Momentum Definition Variants: 12-1, 6-1 and Beyond

Ask three people to describe "recent form" for a sports team and you'll get three different answers: last week's game, the last five games, or the whole season excluding the very latest result because injuries make it unrepresentative. Each is a reasonable definition of "momentum," and each would rank the same set of teams differently. Stock momentum has the identical ambiguity — "buy what's gone up" hides a family of specific rules, and which rule you pick changes both the return you capture and the risk you carry, sometimes drastically.

The two knobs: lookback and skip

A momentum signal is defined by a lookback window $L$ (how far back to measure past performance) and a skip period $S$ (how many of the most recent months to exclude before ranking). The signal for stock $i$ at time $t$ is

$\text{mom}_{i,t} = \frac{P_{i,t-S}}{P_{i,t-S-L}} - 1$

In words: take the stock's price $S$ months ago and divide it by the price $S+L$ months before that, giving the cumulative return over an $L$-month window that ends $S$ months before today — the skip exists specifically to leave out the most recent stretch. "12-1" means $L = 11$ months measured up to one month ago ($S=1$); "6-1" means a shorter 5-month window, also skipping the last month.

The skip month exists because of short-term reversal: a stock's return in the most recent month tends to reverse, not continue, largely because of microstructure effects like bid-ask bounce and overreaction to recent news. Including it would mean partially fighting your own signal.

Worked example 1. A stock's price 13 months ago was $40, one month ago it was $52, and today it's $48 (it just dropped 7.7% in the last month). The 12-1 momentum signal uses the window from 13 months ago to 1 month ago: $\text{mom} = 52/40 - 1 = 30\%$ — a strong positive signal, unaffected by the recent drop. A naive "12-0" signal that includes the last month instead would compute $48/40 - 1 = 20\%$ — still positive, but muted by roughly a third because it's partly capturing the reversal-prone final month rather than pure trend.

Shorter windows trade a different thing entirely

Worked example 2. Novy-Marx (2012) showed that within the 12-month window, the early months (12 to 7 months ago) do almost all the predictive work, and the recent months (6 to 2 months ago) contribute little on their own — he called this "echo" momentum, since the signal that predicts next month's return most strongly is itself already a stale echo from nearly a year back. Take a stock up 25% from 12 to 7 months ago and flat from 6 to 2 months ago: the standard 12-1 signal reads a strong $+25\%$ (roughly), and Novy-Marx's decomposition attributes almost all of the subsequent predictive power to that older 25% move, not to anything more recent. A "6-1" variant built on just the last 5 months, by contrast, would read close to $0\%$ for this same stock and rank it neutrally — the two variants disagree sharply on a stock whose momentum is entirely front-loaded in the far part of the window.

Sample a few paths here and imagine slicing each one into a "recent" half and an "older" half — different lookback-and-skip combinations are, mechanically, just different ways of slicing the same price history, and a stock's path can look strongly trending under one slice and flat under another.

What this means in practice

Shorter-lookback variants (3-1, 6-1) tend to have higher turnover and are more exposed to short-term reversal risk if the skip is too thin; longer-lookback variants (12-1, 24-1) trade less often but react more slowly to genuine regime changes, showing up late to both the initiation and the end of a trend. Multi-factor books commonly blend two or three lookback-and-skip combinations specifically because they are imperfectly correlated with each other — a 6-1 and a 12-1 signal built on the same universe typically correlate around 0.6–0.8, not 1.0, so combining them diversifies away some of each variant's idiosyncratic noise.