Aggregate volatility expectations and threshold CAPM

• We model asset prices in which betas change due to uncertainty about volatility.
• We use the range of VIX index to proxy uncertainty about aggregate volatility.
• Betas change when uncertainty about volatility is beyond a certain threshold.
• Small and value stocks are riskier in periods of high uncertainty about volatility.
• Market risk premium is positive in periods of low uncertainty about volatility.

We propose a volatility-based capital asset pricing model (V-CAPM) in which asset betas change discretely with respect to changes in investors’ expectations regarding near-term aggregate volatility. Using a novel measure to proxy uncertainty about expected changes in aggregate volatility, i.e. monthly range of the VIX index (RVIX), we find that portfolio betas change significantly when uncertainty about aggregate volatility expectations is beyond a certain threshold level. Due to changes in their market betas, small and value stocks are perceived as riskier than their big and growth counterparts in bad times, when uncertainty about aggregate volatility expectations is high. The proposed model yields a positive and significant market risk premium during periods when investors do not expect significant uncertainty in near-term aggregate volatility. Our findings support a volatility-based time-varying risk explanation.