Multivariate test of Sharpe–Lintner CAPM with time-varying beta

Abstract

This study considers two important features of most time series analysis, i.e. nonlinearity and time-varying risk, to test the validity of Sharpe–Lintner Capital asset pricing model (CAPM). By using data on BM- and size-sorted quintile portfolios, this study resolves the problem of error-in-variables by estimating the firm-specific betas, of which the Kalman filter and the betas obtained from based-sectional analysis are used. From pooled data, this study finds time variance in the systematic risk for certain portfolios. Additionally, the proposed model rejects the Shape–Lintner CAPM. Firm BM(size) appears to be the reason for the rejection of CAPM and firm earnings in excess of predicted CAPM appear to increase(decrease) with bigger(smaller) BM(size).