Second-order momentum acceleration
factor.formula
The price P(i,t) of stock i at time t can be fitted with a quadratic function:
in:
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is the price of stock i at time t. The closing price is usually used, but other price types can also be used, such as the highest price, the lowest price, or the weighted average price.
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It is a time series, which represents an arithmetic sequence over a period of time. Usually, the data of the past n days are taken, where t = 1 represents the most recent day, t = 2 represents the second to last day, and so on, t = n represents the nth day in the past.
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The constant term of the quadratic fit represents the intercept of the fitting curve. Its specific value is related to the time series and price unit and is not directly involved in the momentum calculation.
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The linear coefficient of the quadratic fit represents the average speed of price change and reflects the average momentum of the stock price. Its positive and negative signs represent the direction of price increase or decrease, and its absolute value represents the strength of momentum. The estimated value of $beta$ can be obtained by performing a linear regression on the historical price series.
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The quadratic term coefficient of the quadratic fit represents the rate of change of the price change speed, that is, the acceleration of the price, which reflects the speed of change of momentum. The estimated value of $gamma$ can be obtained by performing a quadratic regression on the historical price series. Specifically, a positive $gamma$ value indicates that the price increase trend is accelerating, and a negative $gamma$ value indicates that the price increase trend is decelerating (or the price decrease trend is accelerating). The larger the absolute value of $gamma$, the more obvious the acceleration of the price trend change.
factor.explanation
This factor fits the stock's price trend over the past period of time and extracts the quadratic coefficient $gamma$ as the second-order momentum acceleration factor. $gamma$ reflects the speed of change of price momentum. A positive value indicates that the price is accelerating, and a negative value indicates that the price is accelerating (or the upward trend is slowing down). The larger the absolute value, the more obvious the acceleration. This factor can be used to capture the market's overreaction to the stock price trend, thereby obtaining excess returns. In practical applications, it is usually used in combination with other factors and risk control indicators to improve stock selection results and reduce investment risks.