Beating a constant weight benchmark: easier done than said

Abstract

1 We determine a simple dynamic benchmark for asset allocation by solving an optimal stochas- 2 tic control problem for outperforming the traditional constant proportion benchmark. An ob- 3 jective function based on a time averaged quadratic deviation from an elevated benchmark is 4 proposed. We argue that this objective function combines the best features of tracking error and 5 tracking difference. Assuming parametric models of the stock and bond processes, a closed form 6 solution for the optimal control is obtained. The closed form optimal control is then clipped to 7 prevent use of excessive leverage, and to prevent trading if insolvent. Monte Carlo computations 8 using this clipped control are presented which show that for modest levels of outperformance 9 (i.e. 80-170 bps per year), this easily implementable strategy outperforms the traditional con- 10 stant proportion benchmark with high probability. We advocate this clipped optimal strategy 11 as a suitable benchmark for active asset allocation. 12