Calculating Multi-Month Stock Momentum with Dividend-Adjusted Returns
Summary
The document explains how monthly stock momentum variables can use return windows that end before the current month. For a six-month signal, it describes compounding five monthly returns through the month before the measurement month; the twelve-month version compounds eleven returns on the same basis. The one-month example likewise uses the return from two months earlier to the prior month.
For the 36-month measure, the stated window runs from month t-36 through t-13, excluding the most recent year. The author clarifies that the source dataset uses dividend-adjusted returns, so price-only changes will not reproduce its values. The discussion is a clarification of a dataset convention rather than a general proof that these exact windows are universal; implementations should check the source's timing and adjustment rules.
Key ideas
- Momentum windows may end one month before the date at which the signal is recorded.
- The six-month value compounds five monthly returns, while the twelve-month value compounds eleven.
- The 36-month measure uses returns from t-36 through t-13, leaving out the recent year.
- Dividend-adjusted returns are needed to match the described dataset.
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# How do I calculate 6/12/36-month momentum of individual stocks?
# How do I calculate 6/12/36-month momentum of individual stocks?
I am looking at a particular dataset that contains 1/6/12/36 month momentum variables for individual stocks that were calculated based on Jagadeesh & Titman (1993), but I cannot figure out how the authors of the dataset calculated the 6/12/36 month momentum of individual stocks.
Let's say I have the following monthly data for an individual stock:
According to the authors of the dataset the corresponding 1/6/12/36 month momentum values at October 2016 are:
For October 2016, I get that the 1 month momentum at $t=0$ is simply $\frac{Price_{t-1} - Price_{t-2}}{Price_{t-2}}$, which is $\frac{7.67-7.36}{7.36} = 0.0421195...$, but I am missing how I should calculate longer periods. Is there anyone who could tell me how I can calculate the 6-month momentum value (-0.0378...) in the example above?
UPDATE: I found the answers. There was no way you could have answered this question with the figures above. First of all, the 6-month momentum is calculated as the 5-month cumulative return ending one month before the month's end. Same for the 12-month momentum, except that it is the 11-month cumulative return. The 36-month momentum is the cumulative return from months t-36 to t-13. Moreover, the authors use dividend adjusted returns which wasn't completely obvious.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.