This paper employs weighted least squares to examine the risk-return relation by applying high-frequency data from four … returns and expected risk. However, by using quantile regressions, we find that the risk-return relation moves from negative … to positive as the returns’ quantile increases. A positive risk-return relation is valid only in the upper quantiles. The …

risk is a nonlinear function of market volatility … volatility as measured by the VIX. We propose a new estimator for the shape of the nonlinear forecasting relationship that …, revealing flight to safety: expected returns increase for stocks when volatility increases from moderate to high levels, while …

We investigate the risk-return trade-off on the US and European stock markets. We investigate the non-linear risk … market portfolio. We find that the risk-return trade-off is significantly positive at the upper tail (0.9 quantile), where …, for the median (0.5 quantile), the risk-return trade-off is insignificant. These results are recovered for the US industry …