Market Return Co-skewness (Zhu Jiantao Edition)
factor.formula
Market return coskewness formula (CS):
in:
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The return of stock i at time t. This return is usually calculated using the natural logarithm of the return, and the calculation formula is $r_{i,t} = ln(P_{i,t}) - ln(P_{i,t-1})$, where $P_{i,t}$ represents the price of stock i at time t.
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The average return of stock i over the past n trading days is calculated as $\bar{r}{i} = \frac{1}{n} \sum{t=1}^{n} r_{i,t}$.
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The return of the market benchmark (such as the CSI 300 Index) at time t. This return is usually calculated using the natural logarithm of the return, with the formula $r_{m,t} = ln(P_{m,t}) - ln(P_{m,t-1})$, where $P_{m,t}$ represents the price of the market benchmark at time t.
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The average return of the market benchmark over the past n trading days, calculated as $\bar{r}{m} = \frac{1}{n} \sum{t=1}^{n} r_{m,t}$.
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The number of historical trading days used to calculate coskewness is generally 20 trading days. In order to ensure the validity of the data, at least 15 valid daily yield data are required during the calculation period.
factor.explanation
This factor is based on the theory of coskewness and captures the asymmetric risk of stock returns relative to market returns. Coskewness measures the relationship between stock returns and the square of market returns, that is, how stock returns change when the market returns deviate from its mean. This factor is normalized using the third-order central moment (skewness) of the market return, so it can be understood as the sensitivity of stock returns to the skewness of market returns. Specifically, this factor assumes that stocks with low systematic skewness (i.e., stock returns are negatively correlated with the square of the market return) have a higher risk premium. This is because investors tend to avoid stocks that fall more when the market falls. Therefore, buying a portfolio of stocks with low systematic skewness may bring excess returns. This factor is a risk factor and is related to the momentum effect. It can also be regarded as a sentiment factor because it reflects the market's pricing of stock risk preferences.