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Most asset pricing models postulate a positive relationship between a stock portfolio's expected returns and risk, which is often modeled by the variance of the asset price. This paper uses GARCH in mean models to examine the relationship between mean returns on a stock portfolio and its conditional variance or standard deviation. After estimating a variety of models from daily and monthly portfolio return data, we conclude that any relationship between mean returns and own variance or standard deviation is weak. The results suggest that investors consider some other risk measure to be more important than the variance of portfolio returns.
Baillie et al. (Fri,) studied this question.