Implementing Statistical Criteria to Select Return Forecasting Models: What Do We Learn? Peter Bossaerts California Institute of Technology Pierre Hillion INSEAD Statistical model selection criteria provide an informed choice of the model with best external(i.e.,out-of-sample)validity.Therefore they guard against overfitting ("data snooping").We implement several model selection criteria in order to verify recent evidence of predictability in excess stock returns and to determine which variables are valuable predictors.We confirm the presence of in-sample predictability in an international stock market dataset,but discover that even the best prediction models have no out-of-sample forecasting power.The failure to detect out-of-sample predictability is not due to lack of power. 1.Introduction Almost all validation of financial theory is based on historical datasets. Take,for instance,the theory of efficient markets.Loosely speaking,it asserts that securities returns must not be predictable from past information. Numerous studies have attempted to verify this theory,and ample evidence of predictability has been uncovered.This has led many to question the validity of the theory. Quite reasonably,some have recently questioned the conclusiveness of such findings,pointing to the fact that they are based on repeated reeval- uation of the same dataset,or,if not the same,at least datasets that cover similar time periods.For instance,Lo and MacKinlay (1990)argue that Address corresponcence to Peter Bossaerts.HSS 228-77.California Institute of Technology,Pasadena, CA 91125.or e-mail:pbs@rioja.caltech.edu.P.Bossaerts thanks First Quadrant for financial support through a grant to the Califoria Institute of Technology.First Quadrant also provided the data that were used in this study.The article was revised in part when the first author was at the Center for Economic Research.Tilburg University.P.Hillion thanks the Hong Kong University of Science and Technology for their hospitality while doing part of the research.Comments from Michel Dacorogna,Rob Engle,Joel Hasbrouck.Andy Lo,P.C.B.Phillips,Richard Roll,Mark Taylor,and Ken West.from two anonymous referees.and the editor(Ravi Jagannathan),as well as seminar participants at the Hong Kong University of Science and Technology.University of California San Diego.University of Califomia Santa Barbara the 1994 NBER Spring Conference on Asset Pricing,the 1994 Western Finance Association Meetings. and the 1995 CEPR/LIFE Conference on International Finance are gratefully acknowledged. The Review of Financial Stdies Summer 1999 Vol.12,No.2,pp.405-428 e 1999 The Society for Financial Studies 0893-9454/99/$1.50