On optimal portfolio choice under stochastic interest rates

Abstract

In an economy where interest rates and stock price changes follow fairly general stochastic processes, we analyze the portfolio problem of an investor endowed with a non-traded cash bond position. He can trade on stocks, the riskless asset and a futures contract written on the bond so as to maximize the expected utility of his terminal wealth. When the investment opportunity set is driven by an arbitrary number of state variables, the optimal portfolio strategy is known to contain a pure, preference free, hedge component, a speculative element and Merton–Breeden hedging terms against the fluctuations of each and every state variable. While the first two components are well identified and easy to work out, the implementation of the last ones is problematic as the investor must identify all the relevant state variables and estimate their distribution characteristics. Using the martingale approach, we show that the optimal strategy can be simplified to include, in addition to the pure hedge and speculative components, only two Merton–Breeden-type hedging elements, however large is the number of state variables. The first one is associated with interest rate risk and the second one with the risk brought about by the co-movements of the spot interest rate and the market prices of risk. The implementation of the optimal strategy is thus much easier, as it involves estimating the characteristics of the yield curve and the market prices of risk only rather than those of numerous (a priori unknown) state variables. Moreover, the investor's horizon is shown explicitly to play a crucial role in the optimal strategy design, in sharp contrast with the traditional decomposition. Finally, the role of interest rate risk in actual portfolio risk management is emphasized.