Residual Momentum Based on CAPM
factor.formula
CAPM regression model:
Residual Momentum Calculation:
in:
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The total return of stock i at time t, including dividends and capital gains.
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The risk-free rate at time t is usually approximated by the Treasury bond yield.
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The market return at time t is usually approximated by the return of a broad-based index, such as the CSI 300 Index or the S&P 500 Index.
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The intercept term of stock i represents the expected excess return of stock i when the market risk premium is zero, and can also be regarded as a measure of the risk-adjusted return of the stock relative to the CAPM model.
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The systematic risk coefficient of stock i, which measures the sensitivity of stock i's return to changes in the market return. A beta value greater than 1 indicates that the stock is more volatile than the market, while a beta value less than 1 indicates that the stock is less volatile than the market.
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The residual return of stock i at time t represents the return that is unique to stock i and cannot be explained by the CAPM model. It is also called idiosyncratic risk or unsystematic risk and is the basis for calculating residual momentum.
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The residual momentum value of stock i at time t is obtained by multiplying the residual returns of the past 11 months (from t-2 to t-12).
factor.explanation
The residual momentum factor is based on the gradual information diffusion hypothesis. The hypothesis holds that there is a time lag in the market's response to company-specific information. When information is disclosed, investors do not react immediately to company-specific information, but slowly absorb and adjust their investment behavior. This slow response causes residual returns to persist over a period of time, thus forming a residual momentum effect. Specifically, the CAPM model attempts to explain the part of stock returns that is related to market risk, while residual returns represent information related to the company's own characteristics. Using the residual returns over the past period of time to construct a momentum factor can capture the market's under-reaction to these specific information. In other words, if a stock has a positive residual return over the past period of time, it indicates that the market may have underestimated the intrinsic value of the stock, and its residual returns are likely to continue to be positive in the future.