Tail risk and excess return of mutual funds: loss-premium balance hypothesis

This paper studies the relationship between tail risk exposure and mutual fund returns using samples from January 2007 to December 2022. The TRjl calculated by Generalized Extreme Value Distribution captures the negative correlation between returns and tail risk, with a one-standard-deviation increase (0.0119) leading to 0.24% decrease in three-factor alpha quarterly. TRjl also captures the nonlinear effect in short term, yet the nonlinearity diminishes due to the reversal of the return-risk exposure curve of equity funds in long term. We propose Loss-Premium Balance Hypothesis, positing that risk loss and premium effect are dominant under different tail risk exposures, respectively.