Valuation deviation based on error correction model
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 $Trend_t^i$ is determined by the basic industry trend and the specific factors of individual stocks, which can be expressed as:
Use the Error Correction Model (ECM) to capture valuation deviations and responses to long-term trends:
Among them, the error correction term $ECM_{t-1}^i$ is defined as:
Finally, the valuation deviation factor $DR_t^i$ is defined as the difference between the current valuation and the long-term trend, normalized to the ratio relative to the current valuation:
The meaning of each parameter in the formula is as follows:
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The valuation level of stock i at time t, such as the inverse of the price-to-book ratio (PB), the inverse of the price-to-sales ratio (PS), etc., represents the relative value of the stock.
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The median valuation of the industry to which stock i belongs at time t represents the overall valuation level of the industry and is used to measure industry trends.
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The specific factor coefficient of stock i reflects the difference in valuation level of individual stocks relative to the industry and is usually a constant.
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The change in the valuation level of stock i at time t relative to time t-1, that is, $VR_t^i - VR_{t-1}^i$
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The change in the median valuation of the industry to which stock i belongs at time t relative to time t-1, that is, $SVR_t^i - SVR_{t-1}^i$
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The degree to which changes in the industry valuation of stock i affect changes in the valuation of individual stocks, indicating the short-term elasticity of changes in industry valuations on individual stock valuations.
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The coefficient of the error correction term indicates the speed at which the valuation deviates from the long-term trend, and is usually in the range of [-1, 0]. The closer $\lambda^i$ is to -1, the faster the recovery speed is, and the closer it is to 0, the slower the recovery speed is.
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The error correction term represents the degree of deviation of the valuation of individual stocks at time t-1 from the long-term trend.
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The residual term represents the random disturbance that cannot be explained by the model.
factor.explanation
This factor is designed to measure the short-term deviation of individual stock valuations from their long-term equilibrium levels. By constructing an error correction model (ECM), the valuation level is decomposed into long-term trend terms and short-term deviation terms, and the valuation deviation factor is obtained by dividing the difference between the current valuation and the long-term trend by the current valuation for standardization. The higher the absolute value of the factor, the more obvious the deviation of the current valuation from the long-term trend, the greater the potential valuation regression space, and the higher investment opportunities may be contained. A positive factor indicates that the valuation of the individual stock is underestimated; a negative factor indicates that the valuation of the individual stock is overestimated. This factor can be used to identify stocks whose valuations are wrongly killed or overestimated, and to implement a mean reversion strategy.