Tail risk thickness
factor.formula
Generalized Extreme Value Distribution Function (GEV):
Constraints:
in:
- :
Shape Parameter: Characterizes the thickness of the tail of the distribution. When $\gamma > 0$, it means that the distribution has a heavy-tailed characteristic (Heavy-Tailed), and the probability of extreme events is high; when $\gamma < 0$, it means that the tail of the distribution is thin; when $\gamma = 0$, the distribution degenerates into a Gumbel distribution, which belongs to an exponential distribution.
- :
Location Parameter: Indicates the center position of the extreme value distribution and affects the mean of the distribution.
- :
Scale Parameter: Measures the degree of dispersion of extreme value distribution, similar to the concept of standard deviation, and affects the width of the distribution.
- :
The minimum value of the monthly Fama-French three-factor model residual.
factor.explanation
The tail risk thickness factor is designed to capture the extreme downside risk of the stock return distribution. The factor quantifies the thickness of the left tail of the stock return distribution by fitting the extreme value distribution of the monthly minimum sequence of the residuals of the historical Fama-French three-factor model and extracting its shape parameter $\gamma$. The larger the shape parameter, the higher the risk of extreme negative returns for the stock, and the more attractive the risk-return ratio may be. Empirical studies have shown that this factor has a significant positive correlation with expected returns in the U.S. stock market, but its performance in the A-share market is relatively unstable, which may be affected by factors such as market structure and investor behavior. The effectiveness of this factor may depend on factors such as market microstructure, liquidity, and trading frequency.