Robust Growth-Optimal Portfolios

Abstract

The growth-optimal portfolio is designed to have maximum expected log return over the next rebalancing period. Thus, it can be computed with relative ease by solving a static optimization problem. The growth-optimal portfolio has sparked fascination among finance professionals and researchers because it can be shown to outperform any other portfolio with probability 1 in the long run. In the short run, however, it is notoriously volatile. Moreover, its computation requires precise knowledge of the asset return distribution, which is not directly observable but must be inferred from sparse data. By using methods from distributionally robust optimization, we design fixed-mix strategies that offer similar performance guarantees as the growth-optimal portfolio but for a finite investment horizon and for a whole family of distributions that share the same first- and second-order moments. We demonstrate that the resulting robust growth-optimal portfolios can be computed efficiently by solving a tractable conic program whose size is independent of the length of the investment horizon. Simulated and empirical backtests show that the robust growth-optimal portfolios are competitive with the classical growth-optimal portfolio across most realistic investment horizons and for an overwhelming majority of contaminated return distributions. This paper was accepted by Yinyu Ye, optimization.

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