Optimal funding and investment strategies in defined contribution pension plans under Epstein-Zin utility

A defined contribution pension plan allows consumption to be redistributed from the plan member’s working life to retirement in a manner that is consistent with the member’s personal preferences. The plan’s optimal funding and investment strategies therefore depend on the desired pattern of consumption over the lifetime of the member. We investigate these strategies under the assumption that the member has an Epstein-Zin utility function, which allows a separation between risk aversion and the elasticity of intertemporal substitution, and we also take into account the member’s human capital. We show that a stochastic lifestyling approach, with an initial high weight in equity-type investments and a gradual switch into bond-type investments as the retirement date approaches is an optimal investment strategy. In addition, the optimal contribution rate each year is not constant over the life of the plan but reflects trade-offs between the desire for current consumption, bequest and retirement savings motives at different stages in the life cycle, changes in human capital over the life cycle, and attitude to risk

Strategic Asset Allocation in a Continuous-Time VAR Model

This note derives an approximate solution to a continuous-time intertemporal portfolio and consumption choice problem. The problem is the continuous-time equivalent of the discrete-time problem studied by Campbell and Viceira (1999), in which the expected excess return on a risky asset follows an AR(1)process, while the riskless interest rate is constant. The note also shows how to obtain continuous-time parameters that are consistent with discrete-time econometric estimates. The continuous-time solution is numerically close to that of Campbell and Viceira and has the property that conservative long-term investors have a large positive intertemporal hedging demand for stocks.

Does Portfolio Optimization Pay?

All HARA-utility investors with the same exponent invest in a single risky fund and the risk-free asset. In a continuous time-model stock proportions are proportional to the inverse local relative risk aversion of the investor (1/γ-rule). This paper analyses the conditions under which the optimal buy and holdportfolio of a HARA-investor can be approximated by the optimal portfolio of an investor with some low level of constant relative risk aversion using the 1/γ-rule. It turns out that the approximation works very well in markets without approximate arbitrage opportunities. In markets with high equity premiums this approximation may be of low quality.HARA-utility, portfolio choice, certainty equivalent, approximated choice

Portfolio Choice for HARA Investors: When Does 1/γ (not) Work?

In the continuous time-Merton-model the instantaneous stock proportions are inversely proportional to the investorâs local relative risk aversion γ. This paper analyses the conditions under which a HARA-investor can use this 1/γ-rule to approximate her optimal portfolio in a finite time setting without material effects on the certainty equivalent of the portfolio payoff. The approximation is of high quality if approximate arbitrage opportunities do not exist and if the investorâs relative risk aversion is higher than that used for deriving the approximation portfolio. Otherwise, the approximation quality may be bad.HARA-utility, portfolio choice, certainty equivalent, approximated choice

A Multivariate Model of Strategic Asset Allocation

Much recent work has documented evidence for predictability of asset returns. We show how such predictability can affect the portfolio choices of long-lived investors who value wealth not for its own sake but for the consumption their wealth can support. We develop an approximate solution method for the optimal consumption and portfolio choice problem of an infinitely-lived investor with Epstein-Zin utility who faces a set of asset returns described by a vector autoregression in returns and state variables. Empirical estimates in long-run annual and postwar quarterly US data suggest that the predictability of stock returns greatly increases the optimal demand for stocks. The role of nominal bonds in long-term portfolios depends on the importance of real interest rate risk relative to other sources of risk. We extend the analysis to consider long-term inflation-indexed bonds and find that these bonds greatly increase the utility of conservative investors, who should hold large positions when they are available.

Efficient Intertemporal Allocations with Recursive Utility

In this article, our objective is to determine efficient allocations in economies with multiple agents having recursive utility functions. Our main result is to show that in a multiagent economy, the problem of determining efficient allocations can be characterized in terms of a single value function (that of a social planner), rather than multiple functions (one for each investor), as has been proposed thus far (Duffie, Geoffard and Skiadas (1994)). We then show how the single value function can be identified using the familiar technique of stochastic dynamic programming. We achieve these goals by first extending to a stochastic environment Geoffard's (1996) concept of variational utility and his result that variational utility is equivalent to recursive utility, and then using these results to characterize allocations in a multiagent setting.

Optimal life cycle asset allocation : understanding the empirical evidence.

We show that a life-cycle model with realistically calibrated uninsurable labor income risk and moderate risk aversion can simultaneously match stock market participation rates and asset allocation decisions conditional on participation. The key ingredients of the model are Epstein–Zin preferences, a fixed stock market entry cost, and moderate heterogeneity in risk aversion. Households with low risk aversion smooth earnings shocks with a small buffer stock of assets, and consequently most of them (optimally) never invest in equities. Therefore, the marginal stockholders are (endogenously) more risk averse, and as a result they do not invest their portfolios fully in stocks.

Social Security and Household Portfolio Allocation

The entitlement to social security retirement benefits is a major component of aggregate household wealth. This paper focuses on the impact of social security annuities on household portfolio allocation, extending existing optimizing models of portfolio allocation to explicitly consider the role of social security. The model is implemented using cross-section data. The partial equilibrium impacts of changes in social security benefits on portfolio choice and composition are small but precisely measured. The general equilibrium impacts on asset markets of a social security policy change (focusing onlinks between social security and dynamic wealth accumulation and between social security benefits and private pension benefits) are generally much larger.

Risk Aversion and Intertemporal Substitution in the Capital Asset Pricing Model

When tastes are represented by a class of generalized preferences which -- unlike traditional Von-Neumann preferences -- do not confuse behavior towards risk with attitudes towards intertemporal substitution, the true beta of an asset is, in general, an average of its consumption and market betas. We show that the two parameters measuring risk aversion and intertemporal substitution affect consumption and portfolio allocation decisions in symmetrical ways. A unit elasticity of intertemporal substitution gives rise to myopia in consumption-savings decisions (the future does not affect the optimal consumption plan), while a unit coefficient of relative risk aversion gives rise to myopia in portfolio allocation (the future does not affect optimal portfolio allocation). The empirical evidence is consistent with the behavior of intertemporal maximizers who have a unit coefficient of relative risk aversion and an elasticity of intertemporal substitution different from 1.