Why Naive $ 1/N $ Diversification Is Not So Naive, and How to Beat It?
理论上证明当维度高时，1/N等权组合优于复杂估计策略，并探讨了在小N时结合估计规则、大N时结合异常或机器学习组合来超越它的条件。
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.