Robust Treynor Ratio for Portfolio Selection

Abstract

The portfolio selection problem is fundamental in finance, aiming to construct an optimal portfolio that balances risk and return. Accurate calculation of risk and return is critically important, as market fluctuations can distort beta values and hinder the proper assessment of systematic risk. This study presents a robust portfolio optimization method that combines advanced beta estimation techniques (M, S, and MM estimators) with the Treynor ratio, a measure of portfolio performance, and genetic algorithms to enhance risk-adjusted returns. Using end-of-day stock returns from the Istanbul stock exchange 30 index between January 2, 2017, and December 31, 2024, the genetic algorithm is employed to identify the optimal portfolio by maximizing the robust Treynor ratio. The findings indicate that the MM estimator produces the most stable and efficient risk-adjusted return, outperforming traditional method. The optimal portfolio, identified through the genetic algorithm, consists of 16 stocks and achieves the highest Treynor ratio value. This study contributes to the field by demonstrating the integration of robust statistical methods with genetic algorithms, offering a resilient approach to portfolio management in the presence of potential outliers.