Stochastic Dominance of a New Portfolio Choice Approach

We develop a new portfolio construction strategy to enhance efficiency of the conventional ones. Our analysis shows this new method first-order stochastically dominates the conventional portfolio theory investment strategy. The conventional theories of optimal stock portfolio do not have any suggestion about price behaviour, especially in the future. These methods work well if stock prices behave the same as in the past. Therefore, accurate knowledge of shares prices behaviour is of great importance to improve the performance of the methods. In this way, we try to improve stocks portfolios performances by means of simulating stocks prices behaviour through the restructuring of stock price dynamics by a diffusion process with drift. This will allow us to include the behaviour of the stochastic part of the stocks prices. Making use of a multidimensional geometric Brownian motion (MGBM), we draw on the simulated results to construct the optimal portfolios in the framework of Sharpe ratio maximization method for different investment horizons. Findings indicate that for the stock market under study (Tehran) within the trading dates spanning the interval ۲۴-Mar-۲۰۰۱ to ۱۹-Sep-۲۰۲۰, return, risk (standard deviation) and the Sharpe ratios of the portfolios obtained from applying this simulation scheme for maximization of Sharpe ratio are respectively higher, lower and higher than those realized by the conventional methods.

Keywords:

Portfolio , Multidimensional Geometric Brownian Motion , Sharpe Ratio , Stochastic Dominance