Monday, January 2, 2017

Testing Momentum’s Robustness

Happy new year!

I have noticed that my quantitative posts get the most readership and discussion. So this year, I’ll be posting a lot more research and will start the year off by exploring momentum’s robustness.

There are two good ways to test the robustness of a rules-based trading strategy:
  1. The test of time - how does the strategy behave in different market regimes?
  2. Parameter sensitivity – how stable is the performance if the strategy’s parameters are varied
Let’s look at each of these separately.

Test of Time

The goal is to see how well a strategy performs over a very long-term, under different market conditions. Gary Antonacci has some good articles on the importance of having a long-backtest period (see Bring Data and Bring More Data).

The table below is how the Global Equities Momentum (GEM) strategy has performed from 1971-2015. 

While these results are nice, looking at cumulative outperformance over a backtest period is not enough – we should also look at individual periods within the data.

I did a post a while back showing what happens when we add Gold to the GEM model (see Should we consider gold?). GEM’s annual returns (since 1970) jumped from 18% to 21% by including gold. At first glance, this sounds exciting. But a closer look showed all this additional gain came from the 1970s when the US went off the gold standard. No longer being suppressed, the price of gold rapidly rose in just a few years. We need to be careful not to be misled by these types of one-time events.

The graph below shows that equities (red and green lines) had a secular bear market during the 1970s and 2000s, and a bull market during the 80s and 90s. In both market types, GEM (blue line) did well.

Let’s dig further with a longer period of data. How does momentum do on a decade-by-decade basis?

Meb Faber looked at this in his paper “Relative Strength Strategies” (read here). The table below shows the outperformance each decade of a US sector momentum strategy (hold the top performing sector and rebalance monthly) compared to the entire US stock market.   

While some decades were better than others, momentum had positive alpha every decade since 1930. This is an indication that the momentum anomaly has persistence.

OK, all this looks nice however…

While momentum (and all trend-following) strategies tend to perform well in trending markets, they typically fail in very erratic, sideways markets. An extreme market-regime test is to see how momentum would fare using Japan’s Nikkei stock index, which has traded sideways for 30 years. This will be the topic of my next post. Let’s continue on.

Parameter Sensitivity

Any quantitative strategy has one or more input variables. GEM has two: the lookback period (length of time over which past performance of assets is measured) and rebalancing period (how often you check for a new trading signal). GEM’s recommended parameter settings are 12 months for the lookback and monthly for the rebalance.

By varying these input parameters, we want to see how the strategy’s performance changes. I want to be clear: this is NOT done to find the optimal parameter settings. That would be data mining. Instead, this test is done to determine the model’s sensitivity. A sign of a robust trading strategy is one whose performance is not affected by small changes in its settings.

Note: The analysis that is presented below was done using daily data and MATLAB software. Source code and data is available upon request. 

We first look at how GEM’s performance (between 1988-2016) changes as we vary the rebalancing period from 1 to 100 trading days while keeping the lookback period constant at 12-months.

We see from above that a rebalancing period between 15-25 trading days results in returns performance that is stable while providing high returns and low portfolio turnover. This confirms the recommended setting of 20 trading days (1 calendar month).

It’s interesting to see that a rebalancing period less than 10 trading days results in very high portfolio turnover and with lower returns (due to whipsaw losses). There is absolutely no reason to be doing weekly rebalancing with GEM.

Next, we look at how GEM’s performance changes as we vary the lookback period from 30 to 500 trading days, while keeping the rebalancing period constant at one calendar month.

We see above that any lookback period less than 200 trading days results in higher whipsaw losses and higher portfolio turnover. A lookback between 250-350 trading days results in stable performance with fairly low portfolio turnover. This confirms the recommended setting of 12 calendar months (250 trading days).  

The 12 month look back period was first discovered by Cowles and Jones in 1937. Various other research since then has shown momentum works best with monthly rebalancing and a 12-month lookback period. The results above confirm this, as well as demonstrate how the prior research has held up since it was first published.


Momentum has passed several checks for robustness. It has proven itself over a long backtest period and in different market regimes. In addition, the performance of a simple momentum strategy like GEM is not sensitive to small changes in the strategy’s parameters.

I often get asked about using much shorter rebalancing and lookback periods to be able to adapt faster to market changes. Up until now, I have just verbally been telling people that this would create higher # of trades and whipsaw losses. Now I can back up my recommendation with quantitative evidence.

I leave you with Dilbert’s take on model sensitivity.

Results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Additional information regarding the construction of these results is available upon request. Past performance is no assurance of future success. Please see our disclaimer page for more information.


  1. thanks so much for this site ... Gary Antiknock has changed my thinking 180 degrees regarding investing in the financial markets. I avoided the markets my whole life because it seemed too risky. Now I see that was wrong and I have started to invest.. cost averaging in...Am really looking forward to your next post on the worst case scenario Nikkei..

  2. Have you tried dividing the portfolio into multiple tranches each with a different look back period length? I believe it may lower volatility and drawdowns.

    1. I believe the guys at Newfound do this ( but I don't see that much value. I'll try to do a post on this.

  3. They tranche the portfolio so you don't rebalance the whole portfolio the same day, but each tranche has same look back period.

    1. It's not just the rebalance period that creates timing risk, but also the lookback period. If you really want to reduce this type of risk, you would create tranches with diff lookback and rebalance lengths.

      You'll certainly be trading more. Is it worth it to spend higher transaction costs to reduce a small, unknown loss (maybe even a gain)? I'll add it to my research list.

  4. Was just talking to Gary about DMSR and how the new data affected his thinking. I love the rebalancing comparison, great stuff Gogi!

    1. That's why having lots of data is important

  5. As a further robustness test, what about replacing ACWI-ex and SPX with other indices to create true out-of-sample testing? For example, ACWI-ex + EM; or maybe SPX + Japan; etc.? Or with/without currency hedging on ACWI-ex?

    Nick de Peyster

    1. Way ahead of me. This will be subject of next post, stay tuned

  6. For the benefit of those interesred, here is a copy of an exchange I recently had with Gogi!

    Hi Gogi,

    First of all, thx for sharing with us your ideas and research.

    Now, being canadian and investing part of my money through tax exempt accounts, I wonder what it would be trading xiu instead of an international etf.
    Have you tested xiu, zsp (us) and xbb (bonds) the way GEM trades US, Intl and US bond markets?

    Correlation might be higher between xiu and zsp and impact the results...

    But One might argue that correlation is now higher anyway between developped markets and that currency variations is the main factor that set US and any developped market apart.


    Hi Andre,

    I have looked at adding Canada (but in addition to US and World ex-US). Same for Emerging Market. I'll look at what happens when World ex-US is replaced with Canada.

    Short answer is: Canada is concentrated in Banks & Resource (these make up >70% of XIU). This adds a lot of volatility to GEM and Sharpe Ratio doesn't improve much. All this will be a separate blog post. Can you post this comment and future comments on the blog so that others can benefit?


  7. Hi Gary, could I view the source code and data?

  8. Gogi, what if we get a buy or sell signal at end of month, and the market is severely short-term overbought or oversold? Do you know if it pays to wait a few days (or sometimes a few hours) to let the condition naturally resolve? (so that you get a better price?). It would be very interesting to know how that works out.


  9. Since weird things happen at the end of the month some people re-balance on 33 day schedule. In the long run I've found it doesn't help to try to out-think the model. Those who don't like Fridays and end of month window dressing can maybe just do re-balances every Wednesday in the first week of each month. Often there will be no trades to make anyhow.

  10. You mention that you are checking for robustness, not to optimise. But still, your test indicates that a 350 days LB gives the same performance as 250, but with close to half the trades.

    Why don't you check the robustness of RB and LB all the way back to 1971?