# The Definition(s) of Momentum

I am currently studying the Momentum strategy and its differences in results (returns) when we change the formula describing momentum. There are indeed no accurate formulas for implementing the momentum strategy in an investment fund.

For example, you can use the last close price minus the first close price of the last 6 months (or 1 month); but you can also use the average of the last 6 months prices minus the average of the last 7 days prices.

There are a few examples of definitions/formulas like that.

So I have the purpose of testing a lot of those formulas using a MATLAB code, but I can't find those definitions, especially recent and creative ones.

So if any of you has a link or a list with all those different formulas/definitions, or even any thoughts regarding a recent and decent momentum formula, that would be great.

EDIT: I would like to add more explanation regarding my request.

--> I am looking for more "unofficial" definition of momentum (exactly the opposite of those I gave as an example see above). In other words, definitions that are different from the classic definition of Jegadeesh & Titman

• An example of a creative, and unexpected definitions would be the "physical price momentum" found in the article "Physical Approach to Price Momentum and Its Application to Momentum Strategy" (Jaehyung Choi, 2014). In this article, they use the momentum definition from physics litterature, and compute the momentum returns in S&P500, by using it... and receive larger return than with the "traditional" momentum definition.

• Another example is from the article "Eureka! A Momentum Strategy that Also Works in Japan" (Denis B. Chaves, 2012) that uses the idiosyncratic returns from market regressions for his own definition of momentum.

• there is an interesting paper on "Kinetic Component Analysis" that you might find interesting – user25064 Jul 7 '14 at 17:56
• Although this article is not really easy, this is exactly the kind of paper I am looking for, thanks. – Pierre Jul 8 '14 at 7:06

## 2 Answers

If I am to summarize the work of the authors from a broader view than that which is taken in the abstract, essentially the price process is decomposed into position, velocity and acceleration reminiscent of projectile motion in classical mechanics.

I added this as an answer so that if @Pierre wants to accept it he may.

You may want to have a look at the papers by

• Jegadeesh & Titman (1993) Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency
• De Bondt & Thaler (1985) Does the stock market overreact?

They are (afaik) the by far most cited publications on momentum (and the calendar-time-method to calculate momentum returns). You should get a basic definition of momentum in stock returns and momentum in general after having read both papers. There is also tons of research about momentum in other asset classes.

• Thanks for your answer. Those articles are indeed well known. However, as you correcly said, they give the "classic" definition of momentum. What I am looking for is some modern definition(s) of the momentum. – Pierre Jul 7 '14 at 15:33