## 1. Relative, Absolute, and Macro-Momentum - Three Dimensions

Momentum investing is one of the oldest and conceptually simple methods of investing. The idea is that what is trending up, will continue to rise, and what is declining will continue to decline, regardless of the reasons underlying the price movement. Despite its simplicity, the strategy has received broad empirical confirmation for its ability to consistently produce higher returns than the risk investors take on (Akemann and Keller, 1977; Brush and Boles 1983; Jaegadesh and Titman, 1993, 2001; Chabot, Ghysels and Iagaunathan, 2009; Gsczy and Samonov, 2016).

The approach has also seen some recent improvements. In the past decade, Gary Antonacci developed what has been called the dual momentum method (see Antonacci, 2011, 2012, 2013, 2015). Unlike the traditional single momentum method, which assesses which securities have the best momentum relative to their selection universe (e.g. the top 30 stocks of the S&P500), the dual momentum method puts those securities through a second screen. This screen additionally checks to determine whether the securities, considered absolutely, are trending up (e.g. of those 30 stocks, are they in fact trending up, or are they simply trending down the least, as might be the case in a recession?). Only if the securities pass both screens should one buy. The results from this dual methodology are significant, since they provide evidence of better risk-adjusted returns than the single momentum method. Mr. Antonacci was awarded a prize for his work, and it is well deserved.

The double momentum strategy continues to be useful, and other members here on SeekingAlpha can provide one with regular updates on their results and their analysis.

The present essay takes the next logical step by introducing a third parameter for momentum investing: macro-momentum. Just as Antonacci’s approach produced a significant improvement over the previous form, so the triple momentum methodology produces a significant improvement over his on both an absolute and risk-adjusted basis.

This essay develops the thesis by focusing only on stocks, though it could be used for baskets of ETPs or even cryptocurrencies. In section 2 the essay reviews the data sources and assumptions that went into the backtested study--they are in line with standard data science practices. The essay next reproduces the results of a single momentum strategy (section 3), the advances of Antonacci, corroborating his claims (section 4), and how the triple momentum methodology beats his approach (section 5). I provide enough detail for anyone versed in algorithmic trading to build their own strategy; the rest can just follow me I suppose. The essay concludes with some final thoughts for other asset classes and how the triple momentum strategy can be improved by using a composite macro-measure for a fundamental cum momentum strategy, or a “fundamentum” strategy.

## 2. The Setup (Methodology)

To backtest these strategies, the analysis uses the service provided at Portfolio123. There are other providers, but their selection of data is specifically developed to avoid survivorship bias, and it has most of the features that one needs to assess portfolio quality in-built. To recall, survivorship bias could affect a backtest if the only available stocks for one’s strategy are those that have survived through the testing period, while those that went belly-up were not included in the data set. Portfolio123 makes sure to include all the failed securities in their data sets.

The analysis is limited to stocks in the S&P500. In some ways, then, the strategy that emerges is pre-screened for basic financial health, and it is to that extent a “fundamentum” strategy. Nevertheless, relative to the S&P’s performance as a whole, or relative to other comparables (e.g. the Russell 2000 or the Dow), even the most basic of the momentum strategies out-performs.

With respect to sampling worries, I mention two points. First, for the portfolio size, the analysis uses 30 stocks. The reason is that an N of 30 is statistically significant enough to avoid (many) worries about extrapolating data from small samples. Second, the data only go back to beginning of 1999, i.e., a little more than 20 years. It is enough to test the performance of the portfolios through a range of market collapses, but the results would be helped by assessment through a longer time-frame.

Now let’s turn to some of the results.

## 3. Single (Relative) Momentum

The single momentum strategy ranks all the stocks of the S&P500 by their momentum over the past 160 trading days. This could be done a number of ways, but to keep the data consistent with existing literature on momentum trading, the analysis measured the difference between the closing price 160 trading days previously and the most recent closing price. In quasi-code:

Close(0)/Close(159)

The ratio provides a number, such that the larger it is, the higher the stock is ranked.

The algorithm buys the top 30 stocks ranked this way, and sells when they fall below the 90th percentile. Note that the top 10% of the S&P 500 is 50 stock (not 30). The reason the algorithm only sells after a stock falls out of the top 50 is that limiting the algorithm to the top 30 produces too much noise, requiring too much unnecessary selling. For example, a firm may be hovering in the range between 33 and 27 on any given week. If the algorithm sold as soon as the stock fell below rank 30, it would increase transaction costs (including slippage) without improving performance since the decline in rank was so slight. Finally, the algorithm only checks every 3 trading weeks, again to reduce noise.

What follows is an image of the results.

Here is another showing the annual returns, relative to the SPY as a benchmark.

Finally, some risk adjusted numbers, taken on a monthly basis, are as follows.

A few points are notable. The first, of course, is that this strategy works in the sense that it consistently beats the market on an absolute basis, and comes in a little better on a risk-adjusted basis. Its compound annual growth rate of a little over 12.15% is decent, and it has made a little over 7.2% alpha on a monthly basis since inception. The maximum drawdown is a bit worrying, since it exceeds that of the SPY itself and this is reflected in the relatively mediocre .56 Sharpe ratio (over 1 is ideal). The .82 Sortino ratio (which corrects the Sharpe by not counting positive volatility against the model) is better, but still not over the desired 1. On the balance, then, this is not a bad model and the results confirm previous studies on the persistent alpha of momentum methods of investing.

## 4. Dual Momentum (Absolute and Relative)

The basic difficulty with the simple momentum method is that the algorithm only assesses the performance of the stocks relative to each other, and not relative to their actual gains. It is entirely possible, as a result, that strategy will select the top 30 stocks, but that they are all declining nonetheless, as is likely to happen in a recession or correction.

To correct for this difficulty, one should only buy stocks when they are going up (in the ideal case). In practice one finds that selling stocks as soon as they decline introduces too much noise into the strategy, and so lower returns. The strategy, then, is to buy if the stock has not declined too much in a recent period, say no more than a 8% drop over the last three weeks. And similarly, the algorithm sells if a stock had dropped more than, say, 3% since the last evaluation period (so a 3% noise buffer). Finally, the algorithm sells a stock if it falls below the top 10%. What follows is the general picture of the returns on this strategy.

Here is run-down of performance on an annual basis, again measured against the SPY.

Finally, what follows are the numbers for risk adjusted returns on a monthly basis since inception.

The first thing to note about these results is that they confirm Antonacci’s results. The dual-momentum approach definitively outperforms the simple momentum method on an absolute basis, and relative to the risk an investor takes on. The 13.38% compound annual growth rate handily exceeds the 12.15% of the single momentum method, and it does so with a higher Shapre ratio, at .62, Sortino ratio, at .93, and annualize alpha at almost 8.5%. The remaining difficulty is that the model continues to have a larger drawdown than the benchmark, and this results from the fact that I had to allow for the buying and selling of stocks that were losing (some) value to avoid excess noise in the strategy.

## 5. Triple Momentum

A lingering difficulty with the dual momentum strategy, then, is that the algorithm continues to buy when the overall momentum of the S&P is declining. One way to resolve that difficulty is to shorten the evaluation period to strictly enforce the sell rules. Unfortunately, this strategy also increases noise and portfolio turnover, producing overall lower results. A better solution, then, is simply to introduce the performance of the broader macro trend into the strategy.

The obvious macro trend benchmark for the present strategy is the momentum of the S&P500 itself. The buy strategy thus updates to include an additional rule, so that the model only buys if the S&P500 is not generally declining that much over a standard period of time, say 200 days. The sell strategy similarly updates, so that it sells all stocks if the S&P500 falls too far over a designated period of time, such as a 200 day period. Here is a picture of the overall performance with these adjustments.

And here is the strategy’s performance relative to the SPY on a yearly basis since 1999.

Finally, here are the risk-adjusted results measure of the model on a monthly basis.

The improvements are clear, as the strategy is an improvement over the Dual Momentum approach both on an absolute measure, at 16.83% compound annual growth rate, and (quite significantly) on a risk adjusted basis, achieving a Sharpe of .77, a Sortino ratio well over 1 at 1.22, and an annualized alpha at 11.79%. Finally, this is the only model to have a smaller maximum drawdown than the SPY itself, at 37.88%, as opposed to the SPY’s 55.19%. One notes, in fact, that for several periods, the model simply held cash. The images below represent these states.

## 6. Concluding Thoughts

The triple momentum method thus does significantly better than the established dual momentum methodology, both for absolute returns and on a risk-adjusted basis. One might thus do well to include this additional (macro) dimension into one’s momentum trading strategies.

I shall conclude by addressing a few questions I have received in discussing this model with colleagues, and suggest some broader applications.

A common question about the Dual Momentum methodology is simple: if the max drawdown is the problem, then why not simply introduce a stop-loss into one’s strategy? The answer is that because the strategy is momentum based, stop-losses often prevent the strategy from reaping the returns of a “bounce back.” Pictured below are the results of the most generous stop-loss strategy I could find: it sells a stock if it drops more than 9% below the entry price.

While the strategy does address the max drawdown difficulty, it does so at the cost of lowering overall returns and introducing more risk into the portfolio (Sharpe and Sortino ratios are lower). The point is clear: momentum strategies are rather noisy and so need to allow some room for stocks to bounce around a bit.

Another question I get is concerns Antonacci’s GEM model. It trades globally, and uses ETFs to lower transaction costs. This global reach provides his model with the opportunity to avoid market downturns like the 2008 crash, and this is why his model reportedly returns 17.43% compound annual growth rate. Isn’t his (dual momentum) model really better then?

In response, I begin by noting plainly that I have never been able to get a model to return those exact numbers over a period of time that excludes the 1990s. Using exactly the logic Antonacci describes in his book, and substituting the RSP for the SPY, I get the following.

It’s still an excellent model, and it makes sense to incorporate into one’s broader portfolio. It doesn’t, however, return quite as much as Antonacci publishes, and I suspect the difference turns on the years assessed.

Moreover, when one introduces bond-holding into the Triple Momentum Strategy, as Antonacci’s model does, then the Triple Momentum clearly outperforms, even without moving to hold stocks outside the US. Here are the returns when holding 7-10 year US treasuries in place of cash.

The bonds are chosen on the momentum decline of the S&P500, so by precisely the macro dimension that Antonacci’s model does not incorporate. With a compound annual growth rate of 19.30% and a Sharpe ratio of .92, the superior performance of the Triple Momentum approach is clear.

Finally, I have been asked about overlapping stock selection with well-known portfolios such as Joel Greenblatt’s. The answer, happily, is that the stocks selected do not much overlap, so that both strategies could be used to produce better overall returns (though they do have a .52 correlation). Here’s an image of their combined performance, weighing each strategy at 50% of the overall portfolio and rebalanced every 26 weeks.

The resulting Triple Momentum + Greenblatt portfolio makes use of the Triple Momentum strategy holding bonds rather than cash, since I hope to indicate optimal performance. And the result support this hope with still near 19% compound annual growth rate, and a Sharpe ratio at 1.05, for an outstanding risk-adjusted result.

That is an outline of Triple Momentum Investing, and I look forward to your comments as always.

## References

Akemann, Charles A. and Werner E. Keller (1997), “Relative Strength Does Persist!” Journal of Portfolio Management 4(1), 38-45.

Antonacci, Gary (2011), “Optimal Momentum: A Global Cross Asset Approach,” Portfolio Management Consultants.

Antonacci, Gary (2012), “Risk Premia Harvesting Through Dual Momentum,” Portfolio Management Consultants.

Antonacci, Gary (2013), “Absolute Momentum: A Universal Trend-Following Overlay,” Portfolio Management Consultants.

Antonacci, Gary (2015), Dual Momentum Investing: An Innovative Strategy for Higher Returns with Lower Risk, New York: McGraw Hill.

Brush, John S. and Keith E. Boles (1982), “The Predictive Power in Relative Strength and CAPM,” Journal of Portfolio Management 9 (4), 20-23.

Chabot, Benjamin R., Eric Ghysels, and Ravi Jagannathan (2009), “Price Momentum in Stocks: Insights from Victorian Age Data,” National Bureau of Economic Research Working Paper no 14500.

Geczy, Christopher and Mikhail Samonov (2016), “Two Centuries of Price Momentum (The World’s Longest Backtest 2018-2012), Financial Analysts Journal 72 (5).

Jegadeesh, Narasimhan, and Sheridan Titman (1993), “Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency,” Journal of Finance 48 (1), 65-91.

Jegadeesh, Narasimhan, and Sheridan Titman (2001), “ Profitability of Momentum Strategies: An Evolution of Alternative Explanations,” Journal of Finance 56 (2), 699-720.

**Disclosure:** I/we have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.

**Additional disclosure: **I do have ownership in the SPY, RSP, and IEF, which are discussed in relation to the ETF approach.