The detection and consequences of beta nonstationarity

The development of return-generating models, some of which rely on beta, has provided a means of examining the abnormal performance of stock returns around the time of an event. One of the problems in using such models is that beta is apparently nonstationary.

This study uses simulated daily stock returns to examine the ability of the cumulative sum of the squared recursive residuals (CSRR) and the Quandt log-likelihood ratio (QLLR) to identify a given level of beta change and the effect of a given level of beta change on the results of abnormal returns tests. This study also uses daily stock returns surrounding the listing and delisting of the firms' bonds on Standard and Poor's "CreditWatch" to examine the nature of capital asset pricing model (CAPM) parameter nonstationarity and the effect of allowing for CAPM parameter nonstationarity on abnormal returns test results for these firms.

Analysis of the simulated security returns suggests that, given the range of error variances generally found in daily stock returns, the CSRR and QLLR show little ability to identify even a sudden 50 percent beta change and are highly sensitive to outliers.

This low power appears not to present a problem. Even a 50 percent sudden beta change leaves the rejection frequencies and average p-values of the abnormal returns tests and the average abnormal return and mean square error of the CAPM regressions largely unchanged.

In the CreditWatch samples, the CSRR indicates parameter nonstationarity for nearly every security over a 4-year period. Comparison of the CSRR results with the results of traditional parameter nonstationarity tests suggests that the significant CSRR findings are more often associated with heteroscedasticity or outliers than with a beta change.

In the CreditWatch section, the cumulative average residuals appear sensitive to the periods used in estimating the CAPM parameters and the method used to allow for the apparent parameter nonstationarity. This sensitivity is apparently due primarily to instability in the alpha estimates.