Outperformance Testing of a Dynamic Assets Portfolio Selection Supplemented with a Continuous Paths Levy Process

Abstract

This study aims at getting a better performance for optimal stock portfolios by modeling stocks prices dynamics through a continuous paths Levy process. To this end, the share prices are simulated using a multi-dimensional geometric Brownian motion model. Then, we use the results to form the optimal portfolio by maximizing the Sharpe ratio and comparing the findings with the outputs of the conventional model. To examine the robustness of the results, we have evaluated its performance for different investment horizons and various volumes of price information over a long period (approximately twenty years) in the Tehran Stock Exchange (TSE). Findings indicate that within the trading dates spanning the interval 24-Mar-2001 to 19-Sep-2020, the return of the portfolios obtained from applying this simulation scheme for maximization of Sharpe ratio is (244% on average) higher and their risk (standard deviation) are lower (1227% on average) than those realized by the conventional methods. Additionally, a comparison of the simulation approach with a performance of the actual market portfolios indicates that the Sharpe ratios of the simulation method are higher (0.055% on average) than those resulting from the total market performances. The results of the stochastic dominance test show that our proposed strategy has a first-order stochastic dominance (FSD) over the conventional one and market portfolios, that means at each level of cumulative distribution, the Sharpe ratio of our method is higher, and as FSD test makes no assumptions about the curvature of investors' utility functions, these results do not depend on the degree of risk aversion of investors, and as long as investors prefer a higher Sharpe ratio, they would be better off if they follow our proposed strategy.