BEATING A CONSTANT WEIGHT BENCHMARK: EASIER DONE THAN SAID

Abstract

We determine a simple dynamic benchmark for asset allocation by solving an optimal stochastic control problem for outperforming the traditional constant proportion benchmark. An objective function based on a time averaged quadratic deviation from an elevated benchmark is proposed. We argue that this objective function combines the best features of tracking error and tracking difference. Assuming parametric models of the stock and bond processes, a closed form solution for the optimal control is obtained. The closed form optimal control is then clipped to prevent use of excessive leverage, and to prevent trading if insolvent. Monte Carlo computations using this clipped control are presented which show that for modest levels of outperformance (i.e. 80–170[Formula: see text]bps per year), this easily implementable strategy outperforms the traditional constant proportion benchmark with high probability. We advocate this clipped optimal strategy as a suitable benchmark for active asset allocation.