Beating the Market: Dynamic Asset Allocation with a Market Portfolio Benchmark

Abstract

Beating the market portfolio is a problem faced by many investors. Here, we formulate and solve a dynamic allocation problem that maximizes the utility of relative wealth of the investor's portfolio to that of the market portfolio. We also allow the investor to control the deviation of the optimal allocation from the market portfolio itself, and using stochastic control techniques, provide explicit closed form expressions for the optimal allocation. In addition, we demonstrate how the optimal portfolio can be factored into five passive rule-based portfolios: (i) global minimum variance portfolio; (ii) high-growth portfolio; (iii) high-cash-flow portfolio; (iv) equal-weight portfolio; and (v) risk-parity portfolio. Finally, some numerical experiments based on calibration to real-world data are presented to illustrate the risk-reward profile of the optimal allocation in comparison to these and other commonly used strategies.