Systematic Skewness Risk Premium Factor
factor.formula
Systematic skewness risk premium factor formula:
in:
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is the residual term after linear regression of the daily excess return of stock i on the daily excess return of the market in the past K months. This residual term represents the part of the return of stock i that cannot be explained by the market return, that is, the return volatility unique to stock i.
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is the daily excess return of the market after mean centering in the same period. The calculation method is: $\epsilon_m = r_m - \bar{r_m}$, where $r_m$ is the daily excess return of the market, and $\bar{r_m}$ is the average of the daily excess return of the market in the past K months. The centering process ensures that the market fluctuations revolve around the mean.
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is the length of the lookback period in months. Commonly used K values include 1, 6, and 12. To ensure the robustness of the calculation results, at least 15 valid daily yield data are required within the calculation window.
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The expected value or average operator indicates the average calculation of time series data. For example, E[$\epsilon_i \epsilon_m^2$] represents the average of the product of the daily residual of stock i and the square of the daily residual of the market in the past K months.
factor.explanation
This factor measures the systematic skewness risk of stock returns relative to market returns. The logic behind it is that investors generally dislike negatively skewed assets, that is, assets with a left-skewed return distribution, because such assets may carry a higher risk of loss. Therefore, stocks with low systematic skewness may have a higher premium due to their lower negative skewness risk, thereby generating excess returns. The momentum effect is closely related to this systematic skewness risk. Momentum portfolios with low expected returns tend to have higher negative skewness, which can explain why high momentum stocks usually perform worse than low momentum stocks.