Performance v. Turnover: A Story by 4,000 Alphas

Abstract: We analyze empirical data for 4,000 real-life trading portfolios (U.S. equities) with holding periods of about 0.7-19 trading days. We find a simple scaling C ~ 1/T, where C is cents-per-share, and T is the portfolio turnover. Thus, the portfolio return R has no statistically significant dependence on the turnover T. We also find a scaling R ~ V^X, where V is the portfolio volatility, and the power X is around 0.8-0.85 for holding periods up to 10 days or so. To our knowledge, this is the only publicly available empirical study on such a large number of real-life trading portfolios/alphas.