregate endowment process. These failures are shown not to occur when agents' Epstein–Zin utility has a subjective expected utility representation due to an interdependence of effective discount factors and effective beliefs.

How to Invest and Spend Wealth in Retirement? A Utility-Based Analysis

This paper explores the optimal consumption and investment behavior of an individual who derives utility from the ratio between his consumption and an endogenous habit. We obtain closed-form policies under general utility functionals and stochastic investment opportunities, by developing a non-trivial linearization to the budget constraint. This enables us to explicitly characterize how habit formation a ffects the marginal propensity to consume and optimal stock-bond investments. We also show that in a setting which combines habit formation with Epstein-Zin utility, consumption no longer grows at unrealistically high rates at high ages and investments in risky assets decrease.

The effects of age pension on retirement drawdown choices

We compare alternative drawdown strategies in retirement to a life annuity benchmark when retirees have access to government means-tested Age Pension. By adopting Epstein-Zin utility preferences which enables disentangling relative risk aversion (RRA) from elasticity of intertemporal substitution (EIS), our results suggest that retirees possess RRA levels which are higher than the inverse of EIS. This is evidenced by their preference of phased drawdown strategies to annuitisation, providing an alternative explanation to the annuity puzzle.

Household Overconfidence in the UK Housing Market

Using the Epstein-Zin utility in a consumption-based pricing model, we identify three explanatory variables required for the prediction of house prices – changes in consumption, stock returns, and changes in human capital. When overconfident households try to predict house prices using noisy signals for those three variables, their posterior expectation is biased such that they over-respond to those signals. UK households appear to over-respond to changes in consumption and human capital, but they do not over-respond to stock returns. Interestingly, we find that when household overconfidence is removed, house prices in London have been flat since the 2008 financial crisis, indicating that the recent house price surge in London has been driven by household overconfidence in the outlook of the economy.

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.

Global Warming and a Potential Tipping Point in the Atlantic Thermohaline Circulation: The Role of Risk Aversion

The risk of catastrophes is one of the greatest threats of climate change. Yet, conventional assumptions shared by many integrated assessment models such as DICE lead to the counterintuitive result that higher concern about climate change risks does not lead to stronger near-term abatement efforts. This paper examines whether this result still holds in a refined DICE model that employs the Epstein–Zin utility specification and that is fully coupled with a dynamic tipping point model describing the evolution of the Atlantic thermohaline circulation (THC). Risk is captured by the possibility of a future collapse of the circulation and it is nourished by fat-tailed uncertainty about climate sensitivity. This uncertainty is assumed to resolve in the middle of the second half of this century and the near-term abatement efforts, which are undertaken before that point of time, can be adjusted afterwards. These modelling choices allow posing the question of whether aversion to this specific tipping point risk has a significant effect on near-term policy efforts. The simulations, however, provide evidence that it has little effect. For the more likely climate sensitivity values, a collapse of the circulation would occur in the more distant future. In this case, acting after learning can prevent the catastrophe, implying the remarkable insensitivity of the near-term policy to risk aversion. For the rather unlikely and high climate sensitivity values, the expected damage costs are not great enough to justify taking very costly measures to safeguard the THC. Our simulations also provide some indication that risk aversion might have some effect on near-term policy, if inertia limiting the speed of decarbonisation is accounted for. As it is highly uncertain how restrictive this kind of inertia will be, future research might investigate the effects of risk aversion if additional uncertainty about inertia is considered.

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 supperdifferential 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.