Are momentum models better than moving average models? Some useful tips

There are two major strains of models for generating momentum and trends signals. One, analyze simple past price levels (returns) for some look-back period. This is the classic momentum approach (MOM) extensively analyzed in academic research. For example, if the return for an asset over a nine-month look-back is positive (price today above price nine months ago), buy the asset. Two, use the classic trend approach (MA) and buy an asset if the price is above some moving average, linear average, or exponential weighting. The signal is based on some weighting scheme of past prices. 

Recent research has tried to answer whether one approach is better than the other and it concludes that the classic approach of moving averages is a better approach. (See Trend Following with Momentum Versus Moving Average: A Tale of Differences by Zakamulin and Giner.)

The researchers present details on model comparisons that many trend-followers have intuitively know but may have not formally tested. Their work compares MOM and MA models against different autocorrelation schemes to determine which approach has better forecasting skill as indicated by their ability to properly determine market direction. The authors compare models with different look-back periods and show their predictive skills and correlations. This numerical testing allows the researchers to measure the robustness of different models. Their conclusions make intuitive sense and provide a good guide on where modeling should be focused.

The correlations between MOM and MA models are high and gets higher if there is a strong trend, but the MA approach will have more robust forecast accuracy. It is more forgiving in accuracy for changes in look-back periods. This result suggests that MA models will do better when there is trend uncertainty. In some sense, one moving average is not much different than another. On the other hand, using a simple MOM approach can lead to more error.

Put differently, the correlation between two MA models with different look-back periods will be high and stable. You obtain only limited diversification benefit from using more than one MA sign. You will receive more diversification benefit or differences in correlation between MOM and MA models, but the MOM model will have lower forecast accuracy. There is limited value with choosing a model of MA or MOM models.

The choice of model will also depend on the autoregressive behavior of prices. If there is stable and equal autocorrelation through time, then a MOM model may be better, but if there is declining autocorrelation there will be more value with a MA model like an exponential weighted approach which place more weight on recent data. Researchers need to know the autocorrelation features of price data to pick the right MOM and MA model.

The reasons for the failure of back-tests are because the predicted power of any model will change with change in the autocorrelation of the underlying data. Unstable data structure will mean high variation in what is the best model form. Their numerical tests show that on average, in a changing uncertain world, the MA models will do better than the MOM structure. Still, picking the optimal weights for a MA last period and applying to data next period is a risky business; ask any trend-follower. However, this paper can provide some guide dealing with the problem. 

The practical rules from this paper are simple:

• Prefer MA to MOM models.
• If you diversify signals match different look-backs with MA or a MA and MOM combination.
• Accept that diversification across models may be limited 
• Accept that autocorrelations in prices are uncertain but MA models are more robust (forgiving). 
• Optimizing over a back-test period is a fool's game.