Idiosyncratic return skewness
factor.formula
The formula for calculating the idiosyncratic return skewness is:
CAPM regression:
Fama-French three-factor model regression:
in:
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The idiosyncratic return skewness of stock i in a specified time window reflects the asymmetry of the residual distribution.
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The return of stock i at time t, usually expressed as a logarithmic return.
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The risk-free rate of return at time t is usually approximated by the yield on short-term government bonds.
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The intercept term of stock i, representing the average excess return of stock i, should ideally be close to zero.
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In the CAPM model, the market risk factor of stock i measures the sensitivity of stock returns to changes in market returns.
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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 residual term of stock i at time t represents the idiosyncratic return of stock i that cannot be explained by the model, and can be regarded as a unique risk factor of stock i in addition to systematic risk.
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The market factor at time t, that is, the market portfolio return, is defined in the Fama-French model similarly to that in the CAPM model.
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The size factor at time t represents the difference between the return on the small-cap stock portfolio and the return on the large-cap stock portfolio.
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The value factor at time t represents the difference between the return on the portfolio of stocks with high book-to-market ratio and the return on the portfolio of stocks with low book-to-market ratio.
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The time window size used when calculating the idiosyncratic skewness, that is, the length of the residual sequence.
factor.explanation
Idiosyncratic return skewness measures the degree of skewness of the unique part of stock returns that cannot be explained by systematic risk factors (such as market risk, scale risk, and value risk). This factor captures the asymmetry of the distribution of stock residual returns. A higher idiosyncratic return skewness means that the residual distribution is right-skewed, and vice versa. Empirical studies have shown that idiosyncratic return skewness is negatively correlated with future stock returns, that is, stocks with higher idiosyncratic return skewness tend to have lower expected future returns, which is a counterintuitive low-risk anomaly.