Valuation regression deviation
factor.formula
Assume that the valuation level of individual stocks $VR_t^i$ is determined by the long-term trend term $Trend_t^i$ and the short-term deviation term $Deviation_t^i$:
The long-term trend term $Trend_t^i$ can be considered to be driven by both industry fundamental trends and stock-specific factors, and is calculated as:
In order to capture the dynamic relationship between the valuation level $VR_t^i$ and its long-term equilibrium trend $C^i \times SVR_t^i$, an error correction model is introduced for modeling:
Among them, $ECM_{t-1}^i$ represents the error correction term of the previous period (time t-1), which is defined as:
Finally, the valuation regression deviation $DR_t^i$ is defined as the relative deviation between the current valuation level $VR_t^i$ and its long-term equilibrium trend $C^i \times SVR_t^i$:
The specific meanings of the symbols in the formula are as follows:
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is the valuation level of stock i at time t. Valuation indicators can be selected from the reciprocal of price-earnings ratio (PE), the reciprocal of price-to-book ratio (PB), the reciprocal of price-to-sales ratio (PS), dividend yield, etc. The specific choice depends on the investment strategy and industry characteristics.
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is the median valuation of the industry to which stock i belongs at time t. The median industry valuation represents the overall valuation level of the industry and can be used as a benchmark for the valuation level of individual stocks.
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is the specific valuation factor of stock i, representing the long-term valuation difference of the company relative to the industry. This value is usually assumed to be a constant and can be estimated by linear regression. This value reflects the company's fundamentals and the market's long-term pricing of the company.
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It represents the change in the valuation level of stock i at time t relative to time t-1, that is, $\Delta VR_t^i = VR_t^i - VR_{t-1}^i$.
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It represents the change in the median valuation of the industry to which stock i belongs at time t relative to time t-1, that is, $\Delta SVR_t^i = SVR_t^i - SVR_{t-1}^i$.
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is the elasticity coefficient of the change in the median valuation of the industry to which stock i belongs to the change in the valuation of the individual stock, reflecting the impact of changes in industry valuation on the valuation of the individual stock. It can be estimated by linear regression.
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is the adjustment coefficient of the error correction term, which reflects the recovery speed of the valuation deviation, and its value range is usually [-1, 0]. When λ is a negative value, it means that the valuation deviation will gradually return to the long-term trend; the larger the absolute value of λ, the faster the regression speed. It can be estimated by linear regression.
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It is the error correction term of the previous period (t-1), reflecting the degree to which the valuation level of the previous period deviates from the long-term equilibrium trend. $ECM_{t-1}^i = (VR_{t-1}^i - C^i \times SVR_{t-1}^i)$.
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is a random disturbance term, which represents the valuation changes that the model cannot explain. It is assumed to follow a normal distribution with a mean of 0.
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is the valuation regression deviation of stock i at time t, that is, the relative deviation of the current valuation level from its long-term equilibrium trend.
factor.explanation
This factor aims to quantify the short-term deviation of the valuation level of individual stocks from their long-term equilibrium trend. The larger the absolute value of the deviation, the higher the deviation between the current valuation and the long-term equilibrium trend, which may contain greater investment opportunities or risks. The positive and negative signs of the deviation indicate whether the valuation level is relatively underestimated (positive value) or relatively overestimated (negative value) relative to the long-term trend. This factor is based on the Error Correction Model (ECM), capturing the dynamic process of the valuation level regressing to the long-term trend, and is a commonly used quantitative indicator in the mean reversion strategy. The advantage of this factor is that it takes into account the overall valuation level of the industry and the specificity of individual stocks, and captures the dynamic changes of valuation deviations through a dynamic error correction mechanism, which is more in line with the actual situation of the financial market. This factor can be used to construct a quantitative stock selection strategy to capture investment opportunities brought about by valuation deviations. In practical applications, it is necessary to select appropriate valuation indicators according to specific circumstances, and to reasonably estimate and adjust the parameters.