18 Journal of Economic Literature,Vol.XXXV (March 1997) B.Market Model The market model is an example of a one The market model is a statistical factor model.Other multifactor models model which relates the return of any include industry indexes in addition to given security to the return of the mar- the market.William Sharpe (1970)and ket portfolio.The model's linear specifi- Sharpe,Gordon Alexander,and Jeffery cation follows from the assumed joint Bailey(1995,p.303)provide discussion of index models with factors based on in- normality of asset returns.For any secu- rity i the market model is dustry classification.Another variant of a factor model is a procedure which calcu- Rr=0+β，Rmt+e0 (3) lates the abnormal return by taking the difference between the actual return and E(it=0) var()= a portfolio of firms of similar size,where where Rit and Rmt are the period-t re- size is measured by market value of eq- turns on security i and the market port- uity.In this approach typically ten size folio,respectively,and E is the zero groups are considered and the loading on the size portfolios is restricted to unity. mean disturbance term.di,Bi,and o2 are the parameters of the market model. This procedure implicitly assumes that In applications a broad based stock in- expected return is directly related to market value of equity. dex is used for the market portfolio, with the S&P 500 Index,the CRSP Generally,the gains from employing multifactor models for event studies are Value Weighted Index,and the CRSP limited.The reason for the limited gains Equal Weighted Index being popular is the empirical fact that the marginal choices. The market model represents a poten- explanatory power of additional factors the market factor is small,and hence, tial improvement over the constant mean there is little reduction in the variance of return model.By removing the portion the abnormal return.The variance re- of the return that is related to variation duction will typically be greatest in cases in the market's return,the variance of where the sample firms have a common the abnormal return is reduced.This in turn can lead to increased ability to de- characteristic,for example they are all tect event effects.The benefit from us- members of one industry or they are all ing the market model will depend upon firms concentrated in one market capi- talization group.In these cases the use the R2 of the market model regression. The higher the R2 the greater is the vari- of a multifactor model warrants consid- eration. ance reduction of the abnormal return, The use of other models is dictated by and the larger is the gain data availability.An example of a normal C.Other Statistical Models performance return model implemented in situations with limited data is the mar- A number of other statistical models ket-adjusted return model.For some have been proposed for modeling the events it is not feasible to have a pre- normal return.A general type of statisti- event estimation period for the normal cal model is the factor model.Factor model parameters,and a market-ad- models are motivated by the benefits of justed abnormal return is used.The mar- reducing the variance of the abnormal ket-adjusted return model can be viewed return by explaining more of the vari- as a restricted market model with o con- ation in the normal return.Typically the strained to be zero andβ；constrained to factors are portfolios of traded securities. be one.Because the model coefficients