Pitfalls in linear models for style analysis

We discuss the statistical properties of return-based OLS style analysis introduced by Sharpe (1992). The aim of style analysis is to infer a fund managers investment decisions using only publicly available data on the fund performance and on the time evolution of market indexes. We show that the model proposed by Sharpe suffers of relevant drawbacks, most notably that it fails to yield correct results even in the simple case of a buy-and-hold strategy that only invests in the market indexes. Under this hypothesis we show that a model linear in index levels, as opposed to index returns, estimated via a Kalman filter avoids Sharpes model drawbacks. We further extend our analysis to strategies where the fund manager policy changes with time and the asset classes in which the fund manager invests are not known exactly. In this last case we show that a style analysis is possible only conditional to either an orthogonality hypothesis on the active investment strategy, or by the introduction of suitable instrumental variables.The authors are grateful to the editor and an anonymous referee for many comments which greatly helped in improving the paper. The authors are, obviously, fully responsible for any remaining error.