Abstract
We studied the relationship between expected returns and thirteen risk measures, namely Expected Loss, Value at Risk, Expected Shortfall, Expectile Value at Risk, Entropic, Maximum Loss, Standard Deviation, Negative Semi-Deviation, Shortfall Deviation, Expected Loss Deviation, Shortfall Deviation Risk, Deviation Expectile Value at Risk, and Deviation Entropic. We consider measures that assess the loss, deviation, and both risk concepts simultaneously in a sample of United States (US) stock returns from January 1982 to January 2021. Analyzing the difference between the returns of the higher risk and lower risk portfolios, we report a significant difference for all risk measures tested, except for the Shortfall Deviation. We also perform time-series regressions using the returns of the Fama–French three factors and the Momentum factor as independent variables. When controlling factors are included in the model alphas are not significant, suggesting evidence of no risk premium.
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