Combining Different Momentum Factors

Momentum can be calculated in a number of different ways.  As long as you are measuring the strength of price appreciation over an intermediate time horizon most logical calculation methods will work to one degree or another.  The standard, academic definition of momentum usually means taking the price appreciation of a security over a predefined time period and comparing it to all of the other securities in the universe.  It is common to use a 12 month window to calculate the price appreciation, but 6 and 9 months are also used.  (Note: most academic studies “skip” the most recent month to account for short-term mean reversion, but we will not address that here).  You can also calculate momentum using moving averages, slopes of regression lines, and point and figure relative strength charts.  There is no one right way to calculate momentum that will guarantee you better performance in the future.  This is similar to value investing.  There is no one correct way to determine a company’s intrinsic value and analysts use a lot of different tools to arrive at their valuations.

No matter what calculation method you choose it will have strengths and weaknesses.  What we want to look at here is using a combination of momentum calculations that have different strengths and weaknesses to improve the overall ranking system.  Two such calculation methods are the moving time window approach and point and figure relative strength.  The moving time window approach is very dependent on time.  If you are using a 12 month window, what happened 12 months plus one day ago makes no difference in the calculation.  In addition, anything that happens between those two points is also irrelevant.  All that matters is the distance from point A to point B.  Point and figure, on the other hand, removes time and only focuses on the volatility of ratio between a security’s price and an underlying benchmark.  That volatility can take place at any time in history and it will be reflected in the point and figure chart.  We have written several whitepapers on point and figure relative strength which you can access here if you want to learn more.

One challenge with any time window based approach is what to do with securities that have been extremely strong that begin to underperform.  Usually a system is set up to own securities from the top 10% or 20% or the ranks and sell them when the fall below a given threshold.  But it may take a tremendous amount of underperformance to actually fall out of the top of the ranks.  In the following example, NVIDIA Corp is up about 168% and at the top of the ranks.  In order to fall out of the top decile, NVIDIA would have to fall below the trailing performance of McCormick & Company, which is only up 35%.  Those numbers will be moving targets as the time window moves forward, but you get the idea – extreme performers have to fall quite a ways before they are actually sold.


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Combining point and figure relative strength signals with a time window approach can help solve this problem.  This issue doesn’t affect every security you buy.  It generally only affects the extreme performers, but it does happen often enough that you can substantially enhance returns by using a point and figure relative strength overlay.  Point and figure signals are divided up into “signals” for the long-term and “columns” for intermediate term signals.  We have found that the most bullish configuration is for a security to be on a buy signal and in a column of X’s versus the benchmark.  (You can find a whitepaper about that topic here).  That simply means a security is outperforming the benchmark on an intermediate term basis.

One of the things that makes a security’s point and figure relative strength chart less bullish is if the column reverses from X’s to O’s, which indicate the relative performance is declining over the intermediate term.  In order to get that reversal, the security must underperform the benchmark by 3 units of volatility.  This is known as the three box reversal, and has been around since the 1950’s.  The unit of volatility we are using is simply percentage performance of the performance versus the benchmark, which we set at 6.5% (click here to see research about box sizes).  So if a security underperforms the benchmark by 19.5% (6.5%*3) the column will flip from X’s to O’s and we than have a less bullish configuration.  This is also very similar to a trailing relative strength stop!

Adding a point and figure overlay to the example above would require NIVIDIA to underperform the market by about 20% to get sold from the portfolio.  It wouldn’t have to fall all the way out of the top of the ranks.  This can be a very big help when looking at securities with extreme performance.  The point and figure also does a couple of other things that make it better than a simple trailing stop.  First, it prevents the system from rebuying the security because it may still be the top performer after it hits the trailing stop.  Second, the point and figure configuration allows for an easy re-entry into the security if it reverses and continues to perform well.  If the security rises 19.5% (6.5% box size * 3 boxes) after the point and figure chart reverses to O’s, the chart will reverse back to X’s and the security will be eligible to be purchased again.

To measure the value of adding a point and figure overlay we ran Monte Carlo trials of a high momentum system.  The Monte Carlo trials are designed to eliminate the effect of picking a few lucky securities that might skew the test results.  We used an investment universe made up of the top 1000 stocks by market capitalization traded in the U.S.  The portfolios held 50 stocks at a time, and any new purchases were made out of the top decile of the ranks.  The ranks were based on the trailing 250 day total return performance.  We examined the portfolios each week and any security that fell out of the top quartile of the ranks was sold.  When a new security needed to be purchases we picked a stock out of the top decile at random that we didn’t already own.  There are always more securities in the top decile than we need to own because we had 50 holdings, but the top decile contained 100 securities.  By drawing securities at random we created 100 different equity curves over the period from 1989 through 2015.  The results of the 100 trials are shown below.  The mean is simply the average performance of all 100 trials during the year.  Some trials performed better than others, but since we were using the exact same process most of the performance difference from one model to the next can be attributed to luck.


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Over time, the 250 day trailing performance model does very well.  The average of all 100 trials over the entire test period annualizes at 14.66% (without transaction costs), and all 100 of the trials wound up outperforming the S&P 500.

The model used above was simply a trailing performance ranking.  It didn’t account for the extreme performance problem discussed above.  We ran the same Monte Carlo process using the 250 day performance ranks and added a point and figure relative strength overlay.  We required each security to be on a point and figure buy signal and in a column of X’s on its relative strength chart versus the S&P 500 Total Return Index.  The results of adding the point and figure overlay are shown below.


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The Mean PnF line shows the average of all 100 trials with the point and figure relative strength overlay year by year.  Adding the point and figure overlay improves the average performance of the models 223 basis points per year from 14.66% to 16.89%.  That is a significant increase to an original system that was already generating quite a bit of outperformance.  By running 100 trials of randomly selected high momentum stocks, we can be very confident that the performance difference isn’t the result of a few lucky trades that one system picked up and the other didn’t.

The point and figure relative strength overlay acts similar to a trailing stop, and helps solve the problem of when extreme performers actually cease being high momentum securities.  Adding a point and figure relative strength overlay is an extremely effective way to boost the performance of a time based momentum system.


The returns used within this article are the result of a back-test using indexes that are not available for direct investment.  Returns do include dividends, but do not include transaction costs.  Back-tested performance is hypothetical (it does not reflect trading in actual accounts) and is provided for informational purposes to illustrate the effects of the discussed strategyduring a specific period.  Back-tested performance results have certain limitations.  Such results do not represent the impact of material economic and market factors might have on an investment advisor’s decision making process if the advisor were actually managing client money.  Back-testing performance also differs from actual performance because it is achieved through retroactive application of a model investment methodology designed with the benefit of hindsight.  Dorsey, Wright & Associates believes the data used in the testing to be from credible, reliable sources, however; Dorsey, Wright & Associates, LLC (collectively with its affiliates and parent company, “DWA”) makes no representation or warranties of any kind as to the accuracy of such data. Past performance is not indicative of future results.  Potential for profits is accompanied by possibility of loss.

4 Responses to Combining Different Momentum Factors

  1. Did you test simply using a trailing intermediate return instead of point and figure, e.g. must be in top rank 250 day return plus in top rank (say) 140 day or 100 day also? I wonder if the point and figure is simply capturing something most people can capture more easily just with relative strength over some intermediate period, too.

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  4. Jason Frey says:

    Performance relative to S&P seems to be strongly trailing off since 2011. Just a phase or too many momentum chasers out there?