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This paper analyzes the risk-return trade-off in Europe using recent data from 11 European stock markets. After relaxing linear assumptions in the risk-return relation by introducing a new approach which considers the current state of the economy, we are able to obtain positive and significant evidence for a risk-return trade-off for low volatility states; however, this evidence turns to be lower or even non-significant during periods of high volatility. Maintaining the linear assumption over the risk-return trade-off leads to non-significant estimations for all cases analyzed. These results are robust among countries despite the conditional volatility model used. This concludes that the controversial results in previous studies may be due to strong linear assumptions when modeling the risk-return trade-off. We argue that this previous evidence can only be viewed as partial evidence that fails to cover the global behavior of the relation between return and risk.

This paper estimates linear and non-linear GARCH models to find optimal hedge ratios with futures contracts for some of the main European stock indexes. By introducing non-linearities through a regime-switching model, we can obtain more efficient hedge ratios and superior hedging performance in both in-sample and out-sample analysis compared with other methodologies (constant hedge ratios and linear GARCH). Moreover, non-linear models also reflect different patterns followed by the dynamic relationship between the volatility of spot and futures returns during low and high volatility periods.

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