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 ${\rm{T}}{{\rm{R}}_{{\rm{jl}}}}$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. ${\rm{T}}{{\rm{R}}_{{\rm{jl}}}}$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.