We show that a positive risk premium from holding high-beta stocks (versus low-beta stocks) and small-cap stocks (versus large-cap stocks) is reliably earned only after the expected stock-market volatility breaches a high threshold at about the 80th percentile. When exceeding this threshold at month t-1, then sizable positive average returns from beta and size exposure are persistently evident over months t+1 to t+6; otherwise the premia are near zero. Conversely, we find no comparable threshold behavior for the Fama-French HML, RMW, and CMA factors. Our investigation suggests several economic channels as likely contributors behind these threshold risk-return findings.

Keywords: factor risk premia, nonlinear risk-return relation, stock-market volatility, intermediary asset pricing, illiquidity risk

Continue reading here.