Historical return skewness
factor.formula
Sample return skewness calculation formula:
in:
- :
The size of the time window used to calculate the skewness, which represents the number of trading days included in the time window.
- :
Time index, indicating the tth trading day in the time window, ranging from 1 to T.
- :
The daily return of the ith asset on the tth trading day. The calculation method is usually: $r_{it} = \frac{P_{it} - P_{it-1}}{P_{it-1}}$, where $P_{it}$ is the closing price of the ith asset on the tth trading day.
- :
The average daily return of the i-th asset in the time window T is calculated as: $\bar{r}i = \frac{1}{T} \sum{t=1}^{T} r_{it}$.
- :
The return skewness of the i-th asset in the time window T is used to measure the asymmetry of the return distribution of the asset.
factor.explanation
There is a certain relationship between the historical yield skewness factor and the future yield of stocks. Generally speaking, stocks with high positive skewness often mean that their yield distribution is right-skewed, that is, the probability of large positive returns is relatively high, but it is also accompanied by greater uncertainty, so investors may overestimate them, resulting in lower future returns. On the contrary, stocks with high negative skewness may be underestimated by the market, resulting in the possibility of excess returns. Therefore, this factor can be used as an important reference for risk control and stock selection. In addition, this factor is also related to the behavioral bias of investors. Investors often prefer assets with positive skewness, which leads to their overestimation, further affecting the future risk premium. It should be noted that the yield skewness factor is not a single stock selection factor. Its effectiveness may be affected by multiple factors such as market environment, asset class, time window selection, etc., and should be considered in combination with other factors.