Time Series Momentum (TSMOM)
factor.formula
Time Series Momentum Factor (TSMOM):
Excess returns of individual stocks:
Exponential Moving Average of Returns:
Return Volatility:
in:
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Represents the month, used to identify a specific point in time in time series data.
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Represents a specific stock and is used to identify a specific individual in cross-sectional data.
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represents the excess return of stock $i$ in month $m$ relative to its own historical returns. It is the difference between the actual return $r_{m,i}$ in the current month and the exponential moving average $\bar{r}_{m,i}$ of past returns. Excess returns are intended to capture the deviation of individual stock returns relative to their own historical levels.
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represents the return of stock $i$ in month $m$, usually defined as the percentage change in the stock price during that month.
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It represents the exponential moving average of the monthly returns of stock $i$ before the $m$th month, which is used to smooth the time series of returns, eliminate noise, and capture potential trends. Its calculation method is to take a weighted average of historical returns, and the weight decays exponentially over time, so that the recent returns have a greater impact on the current moving average.
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It represents the volatility of the return of stock $i$ in the $m$th month. It is the square root of the weighted average of the deviations of past returns from the exponential moving average, where the weight decays exponentially over time. This indicator measures the degree of change in the return over a period of time and reflects the risk level of the stock.
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It represents the exponential decay coefficient, which is a parameter between 0 and 1, and determines the degree of influence of historical returns on the exponential moving average. The smaller the $\delta$ value, the faster the decay of historical returns, making the moving average pay more attention to recent returns.
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Represents the number of months used to calculate the mean return in the past, here 12 months. $\frac{1}{N}\sum_{j=1}^{12}\hat{r}_{m-j,i}$ represents the mean excess return in the past 12 months.
factor.explanation
The time series momentum (TSMOM) factor predicts future returns by analyzing the trend of a stock's own historical returns. The core idea is that if a stock has shown positive (negative) excess returns over a period of time in the past, then the trend is likely to continue in the future (although research shows that it is usually the opposite). The factor first calculates the mean of excess returns over the past 12 months and takes its sign as a directional indicator. Then, the excess return of the current month is divided by the volatility of the current month for normalization. The purpose of this is to make the momentum signal more robust and reduce the weight of highly volatile stocks. Therefore, the TSMOM factor can be used to capture the short-term reversal effect of stock prices and construct a corresponding investment portfolio.