## How to Measure Momentum?

#### How to Measure Momentum?

October 14, 2016 Momentum Investing Research
(Last Updated On: October 12, 2016)

Since we’ve released our new book, Quantitative Momentum, we’ve received a handful of basic questions related to momentum–specifically as it relates to stock selection.

At this point, the so-called “momentum effect” has occupied academic researchers for several decades. Researchers have found that, on average, stocks with strong recent performance relative to other stocks in the cross section of returns tend to outperform in the future (see Levy 1967 for an old example and JT 1993 for a newer version). The effect has been well-documented by numerous follow-on researchers and the theory of “why” momentum works has been extensively explored (although we still don’t completely understand why it works).

So if an investor wants to harness momentum and implement it in the real world, a common question arises:

What is the best way to measure momentum for stock picking purposes?

The academic research response is to focus on so-called, “12_2 momentum,” which measures the total return to a stock over the past twelve months, but ignores the previous month. (e.g., Ken French data)

But why use 12_2 momentum? Why shouldn’t we use the 3-month momentum, or the 6-month momentum? Why 12-months? And why drop the most recent month’s returns? Let’s take these questions one at a time.

### Lookback Window

As we show here, a few perturbations of how far back in time we should look have already been tested by academics. The chart below is from Jegadeesh and Titman in 1993. They show that the best performing strategy ranks stocks on their past 12-months returns, and holds for 3 months (forming overlapping portfolios).

Thus, 12-month momentum looks reasonable.

### Why drop the most recent month?

Notice that we look at 12_2 momentum, not 12_1 momentum. But why skip the most recent month?

The reason why relates to the short-term reversal effect associated with momentum.

There is an academic finding that short-term momentum actually has a reversal affect, whereby the previous winners (measured over the past month) do poorly the next month, while the previous losers (measured over the past month) do well the next month. We document the findings here. Researchers often argue that this is due to microstructure issues. Thus, most academics ignore the previous month’s return (or week in the case of JT 1993) in the momentum calculation, and we also do this in order to eliminate this short-term reversal effect when implementing the strategy.  It should be noted, however, that including the previous month’s returns has a marginal affect on the performance of momentum.

For more insight on 12_2 momentum, we invite you to explore a more important factor in momentum investing —  rebalance frequency —  as shown in the table above, and in our post here.

Good luck.

Note: This site provides NO information on our value investing ETFs or our momentum investing ETFs. Please refer to this site.

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Definitions of common statistics used in our analysis are available here (towards the bottom)

#### Jack Vogel, Ph.D.

Jack Vogel, Ph.D., conducts research in empirical asset pricing and behavioral finance, and is a co-author of DIY FINANCIAL ADVISOR: A Simple Solution to Build and Protect Your Wealth. His dissertation investigates how behavioral biases affect the value anomaly. His academic background includes experience as an instructor and research assistant at Drexel University in both the Finance and Mathematics departments, as well as a Finance instructor at Villanova University. Dr. Vogel is currently a Managing Member of Alpha Architect, LLC, an SEC-Registered Investment Advisor, where he heads the research department and serves as the Chief Financial Officer. He has a PhD in Finance and a MS in Mathematics from Drexel University, and graduated summa cum laude with a BS in Mathematics and Education from The University of Scranton.

• BA31

Sorry Jack, I am a bit thick on this. Do you measure performance over the previous 12 months ignoring the previous month which in reality is measuring an 11 month performance within a 12 month window OR do you ignore the previous month (which I assume is the most recent month) and measure the 12 months from that point (13 month from current price)?

• Jack Vogel, PhD

11 month window — previous 12 months excluding last month. Great question!

• BA31

Thanks for the quick response. Just received the new book and look forward to diving in this weekend.

• I count at least 11 ways to calculate momentum. See here: http://undervaluedstocks.info/11-momentum-calculations/

Nick de Peyster
http://undervaluestocks.info/

• Chu chang min

Dr Jack, why do you say overlapping portfolio removes season effect? If we rebalance every quarter, each month we will go in at 1/3 of the capital. Hence we only remove any quarter effect. To remove season effect, which is yearly, we have to go in at 1/12 of the capital each month?

• Jack Vogel, PhD

Overlapping can reduce seasonal effects.

• Hannibal Smith

Okay, this is a disappointing article and not up to the usual in-depth review that I’ve come to expect from AA. There are many ways to measure cross-sectional momentum and they all need a proper horse race to see which is the most robust and profitable.