Linear regression residual net profit
factor.formula
Z(NetProfitᵢ) = α + β₁Z(NonOperatingIncomeᵢ) + β₂Z(CashPaidEmployeesᵢ) + εᵢ
in:
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Represents the i-th quarter, where i ranges from -N+1 to 0, with 0 representing the most recent quarter.
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Indicates the number of historical quarters used for regression. The default value is 8, which means using the data from the most recent 8 quarters.
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It represents the Z-Score standardized value of the net profit in the i-th quarter, that is, (net profitᵢ - mean net profit) / standard deviation of net profit. The standardization process is performed on the same quarter of all samples.
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It represents the Z-Score standardized value of non-operating income in the i-th quarter, that is, (non-operating incomeᵢ - mean non-operating income) / standard deviation of non-operating income. The standardization process is performed on the same quarter of all samples.
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It represents the Z-Score standardized value of the cash flow paid to and for employees in the i-th quarter, that is, (cash flowᵢ - cash flow mean) / cash flow standard deviation. The standardization process is performed on the same quarter of all samples.
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The intercept term of the linear regression model.
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The regression coefficient of non-operating income on net profit reflects the impact of changes in non-operating income on net profit.
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The regression coefficient of cash flow paid to employees on net profit reflects the impact of changes in cash flow paid to employees on net profit.
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Represents the residual of the linear regression model in the i-th quarter. ε₀ (i.e., the residual when i=0) is the linear regression residual net profit factor value. The residual represents the part of the net profit that cannot be explained by non-operating income and cash flow paid to employees, that is, the pure net profit signal after eliminating the noise.
factor.explanation
In financial analysis, net profit is often affected by many factors, some of which may be noise, that is, parts that are irrelevant to the company's actual operating conditions or have weak predictive power. This factor uses linear regression to strip off the part of net profit that is affected by non-operating income and cash flow paid to employees, retaining the residual part, thereby extracting a purer net profit signal with higher stock selection predictive power. Specifically, non-operating income may have one-time or non-recurring gains, which have limited representativeness for the company's sustained profitability; and although cash flow paid to employees is related to the company's operations, it is not directly related to net profit, so this part of the data may also affect the purity of net profit. By eliminating these influences through regression, the signal-to-noise ratio of net profit can be improved, thereby improving its predictive power as a factor. Z-Score standardization ensures that different quarters and different financial indicators are regressed under the same dimension, improving the robustness of the regression.