Momentum Strategies and Universe Selection

It is well established that the momentum effect is robust across individual stocks and broad asset classes. However, one of the biggest issues for implementation at the strategy level is to choose a universe for trading. For example, one might choose a broad index such as the S&P500 for an individual stock momentum strategy, but is that the best choice to use to maximize returns? Or if we wanted to build an asset allocation strategy with momentum, which assets should we include/exclude and why? In general, these issues are rarely if ever addressed in either academic papers or in the blogosphere. The consequence is that the choice of universe can artificially inflate results due to data mining (finding the best universe in hindsight prior to presenting the final backtest), or the choice can be too arbitrary and hence sub-optimal from a strategy development standpoint.

There are good reasons to believe that certain asset universes are likely to be superior to others. In a subsequent post, I will attempt to de-compose mathematically what makes a universe particularly well-suited for momentum strategies. But for now, lets discuss some obvious factors that may drive momentum strategy performance: 1) universe heterogeneity/homogeneity: it stands to reason that having an investment universe comprised of six different large cap ETFs will not lead to desirable results because the universe is too similar (homogeneous). In contrast, choosing different sectors or styles or even asset classes should provide opportunities to find good-performing assets when other assets in the universe are not doing as well. 2) the number of assets in the universe: fewer assets will lead to fewer opportunities other things being equal. 3) co-integration/mean-reversion: choosing a universe comprised of co-integrated assets such as say Coke and Pepsi, or Exxon Mobil and the Energy Sector ETF will probably result in negative momentum performance since deviations from a common mean will eventually revert versus continue. This is not a complete description of the factors that drive momentum performance but rather a list that is likely to make logical sense to most investment professionals.

Since there are good reasons to believe that some universes are simply better than others, it makes sense to determine some heuristic for universe selection to improve the performance of momentum strategies. One logical method to determine the universe for trading/backtesting is to try selecting the best universes on a walk-forward basis rather than in hindsight. In other words, we backtest at each time step with a chosen momentum strategy- for example selecting the top asset by 60-day return- and using another window that is much longer- say 756 days or more- to test each possible universe subset from a chosen universe using a performance metric such as CAGR. We would then select the top n/% of universes by their performance, and then apply the momentum strategy to these universes to determine the assets to trade at each re-balance.

A simple example would be to use the nine different sectors in the S&P500 (sector spyders). Perhaps there are sectors that are better suited to a momentum strategy than using all nine? To test this assumption one might choose all universe subsets that are two assets or more (between 2 and 9 in this case) which results in 502 different momentum portfolios. This highlights a key difficulty with this approach- the computational burden grows exponentially as a function of universe size. Suppose we used a 60-day momentum strategy where we chose the top sector by CAGR and re-balance monthly. Looking back 756 trading days or 3 years, we test all 502 different universes and select the top 10% of universes by CAGR using the momentum strategy. Now at each re-balance, we choose the top asset using 60-day momentum from each of the universes that are in the top 10%. The purpose of this strategy- lets call it momentum with universe selection- is to hopefully enhance returns and risk-adjusted returns versus using all assets in the universe. The results of this walk-forward strategy are presented below:

It appears that universe selection substantially enhances the performance of a basic momentum strategy. Both returns and risk-adjusted returns are improved by using rolling universe selection. There are clearly sectors that are better suited to a switching strategy than just using all of them at once. What about asset classes? Does the same effect hold true? We chose a 10-asset universe that we have used before for testing Adaptive Asset Allocation: S&P500/SPY,Real Estate/IYR,Gold/GLD,Long-Term Treasurys/TLT,Commodities/DBC,10-year Treasurys/IEF,Emerging Markets/EEM,Europe/IEV,International Real Estate/RWX,Japan/EWJ. The results of this walk-forward strategy are presented below:

Once again, the returns and risk-adjusted returns are much higher when employing universe selection. The differences are highly significant in this case. Clearly there are subsets of asset classes that are superior to using the entire universe.

This approach to universe selection is not without flaws however, and the reasons why will be clarified in a subsequent post. However it is still reasonably practical as long as the backtest lookback window (756 in the above example) is much larger than the momentum lookback window (60 in the above example). Furthermore, the backtest lookback window would ideally cover a market cycle–using shorter lookback windows could end up choosing only the best performers during say a bull market–which would lead to a biased universe. In addition, it would be helpful to choose a reasonable number or % of the top universes such as the top 5 or top 10 or even the top 10% in the examples we used above. That helps to mitigate the effect of data-mining too many different combinations and ending up with a universe that simply performed well due to chance. It also improves the reliability of out-of-sample performance.