This paper investigates the risk-return trade-off by taking into account the model specification problem. Market volatility is modeled to have two components, one due to the diffusion risk and the other due to the jump risk. The model implies Merton’s ICAPM in the absence of leverage effects, whereas the return–volatility relations are determined by interactions between risk premia and leverage effects in the presence of leverage effects. Empirically, I find a robust negative relationship between the expected excess return and the jump volatility and a robust negative relationship between the expected excess return and the unexpected diffusion volatility. The latter provides an indirect evidence of the positive relationship between the expected excess return and the diffusion volatility.

We find a strong and robust positive relationship between individual downside variance premia (DVP)–the difference between risk-neutral and physical expected downside variances–and future corporate bond returns. The spread portfolio that longs the high DVP bond portfolio and shorts the low DVP bond portfolio earns a statistically significant excess return of 0.37% (0.42%) per month in value- (equal-)weighted returns. The alpha estimates from various factor models remain statistically significant and economically substantial. The predictive power of the downside variance premium is stronger in noninvestment-grade (long-maturity) corporate bonds than in investment-grade (short-maturity) bonds. We show that the downside variance premium positively relates to the likelihood of future default and cash flow uncertainty and negatively relates to future cash flows.