Momentum... · currencies, global sovereign debt, real estate, etc.2 The general consensus now within the academic community is that momentum is real and persistent; in point of fact,

Investment Insights Series l March 2015

Summary The purpose of this paper is threefold: first, to provide some

degree of definitional clarity for the term momentum, which is frequently

employed in both academic and practitioner settings without a clear

consensus as to what it actually means; second, to provide a plausible

rationale for the relatively widespread persistence of momentum across

financial markets; and third, to present a real-world application of this

risk premium and highlight its potential importance within an overall

asset allocation.

A Core Risk Premium

Momentum

Andrew WeismanChief Investment Officer,Liquid Alternatives Group

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Momentum: What is it?

Momentum, as a concept, became popular in academic finance in 1993 when Jegadeesh and Titman co-authored a paper titled “Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency.”1 This paper staked the claim that strategies that buy stocks that have performed well in the past and sell stocks that have performed poorly in the past generate significant positive returns over three- to 12-month holding periods. Since that time, a host of research has been published that confirms the profitability of related investment strategies across a broad range of equity categories and other asset classes including: U.S. stocks, equity industry categories, foreign equities, emerging market equities, commodities, currencies, global sovereign debt, real estate, etc.2 The general consensus now within the academic community is that momentum is real and persistent; in point of fact, it has been roundly embraced and celebrated.

“… the center stage anomaly of recent years …” “The premier anomaly …” –Eugene Fama, Kenneth French3

In order to conclusively demonstrate the existence of what became known as “momentum,” Jegadeesh and Titman made use of a precisely defined investment strategy involving the simultaneous management of both a large “long” equity portfolio and a large “short” equity portfolio. The beauty of this research is that, given the large number of securities involved and the length of the data set, the authors were able to identify a relatively stable, statistically robust effect, i.e., autocorrelated4 return outcomes, in an ostensibly highly efficient market. At its core, this research succeeded in documenting an “unfair game.” There was, however, an unfortunate side effect of this research, namely that it obscured for many their core underlying accomplishment: the identification of price movement in a relatively efficient financial market that was not a “martingale,” a fair game; more on this in a moment. By structuring their study involving the use of both a long and a short portfolio, the term momentum came, for some, to be uniquely identified as an equity-centric, relative-performance concept, resulting in an additional level of jargon (relative momentum versus absolute momentum); in the author’s opinion, the term momentum need never have been coined as there existed perfectly

satisfactory terms such as serial- and/or autocorrelation. To the extent that this term has any real utility, it represents a terse way of pointing to two things: a general class of risk factors, and a general class of investment strategies that seek to profit from the presence of positively autocorrelated, non-martingale price movement.5

In probability theory, “fair games” have a precise definition and are frequently referred to as martingales. Without getting too far down a definitional rabbit hole, the basic idea of a fair game (a martingale) is that your expected wealth after the next round of betting is equal to your current wealth, irrespective of any outcomes in any previous rounds; each outcome is independent of any prior outcome(s). Generally speaking, in situations where we have autocorrelated returns, outcomes in one period provide information about future outcomes; subsequently, the game is no longer “fair.”

The rigorous documentation of persistent and widespread market inefficiency was no small accomplishment. This is especially true given the reliance by academics and market participants on the assumption of a relatively efficient marketplace as the basis for such important concepts as the Capital Asset Pricing Model, the Black/Scholes Option Model and various interest rate term structure models, to name just a few. While academics initially faced certain conceptual barriers, these conceptual obstacles did not exist within the trading community. The world’s trading community has, in fact, long been aware of the presence of exploitable market inefficiencies associated with autocorrelated price movement; this was not an insight gained at the tail end of the 20th century. In fact, references to trading strategies that, at their heart, rely on autocorrelation appear in the practitioner literature at least as far back as 1688,6 and include a host of relatively well-known books on “technical trading strategies” published from the 1920s through the 1990s.7

The documented presence and long-term survival of market inefficiency (in this case, autocorrelated price movement) would seem to present a virtual modern-day Copernican revolution for economic orthodoxy. After all, one of the towering papers of modern finance, Samuelson’s “Proof That Properly Anticipated Prices Fluctuate Randomly,”8 accomplished precisely what the title indicates; it proved that “competitive prices must display price changes over time … that perform a random walk with no predictable bias.”

1Jegadeesh, Titman, 1993. 2Some of the many papers over the years include: Cutler, Poterba, Summers, 1989; Chan, Jegadeesh, Lakonishok, 1996; Antonacci, 2012. 3Fama, French, 2008. 4The return this period is influenced by the return of the prior period. 5For a useful summary of a number of the econometric techniques used to facilitate momentum/trend trading see Bruder, Dao, Richard, Roncalli, 2011. 6Jose de la Vega, 1688. 7Examples include: Dow, Hamilton, 1930; Murphy, 1999. 8Samuelson, 1965.

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As it turned out, the documented presence of inefficiency in financial markets posed far less of a conundrum for today’s economic theoreticians than might be imagined. In Samuelson’s defense (not that he needs one), in his own paper he expresses the sentiment that there is no a priori necessity for actual market prices to “act in accordance with specific probability models,” and in fact identifies a few instances where they could be expected not to. So how was this seeming conflict resolved?

A good place to start is one of the other seminal works of finance — the Grossman/Stiglitz paper titled “On the Impossibility of Informationally Efficient Markets.”9 The basic intuition developed in this paper is that prices change as markets incorporate new information, but do so in response to the investment activities of “informed arbitrageurs.” Given that trading activity and the act of becoming “informed” require an expenditure of resources, such arbitrageurs require compensation to participate. If they are not appropriately compensated, they will not participate, subsequently there must be some “equilibrium degree of disequilibrium.” The beauty of this paper is that it obviates the need for a complex or overly-creative explanation for the empirical reality that many reasonably competitive markets are not, in fact, martingales. Armed with this insight, we now have a basis for reconciling competitive markets with autocorrelated price movement; we have a sound theoretical basis for rejecting the expectation of an instantaneous jump to a new equilibrium that fully prices in new information. In this more modern theoretical framework, efficiency is understood to be, per force, somewhat inefficient.

There are certainly other explanations for non-martingale price movement. One relatively straightforward case for the presence of autocorrelated price movement is presented in the Samuelson Award-winning book “Asset Pricing.” The author, John Cochrane, shows how risk premiums are time varying and ultimately depend on gradually evolving economic variables associated with the business cycle, subsequently inducing autocorrelation in the movement of asset prices.10

These relatively simple,11 logical explanations for the persistence of some nontrivial degree of market inefficiency have however proven unsatisfactory to many in the research community. Many well-known, well-respected researchers have instead chosen to ascribe the

persistence of autocorrelation to more “creative” origins such as the psychological frailties of market participants. Some of the more notable “behavioral” explanations in the literature are: herding (endogenously determined trading behavior), anchoring (relying too heavily on the first piece of information received), conservatism (tendency to slowly update beliefs in response to new information), extrapolation (inferring too much from small data sets) and disposition (tendency to sell investments that have increased in price but keep investments that have decreased in price). One of the important papers in this category,12 published by Barberis, Shleifer and Vishny (1998), provides a behavioral model to explain the underreaction of stock prices to news such as earning announcements and overreaction of stock prices to a series of good or bad news.13

In the context of the Grossman and Stiglitz framework, herding is the most relevant behavioral explanation for autocorrelation. As it turns out, herding is a well-studied feature of the animal world. This behavioral characteristic has been written about by academics across a broad spectrum of disciplines including: evolutionary biology, psychology, philosophy, sociology, and not to be outdone, economics and finance. In the context of economics and finance, much of the literature points to herd behavior that is the result of heterogeneous information. Conceptually, informed investors trade on their nonpublic information while uninformed investors trade in reaction to the activities of informed investors,14 thereby inducing herd behavior and autocorrelated price changes. As the argument goes, as long as pertinent market information is not simultaneously and freely available to all investors, there will be non-martingale price changes in financial markets. A more recent paper by Hong and Stein provides a closely related explanation for autocorrelation. In their paper they divide the investing world into Newswatchers (similar to informed investors) and Momentum Traders (similar to uninformed investors). In their model, Newswatchers trade on their private information while not extracting other Newswatcher information from the price movement; if information diffuses gradually, prices underreact in the short run and Momentum Traders can profit by trend chasing.15

The bottom line is that autocorrelation is both a logical and empirically persistent feature of even highly competitive markets. We have a plethora of

9Grossman, Stiglitz, 1980. 10Cochrane, 2005. 11The intuition is simple; the papers on the other hand can be rather technically demanding. 12Others include: Chopra, Lakonishok, Ritter, 1991; De Bondt, Thaler, 1985; Fama, 1991. 13Barberis, Shleifer, Vishny, 1998. 14Banerjee, 1992; Grossman, Stiglitz, 1976. 15Hong, Stein, 1999.

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explanations, ranging from hard-core, closed-form mathematical solutions to behavioral explanations rooted in the frailties of our “reptilian” brain.16 We have not, however, completed the picture. When we seek to harvest this relatively persistent, but time-varying feature of markets, what do we expect to be compensated for; is this a true risk premium?

Momentum: Anomaly or Risk Premium?

To usefully answer this question, it is a good idea to pause for a moment and consider what is intended by both terms: anomaly and risk premium.

An anomaly is typically defined as an unexpected outcome given a specified set of assumptions. In the case of momentum (widespread exploitable autocorrelation), it can only be termed an anomaly under the assumption of strong-form market efficiency; as we’ve seen, this is not a reasonable assumption in a world with heterogeneous information and nontrivial costs associated with becoming informed and operationalizing an investment program. It is, however, worth observing that Nobel laureate Eugene Fama refers to momentum as an “anomaly” despite both rapturously acknowledging its existence and the availability of sound theoretical explanations for the widespread persistence of autocorrelated price movement.

A risk premium, on the other hand, is simply expected compensation for an assumed risk.17 For example, your willingness to hold risky equity securities issued by a company in search of investment capital is compensated by your expectation that you will obtain a return in excess of the risk-free rate. We may therefore represent a risk premium with the following simple equation:

E[U(ra)] = U(rf + π)

This equation states that the expected utility of a risky asset is equal to the utility of the risk-free rate plus a transferred, assumed risk that you expect to be compensated for in the form of a premium. In the case of momentum, investors buy assets that are increasing in price (on an absolute or relative basis) and/or sell assets that are decreasing in price (on an absolute or relative basis) in anticipation of a profit driven by autocorrelated price movement as markets incorporate exogenous events such as important newly-available information. Momentum

investors thereby serve the role of responding to changes taking place in markets, thereby accelerating price adjustments to a new equilibrium in response to changing economic conditions (“pricing in” new information) while assuming the associated nontrivial risks that prices overshoot their new equilibrium levels or that what was assumed to be new information was in fact just residual market volatility that required no real price adjustment. Such risks are not to be taken lightly. A study authored in 2013 by Barroso and Santa-Clara showed that while momentum has offered investors higher Sharpe ratios than market, value or size factors, it has also had some of the biggest crashes. The authors argue that proper risk management is vital to the successful implementation of a momentum investment strategy, and that investors could benefit greatly by monitoring the realized volatility of daily returns and adjusting exposures accordingly.18

Interest Rate Momentum: A Practical Application

Momentum has the potential to perform an important role in protecting portfolios. First, from a theoretical standpoint, Gatev and Ross argue that the use of momentum (under the reasonable assumption of short-run asset mispricing due, for example, to autocorrelated price movement) is consistent with the long-term optimum-growth policies of institutional investors.19 Second, from a practical standpoint, momentum strategies tend to be relatively liquid and therefore can offer the required capacity for institutional investors. In a recently published study of trend-following in futures markets, Baltas and Kosowski were able to provide evidence that Commodity Trading Advisors predominantly make use of time-series momentum as the basis for their investing and that there are basically no relevant capacity constraints.20 Finally, momentum has a pronounced tendency to become highly relevant and useful when asset classes and risk factors are producing highly correlated return outcomes due to the emergence of a single dominant risk factor. A recent example that is fresh in the minds of many investors is the bursting of the credit bubble in 2008. During this period, virtually every measure of systemic risk was elevated while most markets performed very poorly due to widespread fears that the world’s banking system would collapse, credit would become unobtainable and a prolonged recession, or even a depression, would ensue. A notable exception during this time period was high-credit-quality sovereign debt. Many investors, in an attempt to protect

16Lo, 2005. 17Not all risks, however, warrant compensation. There is, for example, no inherent, justifiable compensation for jumping off a cliff or in front of a speeding bus as such acts would of course nullify most life insurance policies. Therefore it is more accurate to conceive of “compensated risks” as pre-existing risks that investors are being rewarded for by virtue of their willingness to bear the risk that others wish to transfer. 18Barroso, Santa-Clara, 2013. 19Gatev, Ross, 2009. 20Baltas, Kosowski, 2012.

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themselves from a potential meltdown of the financial system, transferred their wealth into high-quality sovereign debt, resulting in a very pronounced rally in, for example, the U.S. 10-Year Treasury note during the final quarter of the year. Also performing well during much of the year was the short end of both the U.S. and European yield curves as central banks stepped in to help ensure market liquidity by lowering their short-term benchmark interest rates. As we can see from Exhibit 1, during 2008 the Federal Reserve (Fed) lowered their target overnight bank lending rate nine times by a total of 5% to its current level of 0.25%, where it has remained for approximately the last six years.

Exhibit 1Federal Funds Target Rate

Source: Federal Reserve Bank of New York.

There are two obvious points worth making. First, the Fed plays an important role in the determination of interest rates and, second, their policy decisions have been highly autocorrelated; no computer is required to establish this final point. As an example, during the period from 2005 through 2007, the Fed raised the Fed Funds target 25 basis points, every six weeks, 17 times in a row, causing many in the market to speculate that this was part of an unpublicized social welfare program affectionately known as “No Trader Left Behind.” During the year 2008, those investors wise enough to recognize that the Fed would be forced to react to a potential bursting of the credit bubble by undertaking an

aggressive succession of interest rate cuts implemented interest rate momentum investment programs specifically designed to benefit from the expected reaction of the Fed. Such programs, on average, produced outsized returns and played an important role in stabilizing many broad-based investment portfolios.

2008 was of course not the only challenging period for traditional investors where momentum could have played a pivotal role in reducing investment losses. In a study produced in 2012 by Thomas et. al., it was shown that, in general, trend following (momentum) provides substantial improvement in risk-adjusted performance compared to traditional buy-and-hold portfolios or risk-parity asset allocation. They demonstrate that the application of a volatility-managed momentum strategy significantly reduces drawdowns and is particularly useful for more risk averse investors.21 A study presented in 2012 by Glabadanidis demonstrated that the application of simple moving average strategies across 18,000 individual equities provided substantial market timing ability that resembled the returns of “an imperfect at-the-money protective put strategy relative to the underlying portfolio.”22

So what challenges do we face today? While forecasting with precision is difficult, we do have certain important data points that could prove useful in anticipating a plausible course for the economy and the performance of investment portfolios. First, the U.S. government appears structurally incapable of dealing responsibly with fiscal policy. Even the most casual observer of the “Kabuki theatre” that the U.S. Congress has become is aware of this. Second, the Fed has expanded its balance sheet and effectively monetized U.S. debt at a historically unprecedented rate. Publicly available data on the Fed’s website reveals that the Fed’s balance sheet (System Open Market Account or SOMA) has ballooned to $4.5 trillion since 2009 in response to their open market purchases of as much as $85 billion a month in long maturity fixed income securities. One very notable contributor to the growth of SOMA is U.S. Treasury securities; the Fed at one point during quantitative easing (QE) was acquiring approximately 80% of the Treasury’s bond issuance every month.

21Thomas, Clare, Seaton, Smith, 2012. 22Glabadanidis, Paskalis, 2012.

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To understand the implications of these purchases, it is worth reviewing their mechanics (Exhibit 2). The Fed is in a position to affect this prodigious accumulation of assets through the “fiat” creation of money. Money used to purchase debt from the Treasury is created as a “book entry” on the Treasury’s account at the Fed. It is worth noting this behavior is, in a consequence-free world, sustainable in perpetuity. While it is true that the Treasury must continue to make interest and principal payments on any debt it issues, any monies received by the Fed, which include interest and principal payments received on the Fed’s fixed income portfolio, are ultimately remitted to the Treasury. Therefore the Fed need only “mature” the bonds it purchases (hold until maturity) in order to de facto eliminate the Treasury’s obligation. Under these circumstances, the Treasury would receive money from the Fed that it could spend without, in reality, having to pay it back.

The Fed justifies this undertaking by noting that published measures of inflation, most notably the Consumer Price Index (CPI), indicate that the fiat creation of money has not served to debase the national unit of account. If anything, the purchasing power of our money, i.e., inflation as measured by the CPI, has remained stubbornly below the Fed’s 2% annual target and the U.S. dollar has remained relatively stable, while the U.S. stock and bond markets have, at least for now, warmly embraced the Fed’s course of action.

The theoretical argument that supports the Fed’s ability to print money without debasing it is that the “velocity” of money has remained low, i.e., due to a weak risk averse economy, money earned is not being aggressively loaned

out, reinvested, or spent. Subsequently, book-entry money created by the Fed and utilized by the Treasury to pay the government’s bills is not leading to inflation because broader definitions of the money supply are not growing.

The simultaneous problem of large federal deficits and a weak economy have therefore been effectively addressed by having the Fed create money to cover our structural profligacy. We have discovered perpetual motion. Problem solved. Would that this were true!

A more thoughtful examination of the facts provides some basis for concern. Without straying too far off course with a detailed discussion of all of the CPI’s foibles, it is, at the very least, worth observing that the CPI focuses approximately 40% of its calculation on shelter costs as measured by the somewhat fuzzy concept of “owner’s equivalent rent”; essentially a survey-based calculation where owners are asked what they would rent out their homes for, ex-furniture and utilities. Despite the fact that 40% of the CPI is devoted to shelter costs and the Case-Shiller Home Price Index (a well-respected measure of the path of housing costs) has increased year on year by over 13%, the CPI is still registering less than 2% inflation.

The second major cause for concern relates to the Fed’s ability to successfully negotiate its exit from the current briar patch that it has landed in. To gain some perspective on just how temperamental financial markets have become, consider past price behavior in both the equity and fixed income markets. In May 2013, both the U.S. fixed income and equity markets hit record highs, arguably for precisely the same reason: highly-stimulative monetary policy. In June, on the back of a hint, of a whisper of a possibility that, at some unspecified point in the future,

Exhibit 2Money Creation

Treasury Issues Bonds and Sells to Federal Reserve

Fed Credits Account of Treasury

Treasury Makes Interest and Principal Payment to the Fed

The Fed Matures Acquired Bonds and Remits Revenues Received to the Treasury

The Treasury Uses the Proceeds to Pay Bills

United States Federal Reserve

System

Treasury Department

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the Fed would move to a super-highly-stimulative stance from a super-duper-highly-stimulative one (“tapering”), the U.S. 10-year Treasury note increased in yield by more than 100 basis points while the S&P 500 Index experienced a peak to trough loss of almost 7% in just 20 business days. This market reaction illustrates that the Fed must pursue a path of action as narrow as a knife edge. Determining an appropriate path of action will be an extraordinarily difficult task as policy changes by the Fed will produce highly uncertain outcomes that will be difficult to measure in a timely manner; it is a well-established reality of monetary policy that it drives real economic outcomes on a lagged basis of 18 months or more. It is also worth mentioning that the high degree of uncertainty faced by the Fed, in combination with the slow feedback loop used for gauging the impact of policy decisions, could result in highly autocorrelated behavior by the Fed.

During the current interest rate cycle, the Fed will have a great deal to contend with, having to manage both the short- and long-end of the term structure of interest rates (both short and long maturity interest rates); the need to manage both the long- and short-end of the curve being a direct consequence of the unprecedented manipulation of longer maturity fixed income markets.

The third cause for concern is the complex behavior of financial markets engendered by the Fed’s extraordinary efforts to stimulate the economy. When building portfolios, investors have historically been able to diversify away a great deal of market risk by relying on the relatively stable anticorrelation of stocks and bonds; typically when stocks perform poorly, bond markets have done well and vice versa. However, given that both the stock and bond markets simultaneously achieved their respective peak valuations arguably as a result of the Fed’s extraordinary efforts to reflate the economy, it is not the least bit unreasonable to worry that their typically reliable dependence structure could break down. Additionally, while strong economic data has historically been supportive of equity prices, in the current environment, equity markets have had a tendency to react negatively to strong economic data. In the minds of many investors, strong economic data presages the Fed removing stimulus and is therefore, by extension, associated with lower equity prices. These two effects, correlated stock and bond markets and “good news is bad news,” were the key contributing factors to June 2013’s significant losses in ostensibly diversified portfolios. The world’s financial markets have subsequently entered a period where: return outcomes are largely determined by a single factor, i.e., Fed policy decisions; stocks and bonds are becoming

positively correlated; and good equals bad. Welcome to the “New Abnormal.” As noted above, an environment characterized by a concentration of risk factors (correlated stock and bond prices) is precisely the sort of environment where momentum investment strategies have proven useful. In the current environment, the Fed’s policy decisions are likely to prove central to the path of both the stock and bond markets. Mesirow Financial’s chief economist Diane Swonk captured the moment quite nicely, tweeting that the “Fed role makes it (the) only gorilla in the jungle, not just room.”

Finally, the fourth cause for concern is non-synchronous monetary policy across major economic regions. Now that the Fed has exited their aggressive QE program, both the European Central Bank and the Bank of Japan have embarked on aggressive QE programs of their own. Such non-synchronous policy has triggered significant volatility in both the foreign exchange markets (a sustained move higher in the U.S. dollar versus major currencies) and the commodity markets: given that most commodities are priced in U.S. dollar terms, the significant rise in the U.S. dollar has had a depressing effect on commodity prices.

From an investment perspective, in the “New Abnormal” world, sign-constrained (long-only stock and bond investors) face several daunting challenges. The core risk factors in their portfolios have the potential to become highly concentrated due to a single dominant factor: Fed monetary policy. Stocks and bonds have subsequently become increasingly correlated and now frequently respond to economic news in a somewhat perverse but perfectly logical manner, wherein good economic news is frequently bad for both fixed income markets (because it implies “tightening”) and is simultaneously harmful to equity valuations as future earnings must now be, at least conceptually, discounted at a higher rate.

In this “New Abnormal” world, one of the greatest challenges for investors is the possibility of autocorrelated interest rate movement; to wit, the potential for a serious and persistent increase in interest rates that could harm fixed income portfolios while simultaneously harming equity investors as equity prices account for a higher required discount rate — both triggered by stronger economic activity and the required policy response of the Fed. In direct response to this abnormal reality, investors would be well served to consider a core interest-rate momentum investment program that is specifically designed to benefit from medium- to longer-term movements in interest rates, as an addition to a diversified portfolio.

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Momentum in Practice

To gain a clearer insight into the potential value of including momentum in a traditional equity portfolio, consider the following example of returns for a simulated multi-asset momentum portfolio. The annual returns are shown in two formats: annual return and annual return on invested capital (ROIC). Given the highly capital efficient nature of the futures and foreign exchange markets, the

investment in such a risk premium portfolio requires only one-third of the capital to be committed for any desired level of economic exposure. Hence, the return on invested capital (the final column) is approximately equal to three times the annual return on the investment program reported in the second to last column. This is a potential advantage for investors as it allows them to commit less capital to achieve desired exposure as gains and losses are magnified through the use of leverage.

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Exhibit 3Simulated Multi-Asset Momentum Return

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Annual ROIC

2000 0.90% -1.76% 1.03% 0.25% -0.05% 0.81% 0.15% 2.59% -2.02% 1.06% 1.67% -0.76% 3.83% 11.50%

2001 -0.05% -0.94% 1.21% -0.98% 0.63% -0.92% -0.30% 0.48% -0.21% 0.92% -1.26% -0.67% -2.11% -6.32%

2002 -0.22% -0.57% 0.31% -0.68% 1.74% 3.34% -0.77% 0.74% 0.45% -0.09% 0.20% 3.20% 7.80% 23.41%

2003 2.08% 0.97% -2.61% 0.33% 3.43% -0.57% -0.03% 0.39% 0.11% 1.12% 0.59% 1.46% 7.39% 22.18%

2004 0.83% 1.21% 0.28% -1.92% -0.04% -2.43% -1.50% -0.17% -0.88% 1.48% 2.84% 1.17% 0.74% 2.23%

2005 -0.80% 0.26% -1.02% 0.00% 1.64% 0.35% 0.00% -0.98% -0.26% 0.71% 1.91% 0.72% 2.49% 7.46%

2006 0.79% -0.85% -0.78% 2.67% -0.50% -0.05% -1.11% 0.54% 0.52% 1.06% 4.20% -0.49% 6.02% 18.05%

2007 -0.02% -0.45% -0.42% 1.24% 0.86% -0.03% -0.38% -0.28% 2.88% 1.25% 0.72% -0.32% 5.11% 15.32%

2008 1.45% 2.01% 0.74% -0.36% 0.93% 0.84% -1.04% 1.91% 1.49% 1.12% 1.12% 0.50% 11.21% 33.63%

2009 -0.05% -0.69% -1.54% -2.16% 3.91% -1.96% 0.28% 0.24% 1.30% -0.13% 1.82% -0.94% -0.08% -0.23%

2010 -0.72% 1.10% 1.49% 1.73% 3.07% 0.21% -1.01% 0.79% 4.03% 2.80% -0.18% 1.35% 15.53% 46.58%

2011 0.60% 1.31% 0.54% 1.23% -0.49% -0.55% 1.35% 0.71% -1.67% -2.49% -0.42% 0.89% 0.94% 2.82%

2012 0.68% 0.21% 0.27% -0.10% 4.03% -3.18% 1.01% -0.66% 0.41% -1.08% -0.38% 0.14% 1.21% 3.62%

2013 -0.47% -0.58% 1.50% 0.66% -0.71% 0.55% -0.07% -0.88% 2.32% 1.07% -0.55% 0.07% 2.88% 8.63%

2014 -2.37% 1.09% -0.77% 0.53% 0.48% 1.21% -1.05% 3.25% 2.69% 0.90% 2.08% 1.60% 9.93% 29.79%

Simulated returns for a multi-asset momentum strategy invested in commodity, currency, equity and rate momentum strategies. Rebalanced monthly and net of 1.1% annual fees and expenses. Returns represent return on notional exposure, except for ROIC which represents return on invested capital, which is 3x the reported nominal return due to use of leverage. This hypothetical example is used for illustrative purposes only and does not represent the returns of any particular investment. See last page for important information regarding hypothetical and simulated performance.

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Exhibit 3 on the previous page presents the simulated return for a multi-asset momentum strategy, while Exhibit 4 depicts the simulated performance of a multi-asset momentum strategy since the start of 2000 through the end of 2014 and the performance of the S&P 500 Index as a broad measure of market performance.

Exhibit 4Performance of Simulated Multi-Asset Momentum Strategy and S&P 500 Index

Source: Bloomberg, Janus Liquid Alternatives Analytics. Simulated Multi-Asset Momentum returns reflect return of the strategy described in Exhibit 3. See last page for important information regarding hypothetical and simulated performance.

Exhibit 5 reveals just how potentially useful the inclusion of a multi-asset momentum strategy can be for both reducing volatility and enhancing returns. By re-allocating just 10% to this simulated risk premium portfolio, the new combined portfolio (Momentum-Enhanced Hypothetical Blend (MEHB)) experienced a 9% reduction in volatility, a 33% improvement in annualized return (from 3.64% to 4.85%), and a 47% improvement in risk-adjusted return (the ratio of return to volatility). It is worth noting that much of the enhancement, in our opinion, is due to the very low measured correlation (0.05) of the simulated multi-asset momentum strategy versus the equity markets.

Exhibit 5Inclusion of a Multi-Asset Momentum Strategy can Reduce Volatility and Enhance Returns

S&P 500 MEHB Improvement

Annualized Volatility

15.25% 13.86% 9%

Annualized Return

3.64% 4.85% 33%

Return/Volatility

0.24 0.35 47%

Source: Bloomberg, Janus Liquid Alternatives Analytics. Momentum-Enhanced Hypothetical Blend reflects a hypothetical combination of 90% S&P 500 Index and 10% ROIC return of the strategy described in Exhibit 3. See last page for important information regarding hypothetical and simulated performance.

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S&P 500 IndexSimulated Multi-Asset Momentum

12/201412/201312/201212/201112/201012/200912/200812/200712/200612/200512/200412/200312/200212/200112/200001/2000

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Conclusion

The term momentum is used in both academic and practitioner settings without a broadly accepted definition. At the heart of virtually all definitions, however, is the idea that price changes in the current period, be they absolute or relative, provide information with respect to price changes in future periods: higher (lower) prices today presage higher (lower) prices tomorrow. From an empirical perspective, the relatively widespread and persistent presence of autocorrelated price movement is a well-established feature of most markets, even highly competitive markets with transparent pricing. There are a number of well-founded explanations for this empirically observable feature of markets ranging from structural “limits to arbitrage” arguments to behavioral explanations such as herding, conservatism, extrapolation and disposition. There have been myriad papers written outlining the useful role for investment strategies that seek to harvest momentum. Perhaps the most notable potential benefit cited in such research is a reduction in overall portfolio volatility that is consistent with the long-term wealth-maximization goals of prudent institutional investors.

Finally, our current economic environment has created some serious potential challenges for today’s investors. As we emerge from a historically unprecedented period of monetary stimulus, we face the very real prospect of equity and fixed income markets becoming more highly correlated, thereby reducing the diversification benefits found in most traditional investment portfolios. Going forward, momentum could well serve an instrumental role in stabilizing investment outcomes through a challenging period.

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Banerjee. “A Simple Model of Herd Behavior.” Quarterly Journal of Economics, 1992.

Barberis, Shleifer, Vishny. “A Model of Investor Sentiment.” Journal of Financial Economics, September 1998.

Barroso, Santa-Clara. “Momentum Has Its Moments,” April 2013.

Bruder, Dao, Richard, Roncalli. “Trend Filtering Methods for Momentum.” The Lyxor White Paper Series, December 2011.

Chan, Jegadeesh, Lakonishok. “Momentum Strategies.” The Journal of Finance, December 1996.

Chopra, Lakonishok, Ritter. “Performance Measurement Methodology and the Question of Whether Stocks Overreact.” Journal of Financial Economics, 1991: 31:235-268.

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de la Vega, Jose. Confusion of Confusions, 1688.

Dow, Hamilton. Stock Market Theory and Practice. 1930.

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Fama, French. “Dissecting Anomalies” The Journal of Finance, 2008.

Gatev, Ross. “Momentum Trading and Performance with Wrong Return Expectations.” Journal of Portfolio Management, 2009.

Glabadanidis, Paskalis. “Market Timing with Moving Averages.” 25th Australasian Finance and Banking Conference, 9 Nov. 2012.

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Grossman, Stiglitz. “On the Impossibility of Informationally Efficient Markets.” The American Economic Review, 1980.

Hong, Stein. “A Unified Theory of Underreaction, Momentum Trading and Overreaction in Asset Markets.” The Journal of Finance, 1999.

Jegadeesh, Titman. “Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency.” The Journal of Finance, March 1993.

Lo, Andrew. Reconciling Efficient Markets with Behavioral Finance: The Adaptive Markets Hypothesis. SSRN, 2005.

Murphy. Technical Analysis of the Financial Markets: A Comprehensive Guide to Trading Methods and Applications, 1999.

Samuelson. “Proof That Properly Anticipated Prices Fluctuate Randomly.” Industrial Management Review, Spring 1965.

Thomas, Clare, Seaton, Smith. “Trend Following, Risk Parity and Momentum in Commodity Futures.” SSRN, 8 Aug. 2012.

Wheelock. “Monetary Policy and the Great Depression; What the Fed Did and Why.” Federal Reserve Bank of St. Louis Review, March/April 1992.

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This publication is for investors and investment consultants interested in the institutional products and services available through Janus Capital Management LLC and its affiliates. Various account minimums or other eligibility qualifications apply depending on the investment strategy or vehicle.Past performance is no guarantee of future results. Investing involves risk, including the possible loss of principal and fluctuation of value.

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