Residual skewness
factor.formula
Residual skewness calculation formula:
Capital Asset Pricing Model (CAPM) Regression:
Fama-French three-factor model regression:
in:
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The residual skewness value of stock i in the specified time window. This value measures the skewness of the distribution of stock idiosyncratic returns. A positive value indicates a right-skewed distribution, and a negative value indicates a left-skewed distribution.
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The rate of return of stock i at time t is usually a simple rate of return or a logarithmic rate of return. The rate of return calculation needs to be selected according to the actual situation and should be kept consistent.
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The risk-free rate of return at time t is usually represented by the short-term Treasury bond yield. In practice, other asset yields with low-risk characteristics may also be used.
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The intercept term (or alpha) of stock i represents the expected return of stock i without considering market risk factors. In CAPM and the three-factor model, the intercept term represents the excess return of the stock and is an important indicator for measuring stock selection ability.
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In the CAPM model, $\beta_i$ represents the market risk exposure of stock i, measuring the sensitivity of stock returns to changes in market returns. A ( \beta ) value greater than 1 indicates that the stock's volatility is greater than the market, and a value less than 1 indicates that the volatility is less than the market. In the FF three-factor model, $\beta_{1,i}$ represents the market risk exposure, $\beta_{2,i}$ represents the scale risk exposure, and $\beta_{3,i}$ represents the value risk exposure.
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The market return at time t usually uses the index return representing the entire market trend as a proxy variable, such as the S&P 500 Index or the CSI 300 Index.
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The residual term (or idiosyncratic return) of stock i at time t represents the part of the return that cannot be explained by the model. The residual term is the basis for calculating the residual skewness.
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The market factor at time t represents the overall market risk premium and is equal to the market return minus the risk-free rate.
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The size factor at time t represents the excess return of small-cap company stocks relative to large-cap company stocks.
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The value factor at time t represents the excess return of stocks of companies with high book-to-market ratios relative to stocks of companies with low book-to-market ratios.
factor.explanation
The residual skewness factor is a quantitative factor based on statistical skewness, which measures the degree of skewness of the part of stock returns that cannot be explained by the market or traditional factors. This factor captures the asymmetry of the idiosyncratic return distribution. In asset pricing theory, investors' preferences affect the price of assets. Assets with higher positive skewness may be underestimated by investors, while assets with negative skewness may be overestimated. In quantitative investment, residual skewness is usually negatively correlated with stock returns. This means that stocks with higher positive residual skewness (meaning that their idiosyncratic returns tend to be more right-skewed) tend to show lower future returns, which is contrary to the traditional risk-return relationship and is a low-risk anomaly. Therefore, residual skewness can be used to identify and capture this inefficient market behavior.