Advances in factor replication

Factor investing has gained widespread acceptance among institutional investors. Some investors believe it is preferable to stratify the investment universe into factors to manage portfolio risk more effectively, while other investors focus on factors because they believe they yield risk premiums. Factors such as economic variables are not directly investable. Investors, therefore, need to identify a combination of securities that tracks the movements in the economic variable. Other factors, however, are directly investable, such as securities with a certain attribute. Often times, though, investors choose to invest in a subset of the factor securities that are inexpensive to trade. In order to identify the best factor-tracking portfolio, investors must estimate covariances from historical observations whose realizations in the future are prone to several types of estimation error. We introduce a non-parametric procedure to account for estimation error, which enables us to incorporate the relative stability of covariances directly into the factor replication process. We show that adjusting for the stability of covariances in this way produces replicating portfolios that are significantly more reliable than portfolios that are blind to estimation error or formed using Bayesian shrinkage