Momentum 12−2: why the last month does not count

Why the most recent month gets in the way

Over a year, price moves tend to continue. Over a month, they tend to reverse. Every price series contains both at once.

The short-term part was shown independently by two papers in 1990, by Narasimhan Jegadeesh and by Bruce Lehmann: over horizons from one week to one month, prices do not keep going but reverse. What rose strongly over a short period tends to give some of it back afterwards; what fell tends to recover. Research calls this short-term reversal.

For a measure meant to capture the medium-term trend, that is noise. A stock that rose sharply last month would look stronger with that month included, even though that very rise is the part more likely to fade. It shows up in the data of Jegadeesh and Titman: their momentum strategy earns money month after month after formation — except in the first.

With the exception of the first month, this portfolio realizes positive returns in each of the 12 months after the formation date.

Narasimhan Jegadeesh 1993, Conclusions

That is where the method comes from: take a year's return, but leave out the last month. What remains is the part of the price series in which momentum shows — without the part in which it reverses.

Source: Narasimhan Jegadeesh 1990, Abstract, Bruce N. Lehmann 1990

What “12−2” means precisely

Not “from twelve months ago to two months ago”. It means months t−12 to t−2, where t is the month in which the portfolio is held.

The label comes from research, where a portfolio is formed at the end of one month and held during the next. That holding month is t. The month before it, t−1, is the most recent one before formation — and that is exactly the one left out. Returns are measured over months t−12 to t−2, which is 11 monthly returns.

Seen from the day of formation, the window therefore runs from the price twelve months ago to the price one month ago. In Kenneth French's data library, where the momentum factor is freely available, the file header puts it like this:

The portfolios are constructed monthly. […] Prior return is measured from month -12 to - 2.

French Data Library, file header

Mark Carhart, who introduced momentum in 1997 as a fourth factor alongside market, size and value, describes it without the month numbering — and therefore unambiguously:

I construct PR1YR as the equal-weight average of firms with the highest 30 percent eleven-month returns lagged one month minus the equal-weight average of firms with the lowest 30 percent eleven-month returns lagged one month.

Mark M. Carhart 1997, p. 61

“Eleven-month returns lagged one month”: eleven months of returns, shifted back by one month. That is exactly what the column in this list measures.

How the column is calculated here

From daily closing prices, in trading days rather than calendar months — recalculated every day.

A price series knows no months, only trading days. The list therefore uses the usual approximation of 21 trading days per month: the window starts 252 trading days back, i.e. 12 months, and ends 21 trading days back, i.e. 1 month. The result appears in the column as a percentage. If a stock does not yet have 252 trading days of price history, the field stays empty.

Three things set the column apart from the research factor, and none of them is hidden:

• One stock instead of a portfolio. The factor in French's library is the return of portfolios: stocks above the 70th NYSE percentile bought, stocks below the 30th sold short. The column shows only the measure by which they are sorted there — for each stock individually.
• Every day instead of at month-end. The factor's portfolios are formed once a month. The list recalculates after every trading day, so the window moves forward by one day each day.
• Trading days instead of calendar months. 21 trading days are usually, but not always, exactly one month. For a measure over 11 months the difference is small; it is still an approximation.

And one thing applies here as everywhere in this list: nobody has tuned the window lengths. They are taken as they stand in the literature, and the reason for choosing them is the evidence behind them — not how they perform on our data.

Source: French Data Library, file header, Mark M. Carhart 1997, p. 61

A worked example to check by hand

Three made-up prices are enough. The calculation needs only two of them.

Mom 12−2 = 100.00 ÷ 80.00 − 1 = +25.00%. Today's price does not appear in the calculation.

For comparison, the return including the most recent month: 90.00 ÷ 80.00 − 1 = +12.50%. The decline in the last month halves the value here. Mom 12−2 does not see it — on purpose: a single weak month says little about the medium-term trend, and given the findings on short-term reversal, it rather suggests the opposite of what it seems to.

Whether that holds for any particular stock, the number does not say. The research findings apply to broadly diversified portfolios over many years, not to the next week of a single share.

Momentum and RSL: same idea, different measure

Both ask whether a price has risen. They measure it at different points in the price series.

Levy's RSL, by which this list is ranked, divides the current price by an average. Mom 12−2 compares two single prices. That leads to three differences worth knowing when reading the list.

Source: Robert A. Levy 1967, Section II (“Price Ratios”)

The latest price

This is the most important difference. In the RSL, the current price directly shapes the value; a strong rise over the last few days lifts it immediately. Mom 12−2 only responds to that rise once it is a month old. If a stock ranks high on the RSL but not on Mom 12−2, that last month may well be the reason.

Average or single price

The RSL's denominator smooths: a single unusual weekly close shifts the average only a little. Mom 12−2, by contrast, depends on exactly two prices. If the price 12 months ago was unusually low on that one day, the value comes out correspondingly high — and jumps as soon as that day leaves the window.

Length of the window

The RSL looks back about half a year, Mom 12−2 almost a full year. A stock that rose sharply nine months ago and has moved sideways since has a high Mom value and an RSL close to 1.

This list does not decide which measure is “right”. It ranks by the RSL so that it stays comparable with other RSL lists, and shows Mom 12−2 alongside because it is the measure research works with. Where the two diverge, a second look is worthwhile. The RSL 26W −1W column offers a middle ground: the same RSL, calculated one week earlier. Where the RSL comes from is covered in RSL: Method & Origins.

References

Every figure on this page is shown with its exact location in the source — section, table or page. The links lead to the paper via its DOI; the full texts are mostly behind publishers' paywalls, but the bibliographic details are enough for any library.

• Robert A. Levy (1967): Relative Strength as a Criterion for Investment Selection. The Journal of Finance 22(4), pp. 595–610. doi:10.1111/j.1540-6261.1967.tb00295.x
• Narasimhan Jegadeesh (1990): Evidence of Predictable Behavior of Security Returns. The Journal of Finance 45(3), pp. 881–898. doi:10.1111/j.1540-6261.1990.tb05110.x
• Bruce N. Lehmann (1990): Fads, Martingales, and Market Efficiency. The Quarterly Journal of Economics 105(1), pp. 1–28. doi:10.2307/2937816
• Narasimhan Jegadeesh, Sheridan Titman (1993): Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency. The Journal of Finance 48(1), pp. 65–91. doi:10.1111/j.1540-6261.1993.tb04702.x
• Mark M. Carhart (1997): On Persistence in Mutual Fund Performance. The Journal of Finance 52(1), pp. 57–82. doi:10.1111/j.1540-6261.1997.tb03808.x
• Kenneth R. French (2026): Data Library: Momentum Factor (Mom), monthly and annual. Tuck School of Business, Dartmouth College, dataset, CRSP data as of 202607. Data library