Residual market value deviation
factor.formula
Log-Market Value Regression Model:
The formula represents the regression of the logarithmic market value of individual stocks on a cross-section. The following is a detailed explanation of each parameter in the formula:
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The logarithmic market value of stock i in period t is calculated as ln(market value of stock i in period t). Logarithmic processing can reduce the heteroscedasticity in market value data and make the regression results more robust.
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The industry dummy variable of stock i in period t usually adopts CITIC's first-level industry classification or other industry classification standards. This variable is used to capture the differences in market capitalization levels between different industries. For example, the average market capitalization levels of the pharmaceutical industry and the real estate industry may be significantly different.
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The logarithmic net assets of stock i in period t, calculated as ln(net assets of stock i in period t). Net assets are a key measure of a company's book value and usually have a strong correlation with market capitalization.
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The positive part of the net profit of stock i in period t. When the net profit is positive, take the absolute value of the net profit; when the net profit is negative or zero, take the value of zero. Using the logarithm ln(NI^+_{it}) can smooth the impact of this indicator and conform to the distribution characteristics of financial data.
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The negative part of the net profit of stock i in period t. When the net profit is negative, take the absolute value of the net profit; when the net profit is positive or zero, take the value of zero. Using the logarithm ln(NI^-_{it}), the impact of this indicator can be smoothed and conform to the distribution characteristics of financial data. Here I<0 is an indicator function. When the net profit is negative, I<0 is 1, otherwise it is 0. By multiplying it with the absolute value of the negative net profit, the negative net profit part is separated.
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The leverage ratio of stock i in period t is usually measured by the debt-to-asset ratio. The leverage ratio reflects the extent to which a company uses debt financing. A higher leverage ratio may increase the company's financial risk and have a negative impact on its market value.
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In period t, the regression coefficient corresponding to the dummy variable of industry j represents the intercept of industry j in the market value regression model.
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In the tth period, the regression coefficient corresponding to the logarithm of net assets indicates the magnitude of the change in the logarithm of market value for every unit increase in the logarithm of net assets.
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In the t period, the regression coefficient corresponding to the positive logarithm of net profit indicates the magnitude of the change in the logarithm of market value for every unit increase in the logarithm of positive net profit.
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In the t period, the regression coefficient corresponding to the logarithm of negative net profit indicates the magnitude of the change in the logarithm of market value for every unit increase in the logarithm of negative net profit.
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In the tth period, the regression coefficient corresponding to the leverage ratio indicates the magnitude of the logarithmic change in market value for every unit increase in the leverage ratio.
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The residual of stock i in period t is the deviation between the actual logarithmic market value and the logarithmic market value predicted by the model. This residual is considered to be unexplained by fundamental factors and reflects the degree of irrational market pricing of stocks. The larger the residual, the greater the degree to which the market's pricing of the stock deviates from the fundamental value.
factor.explanation
The residual market value deviation factor fits the reasonable market value of stocks based on a series of fundamental factors (such as industry, net assets, net profit and leverage ratio) through a cross-sectional regression model. The model is designed to identify possible deviations in market pricing. The residual term of the regression model, that is, the difference between the actual market value and the market value predicted by the model, is regarded as "idiosyncratic market value", representing the part of the market value that cannot be explained by fundamentals. A positive residual value means that the actual market value of the stock is higher than the reasonable market value predicted by the model, indicating that the stock may be overvalued; while a negative residual value may suggest that the stock is undervalued. This factor is often used to capture market pricing errors and implement value investment strategies.