Residual Momentum Based on the Fama-French Three-Factor Model
factor.formula
Fama-French three-factor model:
Residual momentum calculation formula:
in:
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The rate of return of asset i at time t. Represents the price change of asset i in a specific period of time.
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The intercept term of asset i represents the expected return of asset i when the market risk, scale and value factors are all 0. This term reflects the benchmark return level of asset i and is also an important indicator for measuring stock selection ability.
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The sensitivity (or slope coefficient) of asset i to the market risk premium RMRF. It indicates the expected change in the return of asset i when the market risk premium changes by one unit. It is also called market Beta, which measures the systematic risk exposure of asset i.
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The sensitivity of asset i to the scale premium SMB. It indicates the expected change in the return of asset i when the scale premium changes by one unit. This value measures the degree to which asset i is affected by the scale factor.
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The sensitivity of asset i to the value premium HML. It indicates the expected change in the return of asset i when the value premium changes by one unit. This value measures the degree to which asset i is affected by the value factor.
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The residual of asset i at time t is the difference between the actual return and the return predicted by the Fama-French three-factor model. This residual term represents the part of the return driven by company-specific information in addition to the influence of market, size and value factors, and is the core component of the residual momentum factor.
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The average value of the residuals of asset i during the momentum calculation window (T-12 to T-2). It is used to calculate the standard deviation of the residuals, thereby achieving the standardization of residual momentum.
factor.explanation
This factor is based on the gradual information diffusion hypothesis in behavioral finance. The hypothesis holds that market information, especially company-specific information, takes time to spread among investors, and is not instantaneous. This leads to a lag in investors' response to this information. By stripping away the impact of market risk, size, and value factors through the Fama-French three-factor model, the residual sequence can more purely reflect the value effect of company-specific information. Therefore, if the residual performance has been good over the past period of time, it means that investors may not have fully responded to the relevant information, and the stock may still continue to rise in the future, and vice versa. This factor captures the momentum effect driven by company-specific information and not fully priced by the market.