### Executive Summary:

Dual Momentum, a concept pioneered by Gary Antonacci, intelligently combines elements of two types of momentum investing strategies — absolute and relative momentum — into a comprehensive asset allocation system. His paper shows that the combination of time-series momentum and cross-sectional momentum has generate intriguing results historically.

In this article, we investigate the Dual Momentum strategy and compare it to the timing elements utilized in the Robust Asset Allocation (RAA) strategy. The RAA strategy was developed in conjunction with our FACTS framework and has a simple goal: A low-cost, low-complexity, high-liquidity, diversified, tax-efficient, risk-managed retirement portfolio.

We find that the robust asset allocation (RAA) matches–** and arguably beats**–the performance of a Dual Momentum approach (DUAL MOM).

The bottom line is that both systems are worth a look. However, given our preference for keeping things as simple as possible, in our view, **RAA wins the asset allocation horserace. **

### 1. Background:

Before we start the horserace, let’s meet the horses and walk through the rules of our race.

Momentum strategies have been studied for decades in both practice and academia. Momentum strategies are robust across *different time periods* and also across *different asset classes* (equities, bonds, commodities, real estate, and so forth), making them a good choice for asset allocation.

There is sometimes a lot of confusion associated with so-called “momentum” strategies, and people interpret and apply them in many different ways. We break momentum into two categories below to differentiate between common approaches to implementing “momentum.”

(1) **Absolute, or time-series momentum:** an asset classes’ own past return, considered independently from the returns of other asset classes, predicts its future performance. This could apply at the level of individual securities as well.

(2) **Relative Strength, or Cross-sectional momentum**: an asset classes’ performance, relative to other asset classes, predicts its future relative performance. This could also apply at the individual security level, when performance is compared versus the performance of comparable securities; thus, the term is not exclusive to “asset classes.”

#### 1.1 Dual Momentum Strategy

Step 1: Calculate Relative Momentum within an Asset Pair (RMOM)

- Pick the asset with the highest relative performance over the past 12 months

Step 2: Time Series Momentum Rule (TSMOM) on RMOM asset

- Excess Return = total return over past 12 months less return of T-bill
- If Excess return > 0, go long risky assets. Otherwise, go to alternative assets (T-bills)

#### 1.2 Robust Asset Allocation (RAA):

The Robust Asset Allocation (RAA) framework is risk-managed with a combination of 50% TSMOM and 50% MA. Here is our full article about RAA.

- 50% Time Series Momentum Rule (TSMOM)
- Excess return = total return over past 12 months less return of T-bill
- If Excess return >0, go long risky assets. Otherwise, go alternative assets (T-Bills)

- 50% Simple Moving Average Rule (MA)
- Moving Average (12) = average 12 month prices
- If Current Price – Moving Average (12) > 0, go long risky assets. Otherwise, go alternative assets (T-bills).

### 2. RAA and Dual MOM Horserace By Asset Pair

Our simulated historical period is from 1/1/1977 to 7/31/2014 for the Equity, REIT, and Stress pairs, and 1/1/1986 to 7/31/2014 for the Credit pair. Results are gross, no fees are included, and only index returns are included. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. All returns are total returns and include the reinvestment of distributions (e.g., dividends). Strategies are all monthly-rebalanced.

Below are the 8 asset classes (4 pairs), and the ROBUST system:

**SP500**= S&P 500 Total Return Index**EAFE**= MSCI EAFE Total Return Index**Equity REIT**= FTSE NAREIT All Equity REITS Total Return Index**Mortgage REIT**= FTSE NAREIT All Mortgage REITS Total Return Index**LTR**= The Merrill Lynch 10-year U.S. Treasury Futures Total Return Index**GOLD**= London Gold Market PM Fixing index**High Yield Bond**= Bank of America Merrill Lynch U.S. Cash Pay High Yield Index**BBB US corporate**= The BofA Merrill Lynch 3-5 Year A-BBB US Corporate Index**ROBUST**= 50% MA and 50% TMOM

When analyzing the 4 pairs in the ROBUST system, we do the following. Every month, assume a 50/50 split between the 2 assets. In equity, we would assume 50% SP500 and 50% EAFE. We then assess the risk-management rules on the two assets using 50% time-series momentum and 50% moving-average rules. If the risk-management rules state to be “out” of one of the pairs, we take that portion and invest in RF.

We assessed the historical “winner” based on a combination of Sharpe and Sortino Ratios. If the Sharpe and Sortino were both better it was a clear win; If the Sharpe and Sortino were mixed it was deemed a tie. Let’s take a peak at the results:

Next, here is the detailed analysis:

#### 2.1 Equity Assets Summary Statistics

We assess the Domestic Equity (SP500) and International Equity (EAFE) pair from 1/1/1977 to 7/31/2014.

- DUAL MOM outperforms ROBUST.

#### 2.2 REIT ASSETs SUMMARY STATISTICS

We assess the Equity REIT and Mortgage REIT pair from 1/1/1977 to 7/31/2014.

- ROBUST Outperforms DUAL MOM.

#### 2.3 Stress ASSETS SUMMARY STATISTICS

We assess the Gold Asset and Long-term Bond (LTR) pair from 1/1/1977 to 7/31/2014.

- ROBUST Outperforms DUAL MOM.

#### 2.4 Credit ASSETS SUMMARY STATISTICS

We assess the High Yield Bond and BBB-rating Bond pair from 1/1/1986 to 7/31/2014.

- ROBUST Outperforms DUAL MOM.

### 3. RAA and Dual MOM Horserace with 8 Assets

In this section, we apply ROBUST and DUAL MOM to the 8 assets and our simulated historical period is from 1/1/1986 to 7/31/2014. Results are gross, no fees are included and only index returns are included. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. All returns are total returns and include the reinvestment of distributions (e.g., dividends). Strategies are all monthly-rebalanced.

Below is the legend:

**EW_DUAL_MOM_8**= Dual momentum applied on all 8 asset classes (4 pairs)**ROBUST_8_assets**= Robust applied on all 8 asset classes**ROBUST_8_assets_Parity**= Robust applied on all 8 asset classes, levered to approximately match volatility of DUAL MOM**60/40**= 60% S&P 500 TR Index and 40% 10-Year Treasury Index

#### 3.1 SUMMARY STATISTICS

- ROBUST Outperforms DUAL MOM.

#### 3.2 Drawdown SUMMARY:

- ROBUST has stronger drawdown protection.

### 4. RAA and Dual MOM Horserace with 6 Assets

In this section, we apply ROBUST and DUAL MOM on 6 assets (excluding the Credit pair due to data limitations) and our simulated historical period is from 1/1/1977 to 7/31/2014. Results are gross, no fees are included, and only index returns are included. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. All returns are total returns and include the reinvestment of distributions (e.g., dividends). Strategies are all monthly-rebalanced.

Below is the legend:

**EW_DUAL_MOM_6**= Dual momentum applied on all 6 asset classes (3 pairs)**ROBUST_6_assets**= Robust applied on all 6 asset classes**ROBUST_6_assets_Parity**= Robust applied on all 6 asset classes, levered to approximately match volatility of DUAL MOM**60/40**= 60% S&P 500 TR Index and 40% 10-Year Treasury Index

#### 4.1 SUMMARY STATISTICS

- ROBUST Outperforms DUAL MOM.

#### 4.2 Drawdown SUMMARY:

- ROBUST has stronger drawdown protection.

### 5. Out of Sample Horserace: 6 Assets, 1977/01 to 1985/12

In this section, we apply ROBUST and DUAL MOM on 6 assets (excluding the Credit pair due to data limitations) and our simulated historical period is from 1/1/1977 to 12/31/1985. Results are gross, no fees are included, and only index returns are included. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. All returns are total returns and include the reinvestment of distributions (e.g., dividends). Strategies are all monthly-rebalanced.

Below is the legend:

**EW_DUAL_MOM_6**= Dual momentum applied on all 6 asset classes (3 pairs)**ROBUST_6_assets**= Robust applied on all 6 asset classes**ROBUST_6_assets_Parity**= Robust applied on all 6 asset classes, levered to approximately match volatility of DUAL MOM**60/40**= 60% S&P 500 TR Index and 40% 10-Year Treasury Index

#### 5.1 SUMMARY STATISTICS

- ROBUST is similar to DUAL MOM

#### 5.2 DRAWDOWN SUMMARY:

- ROBUST has stronger drawdown protection.

### 6. Conclusion

At the outset we highlighted that both the DUAL MOM and the ROBUST asset allocation systems are something every investor should investigate. We assessed the historical “winner” based on a combination of Sharpe and Sortino Ratios. Historically, ROBUST has been a better bet than DUAL MOM. Whether this will continue in the future is anyone’s guess…

- The views and opinions expressed herein are those of the author and do not necessarily reflect the views of Alpha Architect, its affiliates or its employees. Our full disclosures are available here. Definitions of common statistics used in our analysis are available here (towards the bottom).
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GuestFebruary 13, 2015 at 7:09 pmNice work.

typo in

4 and 5

under “Below is the legend:”

“ROBUST_3_assets_Parity = Robust applied on all 8 asset classes”

should read

“ROBUST_6_assets_Parity = Robust applied on all 6 asset classes”

What historical period for volatility do you use for the parity adjustment?

Wesley Gray, PhDFebruary 13, 2015 at 7:18 pmthx. fixed.

We just used 1.6x leverage to get the volatility to approximate each other over the entire time horizon…we didn’t do dynamic volatility parity…kept it simple

CherylFebruary 13, 2015 at 10:30 pmIf you account for transaction costs, you might get different results since MA rules have higher ones than TSMOM. As it is now, Sharpe ratios are very close for both the 6 and 8 asset portfolios. Based on CAGR, DUAL is the clear winner in all categories. Also, equities are what most of us use as our core holdings. TSMOM is the clear winner there.

LorenzoFebruary 14, 2015 at 12:26 pmWhy do MA have higher transaction costs ?

GovindMay 22, 2015 at 1:51 pmLorenzo – With MAs, you compare an average price to the current price. With TSMOM, you compare the the current price to the price at the beginning of the time series, which is usually further away than the average price. So MAs naturally give more trades than TSMOM. My testing shows a third more trades with MAs than with TSMOM and many more whipsaws using the same length of look back.

Wesley Gray, PhDFebruary 14, 2015 at 1:15 pmCheryl, to Lorenzo’s point, DUAL MOM is more transaction heavy than the RAA framework.

Ron ComptonFebruary 14, 2015 at 8:10 amIs the CAGR of all systems dropping over the recent years? It looks as though the last four years’ return is much lower than any other average four year return. Is this an aberration or symptomatic of what can be expected in the future?

Wesley Gray, PhDFebruary 14, 2015 at 1:15 pmHey Ron,

Historically, we have always been in a world of risk-free + 400bps. If risk-free = 10 year bond yields that implies ~6% (2+4) in nominal returns going forward. That is a far cry from the 10+% we’ve seen historically (~ risk-free + 400bps), but that is just a fact of life in a low-yield environment. I’m hoping we get lucky, but hope isn’t an investment strategy. The only things we can control are fees, liquidity, complexity, taxes, and transparency

Ron ComptonFebruary 15, 2015 at 11:04 amThanks Wes- makes sense. What happens when we have negative interest rates does it cut into that 400 basis points?

Wesley Gray, PhDFebruary 15, 2015 at 11:21 amThat was all on a nominal basis…so unlikely we’d get negative intermediate-long term nominal rates, but you never know! JGB 10yr is pretty close to zero!!!

Ron ComptonFebruary 16, 2015 at 7:00 amWes,

Sweden has just implemented negative interest rates. With deflation the practice may spread.

http://www.forbes.com/sites/timworstall/2015/02/13/swedens-rates-go-negative-denmarks-more-negative-and-the-death-of-keynesian-fiscal-policy/

GovindFebruary 14, 2015 at 8:57 pm8 sample, 6 sample, and out of sample Sharpe ratios of DUAL MOM and ROBUST are almost identical. I don’t see how you can say one is better than the other. DUAL MOM is clearly better with equities, and that is what most people use as the core of their portfolios. Jeremy Siegel shows that the real return from stocks is almost twice as high as the real return from bonds since 1802. Antonacci emphasizes stocks in his book and says on his website that the portfolio used in his paper (and here) is not a good one and was created just to illustrate dual momentum. Stocks are where you want to be, and where you show that DUAL MOM has higher Sharpe and Sortino ratios than ROBUST.

Wesley Gray, PhDFebruary 14, 2015 at 9:57 pmYes, but Sharpe and Sortino are actually higher. To do an apples to apples you can apply leverage. And as the volatility parity column highlights, RAA is actually better on a risk-adjusted basis. And that doesn’t consider the additional transaction costs and tax management issues with Dual Mom. Anyway, main point is they are both good.

PaulDOctober 4, 2015 at 1:08 amcan you explain why you have to apply leverage to compare apple to apple ?

Wesley Gray, PhDOctober 4, 2015 at 10:10 amTo ensure the volatility is roughly the same so we can compare CAGRs. Without this leverage, you are comparing a 7% vol strategy to an 11% vol strategy. The same logic would apply if you wanted to compare the CAGR of a micro-cap stock to a investment grade bond–you’d need to lever up the bond so the risk is ~same before comparing returns.

PaulDOctober 6, 2015 at 11:48 ambut here we are starting from the same exact investment universe, I would think each strategy should be compared on their own characteristics: returns, volatility, max drawdowns without adding leverage and ignoring the cost of doing it. I’m probably just missing some background on how strategies should be compared.

Wesley Gray, PhDOctober 6, 2015 at 11:50 amSure, that is why we show the unlevered version as well. But the leveraged version is to see how a volatility-matched version would perform. Bottomline: we present it both ways and the reader can decide which method/technique they prefer.

PaulDOctober 6, 2015 at 12:09 pmmakes perfect sense, thank you.

ygFebruary 15, 2015 at 4:50 amInteresting analysis.

Could you please provide the exact turnover figures, in order to get an idea of how much transaction costs would impact on the two strategies?

Thanks

Wesley Gray, PhDFebruary 15, 2015 at 11:32 amwe’ll grind some charts/data out and post to this blog for review…give us a few days…

PaulDOctober 4, 2015 at 5:35 pmcan you add a link to the data ? Do you have good references comparing moving average vs. absolute momentum rules and also the significance of the look back window (for example why does 10/12 months work and what conditions may make them work better or worst in the future).

Wesley Gray, PhDOctober 5, 2015 at 1:53 pmhttp://blog.alphaarchitect.com/2015/08/13/avoiding-the-big-drawdown-is-downside-protection-helpful-or-heresy/

References to data series are embedded in there. We do not have a link to historical data.

As far as how and why these things may work, you may want to explore the following post:

http://blog.alphaarchitect.com/2015/09/02/how-market-volatility-affects-our-brains/

PaulDOctober 6, 2015 at 11:59 amvery useful links, thank you ! I’m still left wondering on why 12 months/200 days are magic and why they would still work well in the future.

I was referring to the data about the number of trades involved in one strategy vs. another. On this topic someone on another forum made a good observation: how many losing trades in a row does one have to go through for a given strategy. It’s probably key to stay the course. One huge advantage B&H has by trading once a year (always dealing with long-term capital gains doesn’t hurt). It probably feels great to move to cash when the financial world seems to come to an end or get back into the market when the trend is going back up after a big drawdown but it probably feels awful to trade multiple times while being whipsawed leading to abandoning the strategy. In other words the trade outcome even more than underperformance may weight on the ability to stick to the strategy. Any study or data on this topic would be very interesting.

Pete NikolaiMarch 14, 2015 at 6:19 pmThanks for the transparency in comparing these strategies.

What are the statistics for Dual Momentum as outlined in Antonacci’s book (invest in the best performing asset from S&P 500, EAFE, and Treasury Bonds if greater than T-bills…) versus the best performing ROBUST scenario?

Seems like a test should allow each strategy to stand on its own merits rather than editing one to align with the other.

Pete NikolaiMarch 14, 2015 at 6:19 pmThanks for the transparency in comparing these strategies.

What are the statistics for Dual Momentum as outlined in Antonacci’s book (invest in the best performing asset from S&P 500, EAFE, and Treasury Bonds if greater than T-bills…) versus the best performing ROBUST scenario?

Seems like a test should allow each strategy to stand on its own merits rather than editing one to align with the other.

Wesley Gray, PhDMarch 15, 2015 at 1:23 pmHi Pete,

The point of this essay was to explore Dual momentum, where we gave Dual Mom the upper hand and let that strategy decide the rules of the game.

If we compare Dual Mom against RAA http://www.alphaarchitect.com/blog/2014/12/02/our-robust-asset-allocation-raa-solution/ (over the same time period and everyone is net of fees), then the horse race goes to RAA.

However, the race is close and both systems are interesting. One probably wants to consider the merits of both when assessing which adventure to pursue (or perhaps you purse both simultaneously!)

Wesley Gray, PhDMarch 15, 2015 at 1:23 pmHi Pete,

The point of this essay was to explore Dual momentum, where we gave Dual Mom the upper hand and let that strategy decide the rules of the game.

If we compare Dual Mom against RAA http://www.alphaarchitect.com/blog/2014/12/02/our-robust-asset-allocation-raa-solution/ (over the same time period and everyone is net of fees), then the horse race goes to RAA.

However, the race is close and both systems are interesting. One probably wants to consider the merits of both when assessing which adventure to pursue (or perhaps you purse both simultaneously!)

KeithJuly 26, 2015 at 11:58 amWhat is RF?

Jack Vogel, PhDJuly 27, 2015 at 8:30 amRisk-free rate, the return to 90-day U.S. Treasury Bills.

OhochbergOctober 15, 2015 at 7:24 amthe Dual momentum model equally weights the different basket tilts (25% each). Does the RAR model apply the same weightings ? the reason I ask is because in your original paper covering RAR, you administer a specific weight allocation to each of these tilts, to come up with a conservative, aggressive, etc..portfolio

Wesley Gray, PhDOctober 15, 2015 at 10:01 amYes, we are trying to run a horse race of the systems against one another so we try and control for the different variables that would muddy the horse race.

I think the punchline is clear: applying trend-following and/or absolute momentum across asset classes has historically worked.

PoolPartyDecember 9, 2015 at 4:13 pmWesley, Why do you bother using a momentum strategy with bonds? When looking at a VBLTX back test there is a higher sharpe ratio for buy and hold than with using a 12 month momentum strategy.

Wesley Gray, PhDDecember 9, 2015 at 4:36 pmYou’re right, there are limited benefits (if any) to trend/momentum in a bond context.

keymasterMarch 4, 2016 at 7:00 amWesley, this was a great article, as are the others on your blog.

At the portfolio level, I think the “RAA 8 asset classes” and the “Dual Momentum 8 asset classes” mentioned in this article are among the portfolios with the highest sharpes out there.(the RAA 8 asset classes portfolio in this article is even better than the RAA_MOD in your RAA article http://blog.alphaarchitect.com/2014/12/02/the-robust-asset-allocation-raa-solution/

Yet, two obvious potential improvements scream out and I was wondering if you had looked at their performance:

(1) portfolio consisting of using Dual Momentum for Equities and RAA for the other asset classes.

(2) adding momentum and value in with the other equity indexes, then choose highest dual momentum of the new set of 4 equity classes (SP500, EAFE, momentum index, value index) as opposed to only two SP500/EAFE.

The latter test might also present an interesting way to integrate your QVAL, IVAL, QMOM, and IMOM etf’s.

Wesley Gray, PhDMarch 4, 2016 at 10:14 amHey Keymaster,

When it comes to value and momentum there are some organic diversification benefits that an investor probably doesn’t want “gamble” away with a relative momentum construct. See the following paper that highlights the combo: http://docs.lhpedersen.com/ValMomEverywhere.pdf

So on one hand an investor might benefit from timing across value and momentum, but on the other hand, they give up the “bird in the hand” benefit of natural diversification benefits associated with value and momentum. We don’t think there is enough evidence out there to suggest there is enough benefit to “time” across val & mom vs. holding them as a static system that always captures the diversification benefit. That said, the “beta” component of value and momentum — or any equity risk asset — should still be considered. If overall market risk sucks, we don’t want to be in anything that has a long beta component — even if it is diversified. A drawdown of -50% sucks, and a diversified equity portfolio that draws down 50% also sucks.

DonMay 21, 2016 at 12:56 pmGreat work as usual. If one is in the accumulation phase and very aggressive it seems that the higher CAGR of Dual Momentum is way more important than the lower volatility and drawdown of RAA, especially since even in Dual Mom they are lower than B&H. What do you think of a Dual Mom portfolio that is 100% equities, 50% Value and 50% Momentum? There would be 2 asset class pairs, VAL_10 INTL_VAL_10 and MOM_10/INTL_MOM_10. This way you don’t try to time Value and Momentum directly but still would get the increase in CAGR from Dual Mom. Adding any other asset class to this would be likely to lower CAGR. Have you ever tested a portfolio like this?

Wesley Gray, PhDMay 23, 2016 at 9:33 amHey Don,

We have not directly tested that, but that seems like a reasonable approach. Bottomline: All these things are interesting, but the trick is finding a system you are comfortable with and seeing it through thick and thin…that “sticking to it” component often proves to be the most difficult aspect.

GovindMarch 14, 2017 at 3:14 pmYou picked a sub-optimal view of dual momentum. Antonacci says on his website’s FAQ that his 4 module paper was meant to illustrate how dual momentum can be applied to different asset classes but is not meant to be a good investment portfolio. His later book shows how dual momentum is best used. With equities as the core holding (that is where you historically get the highest risk premium and best returns), dual momentum clearly outperforms robust. It makes no sense to me to judge something based on where it doesn’t belong.

Wesley Gray, PhDMarch 14, 2017 at 3:18 pmWe discuss that set of results at the outset and highlight that it has worked better in equity. But a robust platform shouldn’t be confined to only working the “best” on one asset class.