The Structural Changes in the Ff Three-Factor Model and its Robustness in the Bear-Bull Market Periods

Abstract

We examine the robustness of the Fama-French three-factor model in several bear and bull market periods. Data on bull and bear market periods are from the website of Global Financial Data. The data on the monthly returns of the 25 Fama French portfolios and the explanatory variablesmR, SMB, and HML are taken from the website of Dr. Kenneth French. We test for the significance of the individual regression parameters as well as for the equality of the coefficient vectors in each of the adjacent bear-bull periods. To make sure that our tests are not influenced by heteroskadisticity we use Toyoda's test to test the equality of the coefficient vectors in each of the adjacent bull-bear periods. We find that the model performs equally well in both bear and bull periods. In comparison to earlier bull-bear periods, however, the coefficient of determination decreases significantly in later periods. Furthermore, using cumulative sum of squares of recursive residuals and log likelihood ratio techniques, we find a structural change in the model in the year 2000. We use the Welch test to identify which regression parameters induce this structural change. We find that all the coefficients associated with explanatory variables undergo significant changes; however, the constant term remains insignificant. We conclude that the parameters of the Fama-French three-factor model are generally not influenced by bear and bull market conditions. This finding may make the FF three-factor model more useful—the prediction of future bull-bear market period may become redundant in estimating the risk premium. The regime change in the FF three-factor model in the year 2000 indicates that one should use post-1999 data to compute the parameters of the FF three-factor model to estimate the risk premium.