In-sample and Out-of-sample Sharpe Ratios of Multi-factor Asset Pricing Models RAYMOND KAN, XIAOLU WANG, and XINGHUA ZHENG∗ This version: November 2020 ∗Kan is from the University of Toronto, Wang is from Iowa State University, and Zheng is from Hong Kong University of Science and Technology. We thank Svetlana Bryzgalova, Peter Christoffersen, Victor DeMiguel, Andrew Detzel, Junbo Wang, Guofu Zhou, seminar participants at Chinese University of Hong Kong, London Business School, Louisiana State University, Uni- versity of Toronto, and conference participants at 2019 CFIRM Conference for helpful comments. Corresponding author: Raymond Kan, Joseph L. Rotman School of Management, University of Toronto, 105 St. George Street, Toronto, Ontario, Canada M5S 3E6; Tel: (416) 978-4291; Fax: (416) 978-5433; Email:
[email protected]. In-sample and Out-of-sample Sharpe Ratios of Multi-factor Asset Pricing Models Abstract For many multi-factor asset pricing models proposed in the recent literature, their implied tangency portfolios have substantially higher sample Sharpe ratios than that of the value- weighted market portfolio. In contrast, such high sample Sharpe ratio is rarely delivered by professional fund managers. This makes it difficult for us to justify using these asset pricing models for performance evaluation. In this paper, we explore if estimation risk can explain why the high sample Sharpe ratios of asset pricing models are difficult to realize in reality. In particular, we provide finite sample and asymptotic analyses of the joint distribution of in-sample and out-of-sample Sharpe ratios of a multi-factor asset pricing model. For an investor who does not know the mean and covariance matrix of the factors in a model, the out-of-sample Sharpe ratio of an asset pricing model is substantially worse than its in-sample Sharpe ratio.