Dynamic Asset Allocation for Stocks, Bonds, and Cash

01 June 2003
By Dr. James Jordan with George Washington University School of Business and Public Management Professor Isabelle Bajeux-Besnainou and CNAM Chair of Finance Roland Portait

Closed-form solutions for HARA optimal portfolios are obtained in a dynamic portfolio optimization model in three asset (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 constant duration 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.

This paper was published in The Journal of Business, 2003, Vol. 76, No. 2, 263-287.