Dynamic Asset Allocation for Stocks, Bonds, and Cash*

Abstract

Closed-form solutions for HARA optimal portfolios are obtained in a dynamic portfolio optimization model in three assets (stocks, bonds and cash) with stochastic interest rates. A Vasicek-type model of stochastic interest rates with a correlated stock price is assumed. The HARA solution can be expressed as a buy and hold combination of a zero-coupon bond with maturity matching the investor's horizon and a "CRRA mutual fund," which is the optimal portfolio for a CRRA investor expressed in terms of the weights on cash, stock, a constantduration bond fund and the (redundant) bond with maturity matching the investor's horizon (a generalization of the Merton's (1971) result of constant weight in stock for a CRRA investor, derived for two assets with constant interest rates). This simple characterization facilitates insights about investor behavior over time and under different economic scenarios and allows fast computation time (without simulation or other numerical methods). We use the model to provide explanations of the Canner-Mankiw-Weil (1997) asset allocation puzzle, the use of "convex" (momentum) and "concave" (contrarian) investment strategies and other features of popular investment advice. The model illuminates clearly the role of the different market parameters, the composition of initial investor wealth, and relative risk aversion in portfolio strategies.

Dynamic Asset Allocation with Uncertain Jump Risks: A Pathwise Optimization Approach

“…In Bajeux-Besnainou et al [3], they obtain closed-form solutions for HARA optimal dynamic portfolios in pure-diffusion models. Specifically, they employ the duality results developed by Karatzas et al [20] in complete markets.…”

“…Here we consider a realistic case with a > 0, that is, the relative risk aversion is decreasing with x. In Bajeux-Besnainou et al [3], they interpret the constant a as "subsistence level".…”

“…See Section 3 for more discussion on the number of stocks and the number of risk sources. 3 The state variable process and the stock price vector in our model are governed by the same Brownian motion B(t). Note that when d ≥ 2, the instantaneous correlation between the diffusions of X t (σ X i dB t ) and stock return (σ b j dB t ) may range from -1 to 1 for each i = 1, ..., l and j = 1, ..., m. Hence in general the state variables are not perfectly correlated with the continuous part of stock prices even if they are driven by the same multi-dimensional Brownian motion.…”

Portfolio Investment in an Intertemporal Setting

“…Samuelson (1991) obtained decreasing portfolio weights for CRRA preferences by assuming mean-reverting stock returns. Bajeux-Besnainou et al (2003) were able to explain the asset allocation puzzle raised by Canner et al (1997) by including stochastic interest rates in the analysis of the portfolio choice problem faced by a HARA (hyperbolic absolute risk aversion) investor in a Vasicek (1977) market. By explicitly including a redundant asset (a bond fund with constant maturity), they were able to decouple the -risk free asset‖ role played by the zero-coupon bond with maturity equal to the investment horizon, and the hedging role against interest rate fluctuations played by the bond fund of constant maturity.…”

Economic Costs and Benefits of Imposing Short-Horizon Value-at-Risk Type Regulation

“…For example, Kim and Omberg (1996) and Wachter (2002) study the optimal portfolio allocation where the price of risk is mean-reverting. Bajeux-Besnainou, Jordan and Portait (2003) and Sorensen (1999) solve the optimal investment problem when interest rates are stochastic. This paper is related to the literature studying the optimal portfolio trading strategy under constraints.…”