Why Naive $ 1/N $ Diversification Is Not So Naive, and How to Beat It?

Ming Yuan and Guofu Zhou

Journal of Financial and Quantitative Analysis, 2024, vol. 59, issue 8, 3601-3632

Abstract: We show theoretically that the usual estimated investment strategies will not achieve the optimal Sharpe ratio when the dimensionality is high relative to sample size, and the $ 1/N $ rule is optimal in a 1-factor model with diversifiable risks as dimensionality increases, which explains why it is difficult to beat the $ 1/N $ rule in practice. We also explore conditions under which it can be beaten, and find that we can outperform it by combining it with the estimated rules when $ N $ is small, and by combining it with anomalies or machine learning portfolios, conditional on the profitability of the latter, when $ N $ is large.

Date: 2024
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