The Misuse of Aggregate Active v. Passive Comparisons

Every six months Standard & Poor’s releases its SPIVA Scorecard, a report on the percentage of active funds that underperformed selected S&P benchmarks. Almost every report says the same thing: If you had randomly selected an actively managed mutual fund, you probably would have underperformed a closely matched benchmark. Is this fact by itself a persuasive argument for passive investing? Not really.

We already know that before costs the typical actively managed dollar and the typical passively managed dollar earn the same return,  but that after costs the typical actively managed dollar underperforms on account of higher costs. This is a mathematical truism commonly known as the arithmetic of active management or the cost matters hypothesis. The SPIVA is simply a noisy repeat measurement of this mathematical fact.

I say noisy because it is possible for most active managers to beat their SPIVA-assigned benchmarks. The typical manager tends to underweight larger-cap stocks relative to their SPIVA-assigned benchmarks. All it takes is a collapse in larger-cap stocks for managers as a whole to look brilliant. This happened in 2000, when 63% of large-cap stock funds beat the S&P 500 as the dot-com bubble burst. Many investors mistook this to mean that active managers are better to own during bear markets.

Even the arithmetic of active investing by itself can’t tell you whether indexing is a good idea for a specific investor or even most investors. You can imagine a world in which a handful of large entities like central banks predictably underperform the rest of the market in pursuit of non-economic goals. This would allow many smaller investors to outperform. You can also imagine a world in which a handful of elite investors predictably outperform the rest of the market because of superior information. This would require many smaller investors to underperform. The decision to go active or passive should depend on a sober assessment of one’s “edges”, or inherent advantages over other market participants, and the composition of other players in the market.

Once these factors are taken into account, active investing may be preferable for some investors and not others. For what it’s worth, I happen to believe that index funds are the best options for most investors, most of the time—just not for all investors, all of the time.


Why Investors Are so Bad at Picking Alternatives

This post first appeared in the February Mutual Fund Observer.

Gateway (GATEX) is the $8 billion behemoth of the long-short equity mutual fund category, and one of the biggest alternative mutual funds. I’ve long marveled at this fund’s size given its demonstrable lack of merit as a portfolio diversifier. Over the past 10 years the fund has behaved like an overpriced, underperforming 40% stock, 60% cash portfolio. Its R-squared over this period to the U.S. stock market index is 0.85.

Not only is its past performance damning, but little in the substance of the strategy suggests performance will radically change. Gateway owns a basket of stocks designed to track the S&P 500, with a slight dividend tilt. On this portfolio the managers sell calls on the S&P 500, capping the potential upside of the fund in exchange for a premium up front, and simultaneously buy puts, capping the potential downside of the fund at the cost of a premium up front. By implementing this “collar” strategy, the managers protect the portfolio from extreme ups and downs.

There is another way to soften volatility: Own less equities and more cash—which is pretty much what this fund achieves in a roundabout manner.

Portfolio theory says that an investment is only attractive to the extent that it improves the risk-adjusted return of a portfolio. That means three things matter for each asset: expected return, expected volatility, and expected correlation with other assets in the portfolio. The first two are intuitive, but many investors neglect the correlation piece. A low return, high volatility asset can be an excellent investment if it has a low enough correlation with the rest of the portfolio.

Consider an asset that’s expected to return 0% with stock-like volatility and a perfectly negative correlation to the stock market (meaning it moves in the opposite direction of the market without fail). Many investors, looking at the asset’s standalone returns and volatility, would be turned off. Someone fluent in portfolio theory would salivate. Assume the expected excess return of the stock market is 5%. If you own the stock market and the negatively correlated asset in equal measure, the portfolio’s expected excess return halves to 2.5% and its expected volatility drops to 0%. Apply some leverage to double the portfolio’s return and you end up with a 5% expected excess return with no volatility.

In practice, many investors do not assess assets from the portfolio perspective. They fixate on standalone return and volatility. Much of the time this is a harmless simplification. But it can go wrong when assessing alternatives, such as with Gateway. Judged by its Sharpe ratio and other risk-adjusted measures, Gateway looks like a reasonable investment. Judged by its ability to enhance a portfolio’s risk-adjusted return, it falls flat.

I don’t believe individual investors are responsible for Gateway’s size. If anything, institutional investors (particularly RIAs) are to blame. You would think that supposedly sophisticated investors would not fall into this trap. But they do. A large part of the blame belongs to committee-driven investment processes, which dominate institutional money management. When a committee is responsible for a portfolio, they often hire consultants. These consultants in turn promise to help members of the committee avoid getting fired or sued.

In this context, the consultants like to create model portfolios that have predefined allocations to investment types—X% in large growth, Y% in small-cap value, Z% in long-short equity, and so on—and then find suitable managers within those categories. When picking those managers, they tend to focus on return and volatility as well as performance relative to peers. If not done carefully, a fund like Gateway gets chosen, despite its utter lack of diversifying power.

Why Vanguard Will Take Over the World

As with the last post, this was originally published in the Mutual Fund Observer.

Vanguard is eating everything. It is the biggest fund company in the U.S., with over $3 trillion in assets under management as of June-end, and the second biggest asset manager in the world, after BlackRock. Size hasn’t hampered Vanguard’s growth. According to Morningstar, Vanguard took in an estimated $166 billion in U.S. ETF and mutual fund assets in the year-to-date ending in August, over three times the next closest company, BlackRock/iShares. Not only do I think Vanguard will eventually overtake BlackRock, it will eventually extend its lead to become by far the most dominant asset manager in the world.

With index funds, investors mostly care about having their desired exposure at the lowest all-in cost, the most visible component of which is the expense ratio. In other words, index funds are commodities. In a commodity industry with economies of scale, the lowest-cost producer crushes the competition. Vanguard is the lowest-cost producer. Not only that, it enjoys a first-mover advantage and possesses arguably the most trusted brand in asset management. These advantages all feed on each other in virtuous cycles.

It’s commonly known Vanguard is owned by its mutual funds, so everything is run “at cost.” (This is a bit of a fiction; some Vanguard funds subsidize others or outside ventures.) “Profits” flow back to the funds as lower expense ratios. There are no external shareholders to please, no quarterly earnings targets to hit. Many cite this as the main reason why Vanguard has been so successful. However, the mutual ownership structure has not always led to lower all-in costs or dominance in other industries, such as insurance, or even in asset management. Mutual ownership is a necessary but not a sufficient condition for Vanguard’s success.

What separates Vanguard from other mutually owned firms is that it operates in a business that benefits from strong first-mover advantages. By being the first company to offer index funds widely, it achieved a critical mass of assets and name recognition before anyone else. Assets begot lower fees which begot even more assets, a cycle that still operates today.

While Vanguard locked up the index mutual fund market, it almost lost its leadership by being slow to launch exchange-traded funds. By the time Vanguard launched its first in 2001, State Street and Barclays already had big, widely traded ETFs covering most of the major asset classes. While CEO and later chairman of the board, founder Jack Bogle was opposed to launching ETFs. He thought the intraday trading ETFs allowed would be the rope by which investors hung themselves. From a pure growth perspective, this was a major unforced error. The mistake was reversed by his successor, Jack Brennan, after Bogle was effectively forced into retirement in 1999.

In ETFs, the first-movers not only enjoy economies of scale but also liquidity advantages that allows them to remain dominant even when their fees aren’t the lowest. When given the choice between a slightly cheaper ETF with low trading volume and a more expensive ETF with high trading volume, most investors go with the more traded fund. This makes it very difficult for new ETFs to gain traction when an established fund has ample trading volume. The first U.S. ETF, SPDR S&P 500 ETF SPY, remains the biggest and most widely traded. In general, the biggest ETFs were also the first to come out in their respective categories. The notable exceptions are where Vanguard ETFs managed to muscle their way to the top. Despite this late start, Vanguard has clawed its way up to become the second largest ETF sponsor in the U.S.

This feat deserves closer examination. If Vanguard’s success in this area was due to one-off factors such as the tactical cleverness of its managers or missteps by competitors, then we can’t be confident that Vanguard will overtake entrenched players in other parts of the money business. But if it was due to widely applicable advantages, then we can be more confident that Vanguard can make headway against entrenched businesses.

A one-off factor that allowed Vanguard to take on its competitors was its patented hub and spoke ETF structure, where the ETF is simply a share class of a mutual fund. By allowing fund investors to convert mutual fund shares into lower-cost ETF shares (but not the other way around), Vanguard created its own critical mass of assets and trading volume.

But even without the patent, Vanguard still would have clawed its way to the top, because Vanguard has one of the most powerful brands in investing. Whenever someone extols the virtues of index funds, they are also extoling Vanguard’s. The tight link was established by Vanguard’s early dominance of the industry and a culture that places the wellbeing of the investor at the apex. Sometimes this devotion to the investor manifests as a stifling paternalism, where hot funds are closed off and “needless” trading is discouraged by a system of fees and restrictions. But, overall, Vanguard’s culture of stewardship has created intense feelings of goodwill and loyalty to the brand. No other fund company has as many devotees, some of whom have gone as far as to create an Internet subculture named after Bogle.

Over time, Vanguard’s brand will grow even stronger. Among novice investors, Vanguard is slowly becoming the default option. Go to any random forum where investing novices ask how they should invest their savings.  Chances are good at least someone will say invest in passive funds, specifically ones from Vanguard.

Vanguard is putting its powerful brand to good use by establishing new lines of business in recent years. Among the most promising in the U.S. is Vanguard Personal Advisor Services, a hybrid robo-advisor that combines largely automated online advice with some human contact and intervention. VPAS is a bigger deal than Vanguard’s understated advertising would have you believe. VPAS effectively acts like an “index” for the financial advice business. Why go with some random Edward Jones or Raymond James schmuck who charges 1% or more when you can go with Vanguard and get advice that will almost guarantee a superior result over the long run?

VPAS’s growth has been explosive. After two years in beta, VPAS had over $10 billion by the end of 2014. By June-end it had around $22 billion, with about $10 billion of that  growth from the transfer of assets from Vanguard’s traditional financial advisory unit. This already makes Vanguard one of the biggest and fastest growing registered investment advisors in the nation. It dwarfs start-up robo-advisors Betterment and Wealthfront, which have around $2.5 billion and $2.6 billion in assets, respectively.

Abroad, Vanguard’s growth opportunities look even better. Passive management’s market share is still in the single digits in many markets and the margins from asset management are even fatter. Vanguard has established subsidiaries in Australia, Canada, Europe and Hong Kong. They are among the fastest-growing asset managers in their markets.

The arithmetic of active management means over time Vanguard’s passive funds will outperform active investors as a whole. Vanguard’s cost advantages are so big in some markets its funds are among the top performers.

Critics like James Grant, editor of Grant’s Interest Rate Observer, think passive investing is too popular. Grant argues investing theories operate in cycles, where a good idea transforms into a fad that inevitably collapses under its own weight. But passive investing is special. Its capacity is practically unlimited. The theoretical limit is the point at which markets become so inefficient that price discovery is impaired and it becomes feasible for a large subset of skilled retail investors to outperform (the less skilled investors would lose even more money more quickly in such an environment—the arithmetic of active management demands it). However, passive investing can make markets more efficient if investors opting for index funds are largely novices rather than highly trained professionals. A poker game with fewer patsies means the pros have to compete with each other.

There are some problems with passive investing. Regularities in assets flows due to index-based buying and selling has created profit opportunities for clever traders. Stocks added to and deleted from the S&P 500 and Russell 2000 indexes experience huge volumes of price-insensitive trading driven by dumb, blind index funds. But these problems can be solved by smart fund management, better index construction (for example, total market indexes) or greater diversity in commonly followed indexes.

Why Vanguard Might Fail

I’m not imaginative or smart enough to think of all the reasons why Vanguard will fail in its global conquest, but a few risks pop out.

First is Vanguard’s relative weakness in institutional money management (I may be wrong on this point). BlackRock is still top dog thanks to its fantastic institutional business. Vanguard hasn’t ground BlackRock into dust because expense ratios for institutional passively managed portfolios approach zero. Successful asset gatherers offer ancillary services and are better at communicating with and servicing the key decision makers. BlackRock pays more and presumably has better salespeople. Vanguard is tight with money and so may not be willing or able to hire the best salespeople.

Second, Vanguard may make a series of strategic blunders under a bad CEO enabled by an incompetent and servile board. I have the greatest respect for Bill McNabb and Vanguard’s current board, but it’s possible his successors and future boards could be terrible.

Third, Vanguard may be corrupted by insiders. There is a long and sad history of well-meaning organizations that are transformed into personal piggybanks for the chief executive officer and his cronies. Signs of corruption include massive payouts to insiders and directors, a reversal of Vanguard’s long-standing pattern of lowering fees, expensive acquisitions or projects that fuel growth but do little to lower fees for current investors (for example, a huge ramp up in marketing expenditures), and actions that boost growth in the short-run at the expense of Vanguard’s brand.

Fourth, Vanguard may experience a severe operational failure, such as a cybersecurity hack, that damages its reputation or financial capacity.

Individually and in total, these risks seem manageable and remote to me. But I could be wrong.

In short:

  • Vanguard’s rapid growth will continue for years as it benefits from three mutually reinforcing advantages: mutual ownership structure where profits flow back to fund investors in the form of lower expenses, first-mover advantage in index funds, and a powerful brand cultivated by a culture that places the investor first.

  • Future growth markets are huge: Vanguard has subsidiaries in Australia, Canada, Hong Kong and Europe. In these markets passive investing has low market share and correspondingly high fees. Arithmetic of active investing virtually guarantees Vanguard funds will have a superior performance record over time.

  • Vanguard Personal Advisor Services VPAS stands a good chance of becoming the “index” for financial advice. Due to fee advantages and brand, VPAS may be able to replicate the runaway growth Vanguard is experiencing in ETFs.

  • Limits to passive investing are overblown; Vanguard still has lots of runway.

  • Vanguard may wreck its campaign of global domination through several ways, including lagging in institutional money management, incompetence, corruption, or operational failure.

AQR Style Premia Alternative: A Review

This analysis originally appeared in the September 2015 Mutual Fund Observer, but I'm republishing it here for completeness's sake. As always, comments welcome.

Objective and strategy

AQR’s Style Premia Alternative, or SPA, strategy offers leveraged, market-neutral exposure to the four major investing “styles” AQR has identified:

Value, the tendency for fundamentally cheap assets to beat expensive assets.

Momentum, the tendency for relative performance in assets to persist over the short run (about one to twelve months).

Carry, the tendency for high-yield assets to beat low-yield assets.

Defensive, the tendency for low-volatility assets to offer higher volatility-adjusted returns than high-volatility assets.

To make the cut as a bona fide style, a strategy has to be persistent, pervasive, dynamic, liquid, transparent and systematic.

SPA offers pure exposure to these styles across virtually all major markets, including stocks, bonds, currencies, and commodities. It removes big, intentional directional bets by going long and short and hedging residual market exposure. As with all alternative investments, the goal is to create returns uncorrelated with conventional portfolio returns.

SPA sizes its positions by volatility, not nominal dollars. In quant-speak, risk is often used as short-hand for volatility, a convention I will adopt. Of course, volatility is not risk (though they are awfully correlated in many situations).

SPA’s strategic risk allocations to each style are as follows: 34% each to value and momentum, 18% to defensive, and 14% to carry. Its strategic risk allocations to each asset class are as follows: 30% to global stock selection, 20% each to equity markets and fixed income, and 15% each to currencies and commodities. There is a bias to the value and momentum styles, perhaps reflecting AQR’s greater confidence in and longer history with them.

Risk allocations drift based on momentum and “style agreement,” where high-conviction positions are leveraged up relative to low-conviction positions. The strategy’s overall risk target falls in steps in the event of a drawdown and rises as losses are recouped. These overlays embody some of the hard-knock knowledge speculators have acquired over the decades: bet on your best ideas, cut losers and ride winners, and cut capital at risk when one is trading poorly.

SPA targets a Sharpe ratio of 0.7 over a market cycle. AQR offers two flavors to the public: the 10% volatility-targeted QSPIX and the 5%-vol QSLIX.


AQR Capital Management, LLC, was founded in 1998 by a team of ex-Goldman Sachs quant investors led by Clifford S. Asness, David G. Kabiller, Robert J. Krail, and John M. Liew. AQR stands for Applied Quantitative Research. The firm’s bread and butter has long been trading value and momentum together, an idea Asness studied in his PhD dissertation at the University of Chicago. (Asness’s PhD advisor was none other than Eugene Fama, father of modern finance and one of the co-formulators of the efficient market hypothesis.)

When the firm started up, it was hot. It had one of the biggest launches of any hedge-fund up to that point. Then the dot-com bubble inflated. The widening gap in valuations between value and growth stocks almost sunk AQR. According to Asness, the firm was six months away from going out of business. When the bubble burst, the firm’s returns soared and so did its assets. The good times rolled until thefinancial crisis shredded its returns. Firm-wide assets from peak-to-trough went from $39.1 billion to $17.2 billion. The good times are back: As of June-end, AQR has $136.2 billion under management.

The two near-death experiences have instilled in AQR a fear of concentrated business risks. In 2009, AQR began to diversify away from its flighty institutional clientele by launching mutual funds to entice stickier retail investors. The firm has also launched new strategies at a steady clip, including managed futures, risk parity, and global macro.

AQR has a strong academic bent. Its leadership is sprinkled with economics and finance PhDs from top universities, particularly the University of Chicago. The firm has poached academics with strong publishing records, including Andrea Frazzini, Lasse Pedersen, and Tobias Moskowitz. Its researchers and leaders are still active in publishing papers.

The firm’s principals are critical of hedge funds that charge high fees on strategies that are largely replicable. AQR’s business model is to offer up simplified quant versions of these strategies and charge relatively low fees.


Andrea Frazzini, Jacques A. Friedman, Ronen Israel, and Michael Katz. Frazzini was a finance professor at University of Chicago and rising star before he joined AQR. He is now a principal on AQR’s Global Stock Selection team. Friedman is head of the Global Stock Selection team and worked at Goldman Sachs with the original founders prior to joining AQR. Israel is head of Global Alternative Premia and prior to AQR was a senior analyst at Quantitative Financial Strategies Inc. Katz leads AQR’s macro and fixed-income team.

Frazzini is the most recognizable, as he has the fortune of having a last name that’s first in alphabetical order and publishing several influential studies in top finance journals, including “Betting Against Beta” with his colleague Lasse Pedersen.

Unlisted is the intellectual godfather of SPA, Antti Ilmanen, a University of Chicago finance PhD who authored Expected Returns, an imposing but plainly-written tome that synthesizes the academic literature as it relates to money management. Though written years before SPA was conceived, Expected Returns can be read as an extended argument for an SPA-like strategy.

Strategy capacity and closure

AQR has a history of closing funds and ensuring its assets don’t overwhelm the capacity of its strategies. When the firm launched in 1998, it could have started with $2 billion but chose to manage only half that, according to founding partner David Kabiller.

Of its mutual funds, AQR has already closed its Multi-Strategy Alternative, Diversified Arbitrage and Risk Parity mutual funds. However, AQR will meet additional demand by launching additional funds that are tweaked to have more capacity. As of the end of 2014, AQR reported a little over $3 billion in its SPA composite return record. Given the strategy’s strong recent returns, assets have almost certainly grown through capital appreciation and inflows.

Because AQR uses many of the same models or signals in different formats and even in different strategies, the effective amount of capital dedicated to at least some components of SPA’s strategy is higher than the amount reported by AQR.

Management’s stake in the fund

As of Dec. 31, 2014, the strategy’s managers had no assets in the low-volatility SPA fund and little in the standard-volatility SPA fund. One trustee had less than $50,000 in QSPIX. Collectively, the managers had $170,004 to $700,000 in the SPA mutual funds.

Although these are piddling amounts compared to the millions the managers make every year, the SPA strategy is tax-inefficient. If the managers wanted significant exposure to the strategies, they would probably do so through the partnerships AQR offers to high-net-worth investors. But would they do that? AQR, like most quant shops, attempts to scarf down as much as possible the “free lunch” of diversification. The managers are well aware that their human capital is tied to AQR’s success and so they would probably not want to concentrate too heavily in its potent leveraged strategies.

Opening date

QSPIX opened on October 30, 2013. QSLIX opened on September 17, 2014. The live performance composite began on September 1, 2012.

Minimum investment

The minimum investment varies depending share class, broker-dealer and channel. For individual investors, a Fidelity IRA offers the lowest hurdle: a mere $2,500 for the I share class of the normal and low-volatility flavors of SPA. Or you can get access through an advisor. Otherwise, the hurdles are steep: $5 million for the I class, $1 million for the N class, and $50 million for the R6 class.

Expense ratio

The I class for the normal and low-volatility versions cost 1.50% and 0.85%, respectively. The N classes costs 0.25% more and the R6 classes costs 0.10% less.

The per-unit price of exposure to SPA is lower the higher the volatility of the strategy. QSPIX targets 10% vol and costs 1.5%. QSLIX targets 5% vol and costs 0.85%. Anyone can replicate a position in QSLIX by simply halving the amount invested in QSPIX and putting the rest in cash. The effective expense ratio of a half QSPIX, half cash clone strategy is 0.75%.


Among right-thinking passive investors who count fees by the basis point, AQR’s SPA strategy elicits revulsion. It’s expensive, leveraged, complicated, hard to understand, and did I mention expensive?

To make the strategy easier to swallow, some passive-investing advocates argue SPA is “passive” because it’s a transparent, systematic, and involves no discretionary stock-selection or market forecasting. This definition is not universally accepted by academics, or even by AQR. The purer, technical definition of passive investing is a strategy that replicates market weightings, and indeed this definition is used by the venerable William Sharpe in his famous essay, “The Arithmetic of Active Management.”

I do not think SPA is passive in any widely understood sense of the word. In fact, I think it’s about as active as you can get within a mutual fund. And I also happen to think SPA is a great fund. Regardless of my warm feelings for the strategy, I consider SPA suitable only for a rare kind of nerd, not the investing public.

Though SPA is aggressively active, its intellectual roots dig deep into the foundations of financial theory that underpin what are commonly thought to be “passive” strategies, particularly value- and size-tilted stock portfolios (DFA has made a big business selling them).

The nerds among you will have quickly caught on that what AQR calls a style is nothing more than a factor, a decades-old idea that sprung from academic finance.

For the non-nerds: A factor, loosely speaking, is a fundamental building block that explains asset returns. Most stocks move together, as if their crescendos and diminuendos were orchestrated by the hand of some invisible conductor. This co-movement is attributed to the equity market factor. According to factor theory, a factor generates a positive excess return called a premium as reward for the distinct risk it represents.

It is now widely agreed that two factors pervade virtually all markets: value and momentum (size has long been criticized as weak). AQR’s researchers—including some of the leading lights in finance—argue there are two more: carry and defensive. They’ve marshalled data and theoretical arguments that share an uncanny family resemblance with the data and arguments marshalled to justify the size and value factors.

The SPA strategy is a potent distillation of the factor-theoretical approach to investing. If you believe the methods that produced the research demonstrating the value and size effects are sound, then you have to admit that those same tools applied to different data sets may yield more factors that can be harvested.

OK, I’ve blasted you with theory. On to more practical matters.

Who should invest in this fund?

Investors who believe active management can produce market-beating results and are willing to run some unusual but controllable risks.

How much capital should one dedicate to it?

Depends on how much you trust the strategy, the managers, and so on. I personally would invest up to 30% of my personal money in the fund (and may do so soon!), but that’s only because I have a high taste for unconventionality, decades of earnings ahead of me, high conviction in the strategy and people, and a pessimistic view of competing options (other alternatives as well as conventional stocks and bonds). Swedroe, on the other hand, says he has 3% of his portfolio in it.

How should it be assessed?

At a minimum, an alternative has to produce positive excess returns that are uncorrelated to the returns of conventional portfolios to be worthwhile.

However, AQR is making a rather bold claim: It has identified four distinct strategies that produce decent returns on a standalone basis and are both largely uncorrelated with each other and conventional portfolios. When combined and leveraged, the resulting portfolio is expected to produce a much steadier stream of positive returns, also uncorrelated with conventional portfolios.

So far, the strategy is working as advertised. Returns have been good and uncorrelated. In back-tests, the strategy only really suffered during the dot-com bubble and the financial crisis. Even then, returns weren’t horrendous.

Is AQR’s 0.7 Sharpe ratio target reasonable?

I think so, but I would be ecstatic with 0.5.

What are its major risks?

Aside from leverage, counterparty, operational, credit, etc., I worry about a repeat of the quant meltdown of August 2007. It’s thought that a long-short hedge fund suddenly liquidated its positions then. Because many hedge funds dynamically adjust their positions based on recent volatility and returns, the sudden price movements induced by the liquidation set off a self-reinforcing cycle where more and more hedge funds cut the same positions. The stampede to the exits resulted in huge and sudden losses. However, the terror was short-lived. The funds that sold out lost a lot of money; the funds that held onto their positions looked fine by month-end.

AQR is cognizant of this risk and so keeps its holdings liquid and doesn’t go overboard with the leverage. However, it is hard for outsiders to assess whether AQR is doing enough to mitigate this risk. I think they are, because I trust AQR’s people, but I’m well aware that I could be wrong.

Bottom line

One of the best alternative funds available to mutual-fund investors.

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.