Portfolio Turnover when IC is Time Varying

Abstract

We develop new formulas for the turnover and leverage of mean-variance optimal long-short market neutral portfolios, where active weights are obtained using a factor model conditional mean forecast, and a conditional forecast error covariance matrix that reflects strategy risk. We show that for eight commonly used quantitative factors, the turnovers and leverages derived using our long-short formulas are quite close to what the practitioners actually implement. We further carry out extensive simulations for long-only active portfolios and develop a highly accurate empirical formula that relates long-only turnover to long-short turnover, a transfer coefficient, portfolio target tracking error, strategy risk, and a benchmark choice coefficient. Our result shows that when the proper risk model is used in factor investing, the optimal portfolio’s turnover and leverage are well within reasonable practically implementable ranges even if no additional constraints are imposed.

Keywords: turnover, leverage, factor model, conditional mean forecast, conditional forecast error covariance matrix, transfer coefficient, fundamental law of active management

JEL Classification: G, C1, C2, C6