Market capitalization nonlinearity deviation
factor.formula
Market value nonlinear deviation factor formula:
Regression model formula:
in:
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is the logarithmic market value of stock i in period t, that is, the natural logarithm of the total market value of stock i in period t.
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is the logarithmic market value factor value of stock i in period t, that is, the logarithmic market value factor, which is the dependent variable of the regression model.
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is the intercept term in period t, which indicates the theoretical factor value when the market value is 0.
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It is the regression coefficient of the logarithmic market value factor in the tth period, indicating the corresponding change in the factor value for every unit change in the logarithmic market value, reflecting the linear relationship between the market value and the factor value.
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is the residual term of the regression model, representing the degree of deviation between the actual logarithmic market value factor value of stock i in period t and the predicted value of the linear regression model. After the residual term is subsequently devalued and standardized, the market value nonlinear deviation factor $LNCAP_{i,t}^{D3}$ can be obtained.
The weighted least squares (WLS) regression is performed on the cross-sectional logarithmic market value factor values of all stocks in period t. The regression weight is the square root of the market value of each stock, which aims to reduce the impact of large-cap stocks in the regression process and enhance the robustness of the model.
factor.explanation
The core idea of the market value nonlinear deviation factor, also known as the mid-market value deviation factor, is to utilize the nonlinear characteristics between market value and stock returns. Although there is a small market value premium in the A-share market, the relationship between market value and returns is not a simple linear relationship. As the market value increases, its marginal effect on returns decreases, that is, the increase in returns brought by market value growth will gradually decrease. If the linear market value factor is used directly, the expected returns of mid-market value stocks may be overestimated. This factor extracts the residual between the market value and its linear expectation through the WLS regression model, which is the market value nonlinear deviation factor. This factor reflects the degree to which the market value of an individual stock deviates from its linear market value expectation. The construction logic of this factor is that if the market value of a stock deviates from the market value level expected by the linear model, the actual performance of the stock may also deviate from expectations. The residual of mid-market value stocks is usually small, which means that its market value is close to the linear model prediction; while the residual value of extremely small and large market value stocks is large, indicating that there is a large deviation between its market value and the linear prediction. This factor is a negative factor. The larger the absolute value, the greater the nonlinear deviation of the market value. It should be noted that the deviation here refers to the deviation relative to the linear model, not the size of the market value itself.