Over 1960 to 2017, 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 an approximate top-quintile threshold. The high conditional average returns with this nonlinear risk-return phenomenon are persistently evident over months t+1 to t+6 following a volatility-threshold breach in month t-1. Conversely, this nonlinear risk-return phenomenon is not comparably evident for the Fama-French HML, RMW, and CMA factors. We present additional evidence that suggests habit-consumption utility, intermediary asset pricing, and stochastic-volatility asset pricing are likely contributing channels.