The Basics of Building a Momentum Strategy:

- How to calculate generic momentum
- Describe how look-back windows affect momentum
- Describe how portfolio construction affects momentum

**HOW TO CALCULATE GENERIC MOMENTUM**

How do we measure the “momentum” of a stock? The simple method is to calculate the total return (including dividends) of a stock over some particular look-back period (e.g., the past 12 months).

A quick example will demonstrate the concept, using the total return of Apple’s stock in 2014. Here we calculate the cumulative return to Apple over the past 12 months (the “look-back” period). To calculate the cumulative return over the past 12 months, we take the net return streams from each month and turn them into gross returns by adding 1. Thus, if Apple’s net returns for January are –10.77 percent, Apple’s gross returns for January are 0.8923 (–0.1077 + 1).

Then, we multiply all the gross return series (i.e., months) and subtract 1 to find the cumulative 12-month net return. For example, based on the data from Apple in 2014, the cumulative returns in December (momentum score; see Table 5.1) are calculated as follows:

(0.8923)(1.0575)(1.0200)(1.0994)(1.0787)(1.0277)(1.0287)(1.0775)

(0.9829)(1.0720)(1.1060)(0.9281) – 1 = 40.62%

Clearly, Apple had a good year in 2014! For reference, the broad market was up 13.46 percent in 2014. A similar exercise could be done over a different look-back period, such as the past month, where the total return would be –7.19 percent (i.e., the return over the past month.

**THREE TYPES OF MOMENTUM**

We examine how returns are influenced by the look-back period we use to calculate momentum. Academic researchers have already thoroughly reviewed this topic and we summarize the main findings associated with three key look-back windows:

- Short-term momentum (e.g., 1-month look-back)
- Long-term momentum (e.g., 5 years, or 60-month look-back)
- Intermediate-term momentum (e.g., 12-month look-back)

*from:

**Quantitative Momentum**