Market Co-skewness (Zhu Jiantao Version)
factor.formula
Market Co-skewness Formula CS:
in:
- :
The return of stock i at time t. This return is usually calculated using the logarithmic return or arithmetic return.
- :
The return of a market benchmark (e.g., CSI 300 Index or CSI 500 Index) at time t. This return is usually calculated using logarithmic return or arithmetic return. The choice of market benchmark should match the investment scope and style of stock i.
- :
The average return of stock i over the past n trading days is calculated as $\bar{r}{i} = \frac{1}{n} \sum{t=1}^{n} r_{i,t}$.
- :
The average return of the market benchmark over the past n trading days, calculated as $\bar{r}{m} = \frac{1}{n} \sum{t=1}^{n} r_{m,t}$.
- :
The number of trading days for backtest calculation, i.e. the length of the time window. Usually 20 trading days are selected, but it can be adjusted according to the specific strategy and backtest results. In order to ensure the validity of the calculation, the number of valid trading days (i.e. trading days with yield data) in the time window should be at least 15, otherwise the coskewness value at that time point should be regarded as a missing value.
factor.explanation
The market coskewness factor measures the asymmetric sensitivity of individual stock returns to changes in market returns. Specifically, the numerator calculates the covariance between the individual stock return and the square of the market return, and the denominator calculates the third-order central moment (skewness) of the market return. A lower market coskewness value may mean that when the market falls, the individual stock will not fall so sharply, or when the market rises, the individual stock will not rise so obviously. Therefore, the risk of such stocks may be considered lower by investors, resulting in a risk premium. In quantitative investment, this factor is often used to construct a risk-diversified investment portfolio, especially in momentum strategies. Selecting stocks with low market coskewness can be used as a means to enhance returns and reduce risks. It should be noted that the choice of market benchmark and the choice of look-back period n will affect the stability and predictive power of the factor value.