Systemic tail risk exposure
factor.formula
Market tail risk intensity ($\lambda_t$):
Systematic tail risk exposure of individual stocks ($\beta_i$):
in:
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It is the 25% quantile of the distribution of daily returns of all stocks in month t, which represents the downside risk threshold of the market in that month.
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It is the kth daily return rate among all daily returns of all stocks in the tth month that is less than $\mu_t$, which is used to capture the specific return situation of the market within the downside risk threshold.
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It is the total number of daily returns of all stocks in month t that are less than $\mu_t$, that is, the number of trading days in that month when the market return is lower than the downside risk threshold, which is used to measure the sample size of the market in downside risk.
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is the market tail risk intensity in the tth month, which is obtained by taking the standardized sum average of all daily returns below $\mu_t$, and it reflects the intensity of the market's downside risk in that month.
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is the daily return of stock i in month t.
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is the intercept term of stock i in the time series regression, which indicates the expected value of the stock return when the market tail risk is zero.
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is the systematic tail risk exposure of stock i, which measures the sensitivity of the stock return to changes in the intensity of market tail risk. A positive value indicates that the stock return changes in the same direction as the market tail risk, and a negative value indicates an opposite change.
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It is the residual term of the regression model, representing the random fluctuation of individual stock returns that cannot be explained by the model.
factor.explanation
This factor evaluates the downside risk characteristics of individual stocks by analyzing the exposure of individual stock returns to the market's systematic tail risk. Market tail risk reflects the possibility and intensity of extreme negative events in the market. This risk factor can capture the performance of individual stocks under extremely adverse market conditions. Stocks with high systematic tail risk exposure tend to perform worse in a down market and may be accompanied by higher expected returns. Therefore, this factor can be used to identify individual stocks with significant downside risk exposure, assisting in risk management and return enhancement of the portfolio.