Recent studies indicate that the widespread assumption of parameter stationarity in empirical applications of asset pricing models may be inappropriate. This paper investigates the feasibility of modeling parameter instability as a sequence of persistent stable regimes. Recursive residual and log likelihood techniques are combined to detect and locate shift points. The results indicate that regime shifts are widespread, frequent, and often large enough to significantly effect empirical findings. The nature of the shifts appears to be a rotation of the regression line, indicating that correction of both alpha and beta parameters is required.