This study takes into account two important features found in most time series, namely, nonlinearity and structural instability, in the test of the Sharpe–Lintner CAPM. Using data on BM- and size-sorted quintile portfolios, we implement the multiple structural change approach of Bai and Perron (2003 Bai, J and Perron, P. 2003. Computation and analysis of multiple structural change models. Journal of Applied Econometrics, 18: 1–22.
) and have the following interesting findings. First, there is overwhelming evidences in support of at least one break in betas for all the portfolios under investigation. Second, in most but not all cases, there exist asymmetries in betas, indicating that the risk measures can be different depending on the market conditions. Finally, in contrast to the findings that all the testing results by single regressions cannot reject the CAPM, we find that the CAPM can be consistent with the data in some regimes but may appear to be inconsistent with the data in some other regimes once the possibility of simultaneous nonlinearity and parameter instability are taken into account. This particularly appealing feature has been completely ruled out under the conventional single-equation framework.