Constructing Size–Momentum Portfolios and Removing Size Exposure

# Kenneth R. French data base on momentum and size: construction and how to use it concretely with momentum only


# Kenneth R. French data base on momentum and size: construction and how to use it concretely with momentum only












So, you can find all the data bases on this site. More explicitly, I would like to take the "Developed Market Factors and Returns" part. Even more explicitly, let us take the "25 Portfolios Formed on Size and Momentum (5 x 5)" part (my questions are based on this specific data base).

By clicking on "details", we have the explanation on the construction of the data base:

> All returns are in U.S. dollars, include dividends and capital gains, and are not continuously compounded. We sort stocks in a region into five market cap and five lagged momentum return groups at the end of each month t. The size breakpoints for a region are the 3rd, 7th, 13th, and 25th percentiles of the region's aggregate market capitalization. For portfolios formed at the end of month t–1, the lagged momentum return is a stock's cumulative return for t–12 to t–2. The momentum breakpoints for all stocks in a region are the 20th, 40th, 60th, and 80th percentiles of the lagged momentum return for big (top 90% of market cap) stocks of the region. The global portfolios use global size breaks, but we use the momentum breakpoints for each region to allocate the region's stocks to the global portfolios. Similarly, the global ex us portfolios use global ex us size breaks and regional momentum breakpoints. The 25 value-weight size-momentum portfolios for a region are the intersections of the independent 5x5 size and momentum sorts.

So my question is that I don't understand how they explain the construction of the database and I am looking for a better (and maybe with "easier" words) explanation. I am not a practitioner in the domain and this words seems to be "logic" for them... but not for me.

1) what does "The size breakpoints for a region are the 3rd, 7th, 13th, and 25th percentiles of the region's aggregate market capitalization" mean?

2) "The momentum breakpoints for all stocks in a region are the 20th, 40th, 60th, and 80th percentiles of the lagged momentum return for big (top 90% of market cap) stocks of the region." what does that mean?

3) "The global portfolios use global size breaks, but we use the momentum breakpoints for each region to allocate the region's stocks to the global portfolios. Similarly, the global ex us portfolios use global ex us size breaks and regional momentum breakpoints. The 25 value-weight size-momentum portfolios for a region are the intersections of the independent 5x5 size and momentum sorts." Well, same what does that mean?

And finally (cherry on the cake), I would like to use this data base to simulate some momentum strategies. However the "size" factor is not really part of my study. Should I use only 1 of the 25 columns (let's say the neutral one) although the stocks might change from small to big and from low to high at any year? if not, which column(s) should I use? The last sub question can be summed up like that:

4) What would you suggest to use this data base if you wanted to simulate a momentum strategy?

Modification after a first answer

Now I understand how the data base is constructed, let me reformulate the question 4).

So my goal is to use this data base to simulate a momentum strategy. However, the "size" part of it is completely useless for me, and I would like it to be removed if can be. As you said I cannot pick one part of the data base (for example the smalls only) because stocks are changing size every time and might be in other columns.

I have a suggestion about that: what if I take 3% of the momentum of the Small companies, 4% (7-3) the next one, 6% (13-7) for the next one, 12% (25-13) and finally 75% (100-25) for the Big companies and I would add all of the data into their respective momentum columns (High or Low) regarding their respective percentage? At then end I would only have momentum values (without the size factor) and the data base will be usable for a momentum strategy.

I give you this suggestion in order for you to understand what I want, please feel free to add other another suggestion (or comment this one).

## Answer by Stefan Voigt (score 3, accepted)

https://quant.stackexchange.com/a/18396

Let me start with a general point: Why do you want to use these datapoints if it is so hard to understand how they are constructed? First of all 4) I am not familiar with testing momentum strategies but you should be aware that the datapoints given are not normal assets you can invest in at the end of the day because at the end of each time period they are reallocated. This mean if you are just tracking for example the first row you will probably end up with tracking the returns of different stocks...not sure whether you want this or not... 1) what does "The size breakpoints for a region are the 3rd, 7th, 13th, and 25th percentiles of the region's aggregate market capitalization" mean?

At the end you obtain 25 different portfolios at each time point based on 2 factors: The Size (Market Capitalization) and Momentum. They build the portfolios by splitting each available asset into one of 25 groups, whereas there are 5 different groups for market capitalization and 5 for momentum (5 x 5 =25). Each asset belongs to either the 3 percent with the lowest market capitalization, the group between 3 and 7% percent and so on.

2) "The momentum breakpoints for all stocks in a region are the 20th, 40th, 60th, and 80th percentiles of the lagged momentum return for big (top 90% of market cap) stocks of the region." what does that mean?

Same holds here for the momentum factor. They define 5 different groups (<20,21-40,41-60,80-100 percentiles).

3) "The global portfolios use global size breaks, but we use the momentum breakpoints for each region to allocate the region's stocks to the global portfolios. Similarly, the global ex us portfolios use global ex us size breaks and regional momentum breakpoints. The 25 value-weight size-momentum portfolios for a region are the intersections of the independent 5x5 size and momentum sorts." As said in 1), 2) the 25 portfolios are constructed with the 25 groups you can build when considering the 5x5 possible combinations.

Added due to your modification I have to repeat again that I doubt that your choice of the French Dataset is appropriate for your aims: The dataset consists of the returns of changing mixtures of different assets, so how do you want to use these datapoints to compute Moment strategies? If you do not want the effects of the size, my simple argument would be as follows: You know that the first five columns of your data consist of portfolios with changing size but equal momentum. So if you just take the average over these groups (column 1 to 5, 6 to 10, etc.) You'll obtain 5 portfolios that are just selected due to their historical momentum.

I am not sure if your suggestion is the same, however, averaging will cancel out the size effect.