This research paper introduces novel mathematical methods to investigate how optimal portfolio size evolves over time, with particular attention to investors of varying skill levels. The study categorizes investors into poor, average, and strong groups based on their risk-adjusted returns (10th, 50th, and 90th percentiles respectively) and examines how portfolio diversification benefits each group differently on an annual basis. The methodology includes regression experiments that analyze quantiles of risk-adjusted returns as functions of portfolio size, testing for trends and curvature across different investor abilities.

The paper's most significant contribution is its temporal analysis spanning more than 20 years of data, which reveals that optimal portfolio strategies differ substantially based on investor skill. Strong investors achieve better results with concentrated portfolios, while poor investors benefit from diversification. For average investors, the optimal portfolio size varies considerably over time without clear patterns, suggesting a more complex relationship between ability and diversification. These findings challenge one-size-fits-all approaches to portfolio construction and provide evidence-based guidance for tailoring investment strategies to individual skill levels.