On the risk return relationship

While the risk return trade-off theory suggests a positive relationship between the expected return and the conditional volatility, the volatility feedback theory implies a channel that allows the conditional volatility to negatively affect the expected return. We examine the effects of the risk return trade-off and the volatility feedback in a model where both the return and its volatility are influenced by news arrivals. Our empirical analysis shows that the two effects have approximately the same size with opposite signs for the daily excess returns of seven major developed markets. For the same data set, we also find that a linear relationship between the expected return and the conditional standard deviation is preferable to polynomial-type nonlinear specifications. Our results have a potential to explain some of the mixed findings documented by previous studies.