In this study, we test whether investor learning, herding, and prospect theory explain the variation of beta across different return regimes and return frequencies. Empirically, we use quantile regressions to analyze beta change on the French financial market from January 2000 to December 2012. For daily data, we find a larger estimated impact of systematic shocks on extreme quantiles of firm's returns as compared to intermediate quantiles. The beta pattern is probably symmetrically suggesting that whatever the type of shocks have similar effects. This finding can be explained by herding behavior and investor learning. These behaviors lead to beta- increasing in the extreme returns case. For monthly data, beta evolves asymmetrically across return regimes with a greater impact of the market in the lower tail of returns distribution. This finding provides strong evidence in favor of prospect theory explanation. Overall, constant beta estimated by ordinary-least squares overestimates the systematic risk of stock in normal times and underestimate the risk in extreme conditions or financial crisis.
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