Tail risk thickness
factor.formula
Generalized Extreme Value Distribution Function (GEV):
Constraints:
in:
- :
Shape Parameter, which measures the thickness of the tail distribution. $\gamma$ > 0 indicates a heavy-tailed distribution (such as a t-distribution), $\gamma$ < 0 indicates a light-tailed distribution (a distribution with an upper limit), and $\gamma$ = 0 corresponds to a Gumbel distribution.
- :
Location Parameter, which determines the center position of the distribution.
- :
Scale Parameter, which determines the discreteness of the distribution, must be greater than 0.
- :
The observed monthly minimum residual return
factor.explanation
The tail risk thickness factor extracts the shape parameter by fitting the generalized extreme value distribution of the residual yield minimum sequence. This parameter can effectively capture the tail characteristics of the yield distribution, especially focusing on extreme downside risk. The larger the shape parameter $\gamma$, the thicker the tail of the yield distribution, the higher the probability of extreme negative yield events, and the greater the risk. Empirical studies have shown that in some markets (such as the U.S. stock market), this factor is positively correlated with the expected returns of stocks, but there may be differences in performance in the A-share market, which requires further study. This factor is a supplement to the traditional volatility factor. It focuses on the extreme cases of the yield distribution rather than the overall volatility level.