In this paper, we show that conditions derived under the CAPM ensure only weak exogeneity in a linear regression setting. Since strong exogeneity is not guaranteed, the OLS estimator of CAPM beta is only consistent but not necessarily unbiased. We provide empirical evidence that individual daily stock returns exibit regime-switching patterns and may violate strong exogeneity conditions. As such, the OLS estimator of CAPM beta is likely biased. Based on the empirical patterns of daily stock returns, we use three regime-switching models to illustrate thatthe OLS estimator of CAPM beta can be consistent but at the same time biased. Simulation results based on these three regime-switching models show that biases of the OLS beta estimator can be substantial.