Ranking-based Momentum Factor
factor.formula
Daily stock return ranking normalized score:
Monthly stock return ranking standardized score average:
Average standardized score of stock return ranking during the factor observation period:
in:
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The daily return of stock i on day d is calculated as: $R_{i,d} = \frac{P_{i,d} - P_{i,d-1}}{P_{i,d-1}}$, where $P_{i,d}$ is the closing price of stock i on day d.
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The daily return $R_{i,d}$ of stock i on day d is ranked in ascending order among all stocks. For example, if there are 100 stocks on that day and the return of this stock ranks 30th, then $y(R_{i,d}) = 30$.
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The total number of stocks participating in the ranking on day d (i.e., the number of stocks with valid return data on day d)
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The total number of trading days in the mth month indicates the number of valid trading days involved in the calculation in that month.
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The normalized score of the daily return ranking of stock i on day d. This normalization step transforms the raw ranking into a distribution with mean 0 and standard deviation 1. $\sqrt{\frac{(N_d + 1)(N_d - 1)}{12}}$ in the denominator is the theoretical standard deviation of the ranking data.
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The average of the standardized scores of the monthly return ranking of stock i in month m. The comprehensive ranking performance of the stock in that month is obtained by averaging the standardized ranking scores of each day in that month.
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The size of the time window is considered, which indicates the number of months to look back when calculating the momentum factor. For example, if N=6, the average of the standardized scores of the monthly return rankings over the past 6 months is calculated.
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Time offset, used to delay the start time of momentum calculation. For example, if M=1, the momentum factor will be calculated from t-N-1 months to t-1 months. This avoids using the latest monthly data and reduces the impact of short-term reversals and other effects.
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The ranked momentum factor value of stock i at time t, based on the past N months and offset by M months. The value is the average of the means of the ranked standardized scores of the monthly returns over the specified time window.
factor.explanation
The ranked momentum factor is constructed by the following steps: first, daily stock returns are calculated and ranked; then, the daily rankings are standardized to have a mean of 0 and a standard deviation of 1; then, the standardized ranking scores for each month are averaged to obtain the monthly ranking score mean; finally, the average of the monthly ranking score means over the past period is calculated to obtain the final ranked momentum factor value. The core advantage of this method is that it uses rankings instead of absolute returns, reducing the impact of abnormal stock price fluctuations on the stability of the momentum factor. Compared with the traditional momentum factor, it pays more attention to the relative position of stocks in the return distribution rather than the absolute size of the return, thereby constructing a more robust momentum strategy.