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This study develops a multi-factor framework where not only market risk isconsidered but also potential changes in the investment opportunity set.Although previous studies find no clear evidence about a positive andsignificant relation between return and risk, favourable evidence can beobtained if a non-linear relation is pursued. The positive and significantrisk-return trade-off is essentially observed during low volatility periods.However, this relationship is not obtained during periods of high volatility.Also, different patterns for the risk premium dynamics in low and highvolatility periods are obtained both in prices of risk and market riskdynamics.

The non-linear trade-off between return and risk: a regime-switching multi-factor framework