Residual Momentum Factor Based on CAPM
factor.formula
Calculate the CAPM regression residuals:
Compute residual momentum:
in:
- :
The rate of return of stock i at time t is usually calculated as (current price - price at previous moment) / price at previous moment.
- :
The risk-free interest rate at time t is usually approximated by the short-term Treasury bond rate.
- :
The market return at time t is usually approximated by the return of an index representing the overall market (such as the CSI 300 Index).
- :
The intercept term of the CAPM regression for stock i represents the expected value of the excess return of stock i relative to the market (when the market return is zero).
- :
The Beta value of stock i measures the sensitivity of stock i's return to changes in market returns. β > 1 indicates that the stock volatility is greater than the market, β < 1 indicates that the stock volatility is less than the market, and β = 1 indicates that the stock volatility is consistent with the market.
- :
The CAPM regression residual of stock i at time t represents the unique return of stock i that cannot be explained by the model, that is, the degree to which the return of stock i deviates from the value predicted by the CAPM model. The larger the residual, the greater the impact of unique factors on the stock.
- :
The residual momentum of stock i at time t represents the cumulative residual returns over the past 11 periods (usually monthly). The cumulative multiplication form is used here to more accurately capture the effect of compounding of returns.
factor.explanation
The residual momentum factor is based on the hypothesis of gradual information diffusion, which believes that investors' response to company-specific information is lagging, resulting in a continuous return signal in the residual term. Specifically, after eliminating the impact of overall market volatility using the CAPM model, the residual term reflects the impact of information specific to individual stocks. Investors usually react slowly to this information, which leads to the residual momentum effect: if the residual term of a stock has been positive for a period of time in the past, the stock may continue to rise in the future, and vice versa. Therefore, we can construct a residual momentum factor by calculating the cumulative residual yield over the past period of time to capture investment opportunities brought about by this information lag.
It is worth noting that the residual momentum in the factor formula uses a cumulative multiplication calculation method. Compared with the cumulative method, the cumulative multiplication can better reflect the compound interest effect of the yield and measure the cumulative yield more accurately. At the same time, the calculation period in the formula is 11, not 12 in the original data, in order to keep consistent with the common momentum calculation period in the industry and avoid the problem of "survivor bias" that may occur in the yield calculation.