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AbstractIn this paper I relate the risk premia in the stock and bond markets to the conditional volatility of returns and time‐varying reward‐to‐volatility variables. I find that the relation between the expected returns on the stocks and bonds and the volatility of returns is time varying. I provide an approach for evaluating the relative importance of the time‐varying volatility of returns and reward‐to‐volatility variables to explain the predictability of risk premia for stock and bond returns. I show that changing reward‐to‐volatility variables explain more predictable variation in the risk premia for stocks and bonds than changing volatility of returns.

AbstractWe assess the relationship between regime‐dependent volatility in S&P 500, economic policy uncertainty, the S&P 500 bull and bear sentiment spread (bb_sp), as well as the Chicago Board Options Exchange's VIX over the period 2000–2018. Our findings from two‐covariate GARCH–MIDAS (GM) methodology, regime switching Markov Chain, and quantile regressions suggest that the association of realized volatility and sentiment varies across high‐ and low‐volatility regimes and depends on investors' sensitivity toward incidents of market uncertainties under these regimes. The findings suggest that these indicators may not be useful in volatility forecasting, especially under high‐volatility regimes.