BFS 2002

Contributed Talk

Time to Wealth Goals in Capital Accumulation

Leonard MacLean, William Ziemba, Yuming Li

This paper considers the problem of continuous investment of capital in risky assets in a dynamic capital market. The information filtration process and the capital allocation decisions are considered separately. The filtration is based on a Bayesian model for asset prices, and an (empirical) Bayes estimator for current price dynamics is developed from the price history. Given the conditional price dynamics, investors allocate wealth to achieve their financial goals efficiently in the time domain. The price updating and wealth reallocations occur when control limits on the wealth process are attained. A Bayesian fractional Kelly strategy is optimal at each rebalancing, assuming that the risky assets are jointly lognormally distributed. The strategy minimizes the expected time to the upper wealth limit while maintaining a high probability of reaching that goal before falling to a lower wealth limit. The fractional Kelly strategy is a blend of the log-optimal portfolio and cash and is equivalently represented by a negative power utility function. By rebalancing when control limits are reached, the wealth goals approach provides greater control over downside risk and upside growth.