This study introduces novel mathematical methods to analyze the optimal portfolio size for investment portfolios over time, taking into account investors with different skill levels. The optimization is performed using both Sharpe ratio and semivariance metrics.
Firstly, the research assesses the impact of portfolio diversification on an annual basis for investors categorized as poor, average, and strong based on the 10th, 50th, and 90th percentiles of risk-adjusted returns, respectively.
Secondly, a comprehensive regression experiment explores quantiles of risk-adjusted returns as a function of portfolio size across varying levels of investor ability, investigating trends and curvature within these functions.
Lastly, the study examines the optimal portfolio size for investors with different skill levels in a continuous temporal manner, leveraging over 5 years of data.