Portfolio optimization: a comparison between the Mean-Variance Optimization model, Mean Absolute Deviation model, and Mean-Semi Absolute Deviation model

Abstract

This study investigates the comparative performance of three portfolio optimization models— Mean-Variance Optimization (MVO), Mean Absolute Deviation (MAD), and Mean Semi- Absolute Deviation (MSAD)—in the context of the Kenyan stock market. The MAD and MSAD have been suggested as improvements to MVO since they use alternative risk measures. The study investigates which model generates a better optimized portfolio while emphasizing on the role of duration and time in determining the appropriate model to use in emerging markets characterized by significant economic volatility. Using monthly stock return data from 2011 to 2020, the study evaluates the models' performance across different investment horizons and distinct 12-month periods, and a comparison is done using the Sharpe and Sortino ratios. The findings were inconsistent across different durations and time periods. They revealed that while the MAD model outperformed during periods of high market uncertainty, the MSAD model proved effective for medium-term (2 years) investment horizons, and the MVO outperformed in short-term investment horizons (1 year). The results underscore the critical importance of duration and time over broader macroeconomic factors in portfolio optimization, providing practical insights for fund managers and investors. These findings contribute to the growing body of knowledge on alternative risk measures and their applicability in dynamic, real-world environments.

Keywords: Portfolio optimization, Mean-Variance Optimization (MVO), Mean Absolute Deviation (MAD), and Mean Semi-Absolute Deviation (MSAD).