Abstract
In this article, the authors establish a connection between the effective number of portfolio constituents and the ex ante ratio of specific to total portfolio risk. Portfolios with a higher effective number of constituents have lower specific risk, and the decay follows a power law. An easy rule of thumb is that doubling the effective number of constituents approximately halves the proportion of stock-specific risk. The authors investigate the proportion of specific risk of the S&P 500 Index and find that in the period 2002–2022 the S&P 500 portfolio had a proportion of specific risk below the expected range, except for the post–COVID-19 period and that the ratio was never abnormally high.
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