Is Gary Antonacci's Global Equity Momentum Strategy Robust?

Gary Antonacci’s excellent book Dual Momentum Investing is a cult hit. Its success is easy to understand. It offers a simple trading system that crushes the market in both absolute and risk-adjusted terms. Antonacci calls it Global Equity Momentum, or GEM.

Here’s how it works: At the end of each month, compare the trailing 12-month total returns of U.S. and foreign stock markets. Select the one with the higher return. If the selected asset’s 12-month total return is higher than the 12-month total return of cash, buy it. Otherwise, buy investment-grade bonds.

The strategy combines a relative momentum signal (what’s doing better?) with an absolute momentum signal (is it positive?) in a simple and intuitive manner.

Antonacci uses the S&P 500, MSCI ACWI ex-US, and Barclays US Aggregate Bond total return indexes to represent U.S. stock, international stock, and investment-grade bond returns, respectively. Here are his back-test results using different lookback windows, including trailing 9, 6, and 3 months.

GEM, 12/1973-12/2013
Annual Return % 17.43 15.85 14.37 13.9 8.85
Standard Deviation % 12.64 12.39 11.84 12.04 15.56
Sharpe Ratio 0.87 0.78 0.71 0.65 0.22
Max Drawdown % -22.72 -18.98 -23.51 -23.26 -60.21
Source: Antonacci, Dual Momentum Investing

GEM almost doubles the annual return of the world stock index. The comparison understates GEM’s advantage. The strategy achieved higher returns with lower volatility and shallower drawdowns. What volatility GEM experienced tended to be on the upside. Moreover, the strategy was uncanny in its consistency, outperforming in almost all periods, even doing better in the past two decades. The exhibit below plots the wealth ratio of the GEM versus a 35-35-30 U.S.-international-bond asset allocation (the results are slightly worse against a 50-50 U.S.-international stock allocation).

When faced with extraordinary back-tested results, we must be extraordinarily skeptical. Good scientists look hard for disconfirming evidence, reasons to knock down a claim, not bolster it. Can we replicate the results? Do they significantly change when we use different indexes? Look at different periods?

I successfully replicated Antonacci’s tests. For good measure, I tried some wacky variations, including lagged windows. GEM1-12, for example, ignores the previous month and uses the 12 months prior to that as its lookback window. Even with six-month returns that are six months stale (GEM6-6), the strategy works.

GEM Replication, 12/1973-12/2013
GEM12 GEM9 GEM6 GEM3 GEM1-12 GEM3-9 GEM6-6
Annual Return % 16.70 15.83 15.49 14.57 16.07 15.23 14.95
Standard Deviation % 12.80 12.73 12.53 12.74 12.88 13.17 13.29
Sharpe Ratio 0.87 0.81 0.80 0.71 0.82 0.74 0.71
Max Drawdown % -19.07 -25.44 -22.40 -23.26 -19.19 -26.85 -26.56
Risk-free Rate: 5.52% Sources: MSCI, Morningstar, author's calculations

My results are slightly worse than Antonacci’s. I never found the return broke 17% annualized. However, I used the Barclays US Aggregate Treasury Bond Index rather than the Barclays US Aggregate Bond Index. I was careful to match his methodology otherwise, splicing the MSCI World ex-US Index with the MSCI ACWI ex-US Index in 1988, using 90-day T-bill returns, and so on.

Note that the 12-month window also happens to be the best-performing strategy. While there is a good economic argument to be made for momentum, there’s no good argument that says momentum should work best over 12-month periods. Why not 10 months? Or even 9? If 9-month momentum worked best, we'd be hearing about that, not 12-month momentum. There is some data-mining here (as there are in all back-tests--you wouldn't be reading this if the back-test didn't work).

Is Stock-Bond Timing Robust?

I was intrigued by the efficacy of the stock-bond switching strategy, which Antonacci calls absolute momentum. Almost all of Antonacci's tests begin in 1974, but there is reasonably good U.S. stock and bond return data going back to 1926. How does Antonacci's absolute momentum rule work prior to 1974? (Relative momentum has been beaten to death and is well-established, so I won't be testing it here.)

I obtained monthly market and 30-day T-bill returns from the French Data Library. I have, courtesy of my former employer, monthly returns for the Ibbotson US Intermediate Term Government Bond Index. The common start date for these return series is June-end 1926. With these data, I tested the absolute momentum stock-bond switching strategy from June-end 1927 to May-end 2015. Each month, the strategy compares the trailing total return of the stock market to the trailing total return of cash. If the stock market’s return is higher, hold stocks. Otherwise, hold bonds.

I tested permutations of the strategy, with 3-, 6-, 9-, and 12-month lookback windows. I also tested lagged lookback windows. Here are my results.

US Stock-Bond Timing, 06/1927-05/2015
Timing12 Timing9 Timing6 Timing3 Timing1-12 Timing3-9 Timing6-6 70-30
Excess Return % 7.98 7.88 6.57 6.14 6.06 6.44 7.36 5.23
Standard Deviation % 12.81 13.29 12.64 13.42 13.01 13.08 13.66 13.30
Sharpe Ratio 0.62 0.59 0.52 0.46 0.47 0.49 0.54 0.39
Maximum Drawdown % -41.76 -44.59 -54.30 -61.13 -34.11 -41.16 -34.81 -71.11
Sources: French Data Library, Morningstar, author's calculations

A couple of notes on my presentation. I show excess returns rather than nominal returns. Excess return is calculated by subtracting the cash return (in this case, 30-day Treasury bill returns) from total return. A 10% return is unimpressive if cash yields 13%, but is phenomenal if cash yields 0%. Excess returns are comparable across different interest-rate regimes whereas total returns are not. My drawdowns are also computed in terms of excess returns. A strategy that earns 0% while cash yields 10% has incurred a 10% opportunity cost; it's only fair to penalize the strategy.

OK, back to the table. Every variation beat the stock market and the blended 70-30 stock-bond portfolio in risk-adjusted terms.  However, tweaking the lookback window strongly affected results. If you lag the 12-month lookback window by a month, the excess return deteriorates to 6% from almost 8%. Bizarrely, if you lag the 6-month window by 6 months, your returns are almost as good as the 12-month unlagged signal.

The results are heavily influenced by returns from the 1930s and 1940s. I looked at the results from 1960 on. The strategy still beats the 70-30 benchmark on a risk-adjusted basis, with the exception of the 1-12 variation. Maximum drawdowns are lower across the board.

US Stock-Bond Timing, 12/1959-05/2015
Timing12 Timing9 Timing6 Timing3 Timing1-12 Timing3-9 Timing6-6 70-30
Excess Return % 6.64 6.28 5.96 6.13 4.82 4.88 5.28 4.35
Standard Deviation % 11.66 11.22 11.17 10.95 11.94 11.70 11.81 11.00
Sharpe Ratio 0.57 0.56 0.53 0.56 0.40 0.42 0.45 0.40
Maximum Drawdown % -25.23 -26.45 -27.89 -27.70 -31.04 -31.04 -31.04 -42.96
Sources: French Data Library, Morningstar, author's calculations

What’s the catch? When the stock market is in a secular bull phase, timing strategies can lag—a lot. Below is a wealth ratio chart of the 12-month stock-bond timing strategy against the market. While the strategy protected against declines in all five major bear markets, it could lag for decades. I don't think many investors understand how extreme the tracking error can get.

However, it is unfair to compare a strategy that is far less exposed to market risk with the stock market. A fairer benchmark is a blend of the average exposures of the timing strategy (though we can't know it ex-ante). On average, the timing strategy was in the market 70% of the time and in bonds 30% of the time. Below is the wealth ratio of the strategy against the 70-30 stock-bond benchmark. The performance looks better, but you can still go decades treading water. After taxes and trading costs, your returns would've been much worse.

Again, keep in mind the 12-month timing strategy is the best-performing of all the permutations I’ve tested. That 1) tweaking the lookback window universally hurts the results and 2) the few extreme episodes that drive all the returns means we should apply a discount to our expectations of the strategy going forward.


To answer the initial question: Yes, Antonacci's GEM is robust to changing specifications. Risk-adjusted returns are universally better across a wide range of parameters. Even when we extend stock-bond timing back to 1926, the strategy works. However, returns tend to degenerate—sometimes significantly—when we move away from a 12-month lookback window.

I ignored costs. However, the strategy still would've worked over the past twenty years (better, in fact), when trading costs were cheap. That the market does not seem to have arbitraged away these profits should be disturbing. Either the market is disgustingly inefficient, allowing this kind of simple price-based strategy to work (it violates the weak-form efficient market hypothesis) or we are chasing a will-o'-the-wisp created by data-mining.

A more important question: Would I put my own money into this strategy? Yes. In fact, I have been applying a trading system very similar to GEM with over a third of my personal assets since 2011. My live performance has been in line with the back-tests, bolstering my confidence in the strategy. There is no substitute for out-of-sample, live, real-money performance.

Three Ways Advisors Hurt Their Clients

Financial advisors like to talk about how they add value; I want to talk about three ways they subtract it.

1. Sell crappy, overpriced products.

A good sign of a huckster masquerading as an advisor is if he hawks any of the following:

closed-end fund initial public offerings
non-traded real estate investment trusts
non-traded business development companies
structured notes
private placements

The common denominator is a fat kickback. Many are sold to small investors. David Lerner Associates' notorious Apple REIT series is a prime example of a crappy, overpriced product. In 2012 FINRA fined the firm $2.3 million and forced it to pay about $12 million in restitution to elderly retail investors it had tricked into buying the non-traded REITs and paying excessive markups on municipal bonds and collateralized mortgage obligations.

Of course, large investors are also sold crappy products. Rather than anything as vulgar as non-traded REITs and BDCs, high-net-worth families are sold access to private-equity and hedge-fund strategies. This is the rich man’s timeshare: a slice of faux luxury bought at a premium, later regretted. The cognoscenti like to talk about how “top-quartile” hedge-fund and private-equity managers generate all the alpha, while the rest lose money. Who keeps plowing money into the losers? My theory: High-net-worth families who are sold the story that their wealth enables them to buy better managers, the same way it enables them to buy big houses and luxury cars. That just ain't so.

I have seen clients gush about advisors who are remorselessly pillaging their assets. This may seem odd, but the financial predators reddest in tooth and claw are often leaders in local charities and the church. In his Bible for would-be wolves, The Million-Dollar Financial Advisor, David Mullen writes, “Many of our top advisors individually donate more than $10,000 to nonprofit organizations that they are involved in. They view these expenditures as retained earnings.” (Tellingly, none of the practicing "top advisors" he interviewed for the book wished to be identified.) It makes perfect sense. The wealthy retired often find purpose by throwing their time and energy into passion projects. Being active in the same causes not only brings you in contact with them, but it signals that you are a good, trustworthy person, even when you're not.

While the crooks seem to be overwhelmingly commission-based brokers governed by the weak suitability standard, fee-only advisors governed by the fiduciary standard also have conflicts with clients that can result in suboptimal advice. The next two apply to both types of advisors.

2. Advise clients to cash out pensions or take Social Security early.

Here’s a common scenario: A company offers to cash out an employee’s pension for a hefty lump sum. Its helpful representatives and brochures make the payout seem more than fair. A savvy employee, observing that the company is not a disinterested party, might go to a financial advisor and ask for his advice.

Here’s what a “bad” advisor would say:

Look at the expected return on the pension. Given your life expectancy, you'll only earn 6% to 7% (or some number thereabouts). We can do better. The stock market has historically returned 10%. Small-cap value stocks have returned several percentage points more than that. Besides, what if the company goes bankrupt? You could end up with nothing.

Here’s what a good advisor would say:

Are you healthy? If yes, you should probably keep the pension. The main reason a company would cash you out is because the lump sum is smaller—sometimes much smaller—than the pension's expected cost. Pensions are valuable not because they offer the highest expected returns, but because they hedge longevity risk (and inflation risk, if you're lucky). Longevity risk is expensive to hedge with private insurance; you cannot buy the same stream of lifetime income with the lump sum. Let’s not forget there is a huge behavioral benefit to having a professionally managed asset that doesn’t have a daily quoted price and that cannot be redeemed on a whim.

This scenario is much more common than you think. Uncle Sam gives all Social Security beneficiaries the option to effectively redeem their pensions early by taking benefits at age 62. For many retirees, particularly married couples, delaying Social Security for at least one spouse until age 70 makes sense. It is often worth drawing down savings to fund the gap before Social Security kicks in. The strategy feels like a money loser because Social Security does not have a visible price, while one’s assets do. Bad financial advisors are happy to encourage clients to claim Social Security early for the same reasons they recommend clients cash out their pensions: they get more money to manage.

The numbers at stake can be surprisingly big. The present value of foregone benefits from taking a pension as a lump sum or claiming Social Security suboptimally can be greater than $100,000. If an advisor put you in a product that instantly lost you $100,000 for no reason other than incompetence, you'd fire him and take him into arbitration. But because we are homo sapiens, not homo economicus, we care less about foregone opportunities than losses caused by direct actionbringing us to our next advisor screwup.

3. Keep cash in money-market accounts and ultra-short-term bond funds.

Warren Buffett, that rational calculator, is unusual in that he treats sins of omission just as seriously as sins of commission. Most of us are not calculators: opportunity cost is simply not as real as losing money to an active decision. This may explain why so many advisors and investors keep their cash in money-market funds and ultra-short-term bond funds when there are FDIC-insured bank products that offer comparable or higher yields for lower risk. By the lights of homo economicus, this is just as bad as lighting up dollar bills.

Consider a retiree who has $1,000,000 in short-duration bond funds. In today’s low-yield environment, he’s earning a yield of around 1%. He would be better off putting his money in an FDIC-insured bank 5-year bank CDs from Synchrony or Barclays, which can yield 2.2% or more. Because the bank CDs are puttable at par, minus a 180-day interest penalty, their effective duration is low. The advisor, for his services, has incurred an opportunity cost of 1% a year on that money in addition to his customary 1% fee. The advisor is destroying $20,000 a year.

There is also self-interest at work. Many advisors would rather stick a client’s cash in a sub-par, low-yielding opportunity they can collect a fee upon than in a superior one they can’t. Hence the proliferation of ultra-short-term bond funds like iShares Short Maturity Bond NEAR and PIMCO Enhanced Short Maturity Active MINT and now Vanguard Ultra-Short-Term Bond VUBFX.

Of course, just because an advisor uses short-duration funds doesn't mean he’s a fool or a crook. Cash-like funds are OK places to park money for a short while. Sometimes it is more practical to keep cash in an investment account rather than shuttling it in and out of bank accounts.

Too Good to be True?

In March, MSCI came out with the Diversified Multi-Factor Index family, or DMFI. It is MSCI’s most ambitious index family to date. With it, MSCI has made the leap from purveyor of simple index strategies to become a sophisticated quantitative equity manager. If the back-test is to be believed, the ACWI DMFI would have beaten the ACWI, a global market-weighted index, 15 out of the past 16 years, the sole exception being 2008.

Here is a chart plotting the cumulative wealth ratio between the ACWI DMFI and the ACWI. When the line slopes up, the DMFI is beating its benchmark. The slope is unreasonably smooth. The same exercise done with the USA flavor of the DMFI shows a similar pattern.

Source: MSCI, my calculations

MSCI must have worked with iShares. Just a month after MSCI announced the index, iShares launched FactorSelect exchange-traded funds tracking various DMFI flavors.

This sets up an interesting experiment. If a back-tested strategy beats its benchmark year after year, there’s nowhere to hide if it flops in a live environment. You can't explain away its failure as statistical noise. Either the strategy was data-mined or the market evolved to render it obsolete.

You may want to dismiss the DMFI as a product of back-testing gone amok. However, MSCI is an imitator. All the firm has done is apply popular academic and practitioner research that purports to have identified stock characteristics associated with excess returns: value, momentum, quality and size. The DMFI is hybrid knockoff of strategies offered by Dimensional Fund Advisors and AQR, two fund managers supported by a roster of academic finance superstars.

I'm a skeptical believer in these factors (except size). I'm a believer because I think there is some excess return to be had from factor strategies; I'm a skeptic because I doubt the return will be as smooth as indicated by the backtests. Time will tell if the DMFI flops. If it does, there’s a good chance DFA’s and AQR’s multi-factor strategies will flop right alongside it.

Why I Joined the Dark Side

Six months ago I decided to quit my job at Morningstar, where I was an exchange-traded fund strategist, to become a financial advisor. Three months ago I told my boss. Six weeks ago I left.

While I enjoyed my role as editor of the Morningstar ETFInvestor newsletter, I couldn't see myself doing the same thing three years down the line. What I wanted to do was work for myself. Not to make lots of money (though that would be nice), but to be free to say what I want, do what I want, and work only with the people that I want. I was unsure how to achieve this, but I knew I wanted to manage money.

In late December, “Elvis” made a case that I could be a very successful advisor. I disagreed, pointing out that an advisor with good people skills and zero investment knowledge will make gobs more money than an advisor with mediocre people skills and actual expertise. For this reason the business overwhelmingly attracts salesmen, hustlers, hucksters.  It's an open secret that many advisors are so ignorant they couldn’t justify their services for free.

Despite my skepticism and harsh assessment of advisors, I couldn't get the idea out of my brain. My 29th birthday was coming up and the opportunity cost of striking out on my own was rising fast. I knew that at some point I would be making enough money that my risk-averse nature would overwhelm my budding entrepreneurial streak. And the more I thought about it, the more appealing the job seemed. Not only did it fulfill my need for autonomy and passion for investing, it was a challenge. Could I succeed in spite of the sales-y nature of the job? Could I run a business in a manner consistent with my values? I wasn't sure.

My lucky break came in January, when “Warren” broached the idea of me managing his money. I was stunned. I had emailed back and forth with him for a couple of years at that point. At first I wasn't sure he was serious, but that quickly changed as we talked. Despite a big age gap, Warren and I became good friends. I was comfortable quitting my job for him, and I had never met the guy (we eventually did meet). So here I am.