Instability in Risk Premia

Abstract

We apply a new methodology for identifying pervasive and discrete changes (``breaks'') in cross-sectional risk premia and find empirical evidence that these are economically important for understanding returns on US stocks. Size and value risk premia have fallen off to the point where they are insignificantly different from zero at the end of the sample. The market risk premium has also declined systematically over time but remains significant and positive as does the momentum risk premium. We construct a new instability risk factor from cross-sectional differences in individual stocks' exposure to time-varying risk premia and show that this factor earns a premium comparable to that of commonly used risk factors. Using industry- and characteristics-sorted portfolios, we show that some breaks to the return premium process are broad-based, affecting all stocks regardless of industry- or firm characteristics, while others are limited to stocks with specific style characteristics. Moreover, we identify distinct lead-lag patterns in how breaks to the risk premium process impact stocks in different industries and with different style characteristics.