Portfolio formations can affect asset pricing tests
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Ingrid Lo received her PhD (economics) from the University of Western Ontario and is presently a senior lecturer in finance at the University of Waikato. Her research interests are concentrated on asset pricing and market microstructure. Department of Finance, Waikato Management School, University of Waikato, Hamilton, New Zealand E-mail: [email protected]
Abstract This paper investigates the issues of portfolio formation and asset pricing tests. Since much empirical work in finance starts with grouping individual stocks into portfolios based on a particular attribute of the stocks, this paper examines the effect of this practice and whether using individual stocks solves the problem of grouping. Canadian stock return data are used. Three asset pricing tests, the multivariate F test, the average F test and a robust specification test by Hansen and Jagannathan (Journal of Finance, 52(2), 557–90, 1997) are considered. It is found that (i) grouping of stocks based on different attributes can give different asset pricing inference using the same pool of stocks, (ii) using individual assets introduces survivorship problems and (iii) the three asset pricing tests can give different inference on the same model specification. Keywords: portfolio formation, asset pricing test, multivariate F test, average F test, robust specification test
Introduction One universal practice in any asset pricing test is to sort stocks into portfolios based on a particular attribute of the stocks. Size, estimated beta and book-to-market ratio are some of the most common attributes used in sorting stocks (see eg Fama and French, 1992, 1993; Gibbons et al., 1989; Jagannathan and Wang, 1996). There are two reasons for sorting stocks into portfolios to implement asset pricing tests: first, grouping stocks into portfolios diversifies away idiosyncratic risks of individual stocks. Secondly, the cross-section of individual stocks is very often larger than the number of time series observations available. To make estimation feasible, it
䉷 Henry Stewart Publications 1479-179X (2004)
is necessary to group stocks into portfolios. The theoretical implication of using an attribute correlated with a stocks’ return has been examined by Berk (2000) and Lo and MacKinlay (1990). Lo and MacKinlay (1990) point out that sorting without regard to the data-generating process may lead to spurious correlation between the attributes and the estimated pricing errors. They advocate using data from different sampling periods to avoid data-snooping bias. Berk (2000) shows that sorting assets into portfolios using an attribute can lead to bias toward rejecting the model when asset pricing tests are implemented within the portfolio. Since grouping of stocks is unavoidable in an
Vol. 5, 3, 203–216
Journal of Asset Management
203
Lo
empirical context, this paper studies whether different attributes used in sorting the same pool of stocks would lead to different asset pricing inference.1 This issue is important because, if different attributes used in sorti
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