Multi-period Moving Average Momentum Factor
factor.formula
Simple Moving Average (SMA):
Normalized Moving Average Price:
Multifactor regression model:
Factor return forecasts (rolling average):
Stock Return Forecast:
in:
- :
The closing price of stock j on the kth trading day of month t, where k is in the range [d-L+1, d] and d is the last trading day of month t.
- :
The moving average window length indicates the number of historical trading days used to calculate the moving average. For example, L=20 represents a 20-day moving average.
- :
The simple moving average price of stock j in month t, calculated over a window length L. It is the arithmetic mean of the closing prices over the past L trading days.
- :
The standardized moving average price is the moving average price $SMA_{j,t,L}$ divided by the closing price $P_{j,d}^{t}$ of the current period (the last trading day of the tth month). This standardization process is intended to eliminate the differences in the price levels of different stocks, making the momentum factors of different stocks comparable.
- :
The return of stock j in period t is usually calculated using the logarithmic return, that is, $r_{j,t} = log(P_{j,d}^{t}) - log(P_{j,d-1}^{t})$
- :
The intercept term of the regression model represents the expected return of the stock when all moving average factors are 0.
- :
The factor return of the i-th moving average factor represents the expected change in stock returns when the i-th standardized moving average price $M\bar{A}_{j,t-1,L_i}$ changes by one unit. This coefficient reflects the contribution of moving average momentum to stock returns at different time scales.
- :
The residual term of the regression model represents the part of the stock return that the model cannot explain, that is, the model error.
- :
The expected factor return of the ith moving average factor in period t+1 is obtained by simply averaging the factor returns over the past 12 months. This represents our expectation of future factor returns based on the factor returns observed in the past.
- :
The expected return of stock j in period t+1 is obtained by multiplying the standardized moving average price $M\bar{A}{j,t,L_i}$ in period t with the predicted factor return $E_t[\beta{i,t+1}]$ and summing the factors over all time scales. This value represents an estimate of the stock's future return based on historical information and model predictions.
factor.explanation
The multi-period moving average momentum factor captures the price trend momentum effect of stocks at different time scales by calculating the moving average price of different time windows (such as 5 days, 20 days, 60 days, etc.) and standardizing it. The regression model uses these standardized moving average prices as input features and combines them with factor return predictions to construct a multi-factor model that aims to predict future stock returns. By introducing momentum information at different time scales, the factor seeks to improve the accuracy of return forecasts and capture momentum or reversal effects that may exist in different time periods.