Stochastic Portfolio Theory Optimization and the Origin of Alternative Asset Allocation Strategies

Abstract

What is the theoretical reason why a particular alternative allocation strategy, or a combination thereof, should offer a superior return vs. risk tradeoff? Can we derive an optimal alternative allocation strategy from first principles, both from an absolute return perspective, to identify the most appropriate long-term strategic benchmark, and from a relative return perspective, to identify the alternative allocation strategy with the highest expected information ratio relative to a market-cap weighted index? We attempt to answer these questions, by building on the stochastic portfolio theory framework of Fernholz, to study the evolution of portfolio wealth, both in absolute terms and relative to a market index. We prove that the portfolio maximizing the expected value of logarithmic portfolio wealth at a fixed level of volatility differs from the traditional mean-variance portfolio solution by the linear combination of three further terms: an equally weighted portfolio, a risk parity portfolio, and a high cash flow rate of return portfolio. Most importantly, we prove that, given any market capitalization weighted index, the portfolio maximizing relative logarithmic growth with respect to this index deviates from the market benchmark by the linear combination of four subportfolios: an equally weighted portfolio, a risk parity portfolio, a high cash flow rate of return portfolio, and a global minimum variance portfolio. Consistent with previous empirical research, we prove that an investor can profit from diversification effects when spreading his investment across different alternative asset allocation methods, and we show the four alternative asset allocation building blocks which constitute the optimal portfolio.