Mean-Variance Asset Allocation for Long Horizons

01 December 2001
By Dr. James Jordan with Department of Finance, George Washington University Professor Isabelle Bajeux-Besnainou

The authors investigate whether mean-variance portfolio theory can produce the conventional wisdom that investors with long horizons should make a large initial allocation to stocks and then decrease the allocation as time passes. For the case of a risk-free asset and a stock index following geometric brownian motion, we derive closed-form solutions for the mean-variance portfolio problem allowing continuous rebalancing based on realized prices and wealth (called a stochastic strategy).

This optimal stochastic strategy is in general a conventional wisdom strategy as it involves large initial allocation to stocks which then decreases with time. The authors relate this strategy to the concave strategies described by Perold and Sharpe and explain the role played by relative risk aversion in this result. They also derive the optimal deterministic strategy (predetermined schedule of weights, independent of new price and wealth realizations) and find it to be a constant-weight strategy.

This paper was published in the December 2001 issue of Finance, the Journal of the French Finance Association, Vol. 22, pp. 7-23.