*This post is available as a PDF download here.*

# Summary

- In HIMCO’s May 2018 Quantitative Insight, they publish a figure that suggests the optimal holding length of a momentum strategy is a function of the formation period.
- Specifically, the result suggests that the optimal holding period is one selected such that the formation period plus the holding period is equal to 14-to-18 months: a somewhat “magic” result that makes little intuitive, statistical, or economic sense.
- To investigate this result, we construct momentum strategies for country indices as well as industry groups.
- We find similar results, with performance peaking when the formation period plus the holding period is equal to 12-to-14 months.
- While lacking a specific reason why this effect exists, it suggests that investors looking to leverage shorter-term momentum signals may benefit from longer investment horizons, particularly when costs are considered.

A few weeks ago, we came across a study published by HIMCO on momentum investing^{1}. Contained within this research note was a particularly intriguing exhibit.

*Source: HIMCO Quantitative Insights, May 2018*

What this figure demonstrates is that the excess cumulative return for U.S. equity momentum strategies peaks as a function of both formation period and holding period. Specifically, the returns appear to peak when the sum of the formation and holding period is between 14-18 months.

For example, if you were to form a portfolio based upon trailing 6-1 momentum – i.e. ranking on the prior 6-month total returns and skipping the most recent month (labeled in the figure above as “2_6”) – this evidence suggests that you would want to *hold *such a portfolio for 8-to-12 months (labeled in the figure above as 14-to-18 months since the beginning of the uptrend).

Which is a rather odd conclusion. Firstly, we would intuitively expect that we should employ holding periods that are shorter than our formation periods. The notion here is that we want to use enough data to harvest information that will be stationary over the next, smaller time-step. So, for example, we might use 36 months of returns to create a covariance matrix that we might hold constant for the next month (i.e. a 36-month formation period with a 1-month hold). Given that correlations are non-stable, we would likely find the idea of using 1-month of data to form a correlation matrix we hold for the next 36-months rather ludicrous.

And, yet, here we are in a similar situation, finding that if we use a formation period of 5 months, we should hold our portfolio steady for the next 8-to-10 months. And this is particularly weird in the world of momentum, which we typically expect to be a high turnover strategy. How in the world can having a holding period *longer *than our formation period make sense when we expect information to quickly decay in value?

Perhaps the oddest thing of all is the fact that all these results center around 14-18 months. It would be one thing if the conclusion was simply, “holding for six months after formation is optimal”; here the conclusion is that the optimal holding period is a function of formation period. Nor is the conclusion something intuitive, like “the holding period should be half the formation period.”

Rather, the result – that the holding period should be 14-to-18 months minus the length of the formation period – makes little intuitive, statistical, or economic sense.

**Out-of-Sample Testing with Countries and Sectors**

In effort to explore this result further, we wanted to determine whether similar results were found when cross-sectional momentum was applied to country indices and industry groups.

Specifically, we ran three tests.

In the first, we constructed momentum portfolios using developed country index returns (U.S. dollar denominated; net of withholding taxes) from MSCI. The countries included in the test are: Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany, Hong Kong, Ireland, Israel, Italy, Japan, Netherlands, New Zealand, Norway, Portugal, Singapore, Spain, Sweden, Switzerland, the United Kingdom, and the United States of America. The data extends back to 12/1969.

In the second, we constructed momentum portfolios using the 12 industry group data set from the Kenneth French Data Library. The data extends back to 7/1926.

In the third, we constructed momentum portfolios using the 49 industry group data set from the Kenneth French Data Library. The data extends back to 7/1926.

For each data set, we ran the same test:

- Vary formation periods from 5-1 to 12-1 months.
- Vary holding periods from 1-to-26 months.
- Using this data, construct dollar-neutral long/short portfolios that go long, in equal-weight, the top third ranking holdings and go short, in equal-weight, the bottom third.

Note that for holding periods exceeding 1 month, we employed an overlapping portfolio construction process.

Below we plot the results.

*Source: MSCI and Kenneth French Data Library. Calculations by Newfound Research. Past performance is not a predictor of future results. All information is backtested and hypothetical and does not reflect the actual strategy managed by Newfound Research. Performance is net of all fees except for underlying ETF expense ratios. Returns assume the reinvestment of all dividends, capital gains, and other earnings.*

While the results are not as clear as those published by HIMCO, we still see an intriguing effect: returns peak as a function of both formation and holding period. For the country strategy, formation and holding appear to peak between 12-14 months, indicating that an investor using 5-1 month signals would want to hold for 7 months while an investor using 12-1 signals would only want to hold for 1 month.

For the industry data, the results are less clear. Where the HIMCO and country results exhibited a clear “peak,” the industry results simply seem to “decay slower.” In particular, we can see in the results for the 12-industry group test that almost all strategies peak with a 1-month holding period. However, they all appear to fall off rapidly, and uniformly, after the time where formation plus holding period exceeds 16 months.

While less pronounced, it is worth pointing out that this result is achieved without the consideration of trading costs or taxes. So, while the 5-1 strategy 12-industry group strategy return may peak with a 1-month hold, we can see that it later forms a second peak at a 9-month hold (“14 months since beginning uptrend”). Given that we would expect a nine month hold to exhibit considerably less trading, analysis that includes trading cost estimates may exhibit even greater peakedness in the results.

**Does the Effect Persist for Long-Only Portfolios?**

In analyzing factors, it is often important to try to determine whether a given result is arising from an effect found in the long leg or the short leg. After all, most investors implement strategies in a long-only capacity. While long-only strategies are, technically, equal to a benchmark plus a dollar-neutral long/short portfolio^{2}, the long/short portfolio rarely reflects the true factor definition.

Therefore, we want to evaluate long-only construction to determine whether the same result holds, or whether it is a feature of the short-leg.

*Source: MSCI and Kenneth French Data Library. Calculations by Newfound Research. Past performance is not a predictor of future results. All information is backtested and hypothetical and does not reflect the actual strategy managed by Newfound Research. Performance is net of all fees except for underlying ETF expense ratios. Returns assume the reinvestment of all dividends, capital gains, and other earnings.*

We find incredibly similar results. Again, country indices appear to peak between 12-to-14 months after the beginning of the uptrend. Industry group results, while not as strong as country results, still appear to offer fairly flat results until 12-to-14 months after the beginning of the uptrend. Taken together, it appears that this result is sustained for long-only portfolio implementations as well.

**Conclusion**

Traditionally, momentum is considered a high turnover factor. Relative ranking of recent returns can vary substantially over time and our intuition would lead us to expect that the shorter the horizon we use to measure returns, the shorter the time we expect the relative ranking to persist.

Yet recent research published by HIMCO finds this intuition may not be true. Rather, they find that momentum portfolio performance tends to peak 14-to-18 months after the beginning of the uptrend in measured. In other words, a portfolio formed on prior 5-month returns should hold between 9-to-13 months, while a portfolio formed on the prior 12-months of returns should only hold 2-to-6 months.

This result is rather counter-intuitive, as we would expect that shorter formation periods would require shorter holding periods.

We test this result out-of-sample, constructing momentum portfolios using country indices, 12-industry group indices, and 49-industry group indices. We find a similar result in this data. We then further test whether the result is an artifact found in only long/short implementations whether this information is useful for long-only investors. Indeed, we find very similar results for long-only implementations.

Precisely why this result exists is still up in the air. One argument may be that the trade-off is ultimately centered around win rate versus the size of winners. If relative momentum tends to persist for only for 12-to-18 months total, then using 12-month formation may give us a higher win rate but reduce the size of the winners we pick. Conversely, using a shorter formation period may reduce the number of winners we pick correctly (i.e. lower win rate), but those we pick have further to run. Selecting a formation period and a holding period such that their sum equals approximately 14 months may simply be a hack to find the balance of win rate and win size that maximizes return.

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