Specific return volatility
factor.formula
Specific return volatility:
Fama-French three-factor model regression:
in:
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The logarithmic return of stock i at time t. Using logarithmic returns can better handle the non-normal distribution of returns.
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The intercept term of stock i represents the expected return when the market, size and value factors are all 0, that is, the specific return level of the stock. It is usually used to measure the stock selection ability of stocks and is also called Jensen's Alpha.
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The market risk premium factor at time t is equal to the market portfolio return minus the risk-free rate. It represents the risk level of the overall stock market. The market factor is usually calculated by constructing the return of a market index (such as the CSI 300 Index) minus the risk-free rate.
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The size risk factor at time t represents the excess return of small-cap stocks relative to large-cap stocks. SMB is usually calculated as: the mean return of the high-cap group minus the mean return of the low-cap group.
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The value risk factor at time t represents the excess return of high book-to-market ratio stocks relative to low book-to-market ratio stocks. HML is usually calculated as: the mean return of the high book-to-market ratio group minus the mean return of the low book-to-market ratio group.
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The residual term of stock i at time t represents the specific return part that cannot be explained by the Fama-French three-factor model. This residual term is considered to be the specific risk of stock i and may contain company-level information or noise.
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The goodness of fit of the Fama-French three-factor model regression indicates the proportion of stock return changes that the model can explain. The value range of $R^2$ is [0,1]. The closer $R^2$ is to 1, the stronger the explanatory power of the model.
factor.explanation
The idiosyncratic return volatility factor reflects the part of individual stock returns that cannot be explained by the three common risk factors of market, size and value, that is, the idiosyncratic risk of individual stocks. The higher the value, the more susceptible the individual stock returns are to the company's own fundamental information or market noise, and the lower the correlation with the overall market style. High idiosyncratic return volatility is usually associated with higher speculative behavior and uncertainty, indicating that individual stocks may have higher information asymmetry and pricing deviation risks. Low idiosyncratic return volatility means that the volatility of individual stock returns comes more from factors such as market, size or value, and the volatility is relatively more predictable.