Tag: trend following

Diversifying the What, How, and When of Trend Following

On April 2, 2018

In Craftsmanship, Risk & Style Premia, Risk Management, Trend, Weekly Commentary

This post is available as a PDF download here.

Summary

Naïve and simple long/flat trend following approaches have demonstrated considerable consistency and success in U.S. equities.
While there are many benefits to simplicity, an overly simplistic implementation can leave investors naked to unintended risks in the short run.
We explore how investors can think about introducing greater diversification across the three axes of what, how, and when in effort to build a more robust tactical solution.

In last week’s commentary – Protect & Participate: Managing Drawdowns with Trend Following – we explored the basics of trend following and how a simple “long/flat” investing approach, when applied to U.S. equities, has historically demonstrated considerable ability to limit extreme drawdowns.

While we always preach the benefits of simplicity, an evaluation of the “long run” can often overshadow many of the short-run risks that can materialize when a model is overly simplistic. Most strategies look good when plotted over a 100-year period in log-scale and drawn with a fat enough marker.

With trend following in particular, a naïve implementation can introduce uncompensated risk factors that, if left unattended, can lead to performance gremlins.

We should be clear, however, that left unattended, nothing could happen at all. You could get lucky. That’s the funny thing about risk: sometimes it does not materialize and correcting for it can actually leave you worse off.

But hope is not a strategy and without a crystal ball at our disposal, we feel that managing uncompensated risks is critical for creating more consistent performance and aligning with investor expectations.

In light of this, the remainder of this commentary will be dedicated to exploring how we can tackle several of the uncompensated risks found in naïve implementations by using the three axes of diversification: what, how, and when.

**The What: Asset Diversification**

The first axis of diversification is “what,” which encompasses the question, “what are we allocating across?”

As a tangent, we want to point out that there is a relationship between tactical asset allocation and underlying opportunities to diversify, which we wrote about in a prior commentary Rising Correlations and Tactical Asset Allocation. The simple take is that when there are more opportunities for diversification, the accuracy hurdle rate that a tactical process has to overcome increases. While we won’t address that concept explicitly here, we do think it is an important one to keep in mind.

Specifically as it relates to developing a robust trend following strategy, however, what we wish to discuss is “what are we generating signals on?”

A backtest of a naively implemented trend following approach on U.S. equities over the last century has been exceptionally effective. Perhaps deceivingly so. Consider the following cumulative excess return results from 12/1969 to present for a 12-1 month time-series momentum strategy.

Source: Kenneth French Data Library. Calculations by Newfound Research. Past performance is not an indication of future returns. All performance information is backtested and hypothetical. Performance is gross of all fees, including manager fees, transaction costs, and taxes. Performance is net of withholding taxes. Performance assumes the reinvestment of all dividends. Benchmark is 50% U.S. equity index / 50% risk-free rate.

While the strategy exhibits a considerable amount of consistency, this need not be the case.

Backtests demonstrate that trend following has worked in a variety of international markets “over the long run,” but the realized performance can be much more volatile than we have seen with U.S. equities. Below we plot the growth of $1 in standard 12-1 month time-series momentum strategies for a handful of randomly selected international equity markets minus their respective benchmark (50% equity / 50% cash).

Note: Things can get a little whacky when working with international markets. You ultimately have to consider whose perspective you are investing from. Here, we assumed a U.S. investor that uses U.S. dollar-denominated foreign equity returns and invests in the U.S. risk-free rate. Note that this does, by construction, conflate currency trends with underlying trends in the equity indices themselves. We will concede that whether the appropriate measure of trend should be local-currency based or not is debatable. In this case, we do not think it affects our overall point.

Source: MSCI. Calculations by Newfound Research. Past performance is not an indication of future returns. All performance information is backtested and hypothetical. Performance is gross of all fees, including manager fees, transaction costs, and taxes. Performance is net of withholding taxes. Performance assumes the reinvestment of all dividends. Benchmark is 50% respective equity index / 50% U.S. risk-free rate.

The question to ask ourselves, then, is, “Do we believe U.S. equities are special and naive trend following will continue to work exceptionally well, or was U.S. performance an unusual outlier?”

We are rarely inclined to believe that exceptional, outlier performance will continue. One approach to providing U.S. equity exposure while diversifying our investments is to use the individual sectors that comprise the index itself. Below we plot the cumulative excess returns of a simple 12-1 time-series momentum strategy applied to a random selection of underlying U.S. equity sectors.

While we can see that trend following was successful in generating excess returns, we can also see that when it was successful varies depending upon the sector in question. For example, Energy (blue) and Telecom (Grey) significantly diverge from one another in the late 1950s / early 1960s as well as in the late 1990s / early 2000s.

If we simply equally allocate across sector strategies, we end up with a cumulative excess return graph that is highly reminiscent of the of the results seen in the naïve U.S. equity strategy, but generated with far more internal diversification.

A potential added benefit of this approach is that we are now afforded the flexibility to vary sector weights depending upon our objective. We could potentially incorporate other factors (e.g. value or momentum), enforce diversification limits, or even re-invest capital from sectors exhibiting negative trends back into those exhibiting positive trends.

**The How: Process Diversification**

The second axis of diversification is “how”: the process in which decisions are made. This axis can be a bit of a rabbit hole: it can start with high-level questions such as, “value or momentum?” and then go deeper with, “which value measure are you using?” and then even more nuanced with questions such as, “cross-market or cross-industry measures?” Anecdotally, the diversification “bang for your buck” decreases as the questions get more nuanced.

With respect to trend following, the obvious question is, “how are you measuring the trend?”

One Signal to Rule Them All?

There are a number of ways investors can implement trend-following signals. Some popular methods include:

Prior total returns (“time-series momentum”)
Price-minus-moving-average (e.g. price falls below the 200 day moving average)
Moving-average double cross-over (e.g. the 50 day moving average crosses the 200 day moving average)
Moving-average change-in-direction (e.g. the 200 day moving average slope turns positive or negative)

One question we often receive is, “is there one approach that is better than another?” Research over the last decade, however, actually shows that they are highly related approaches.

Bruder, Dao, Richard, and Roncalli (2011) united moving-average-double-crossover strategies and time-series momentum by showing that cross-overs were really just an alternative weighting scheme for returns in time-series momentum.[1] To quote,

“The weighting of each return … forms a triangle, and the biggest weighting is given at the horizon of the smallest moving average. Therefore, depending on the horizon n2 of the shortest moving average, the indicator can be focused toward the current trend (if n2 is small) or toward past trends (if n2 is as large as n1/2 for instance).”

Marshall, Nguyen and Visaltanachoti (2012) proved that time-series momentum is related to moving-average-change-in-direction.[2] In fact, time-series momentum signals will not occur until the moving average changes direction. Therefore, signals from a price-minus-moving-average strategy are likely to occur before a change in signal from time-series momentum.

Levine and Pedersen (2015) showed that time-series momentum and moving average cross-overs are highly related.[3] It also found that time-series momentum and moving-average cross-over strategies perform similarly across 58 liquid futures and forward contracts.

Beekhuizen and Hallerbach (2015) also linked moving averages with returns, but further explored trend rules with skip periods and the popular MACD rule.[4] Using the implied link of moving averages and returns, it showed that the MACD is as much trend following as it is mean-reversion.

Zakamulin (2015) explored price-minus-moving-average, moving-average-double-crossover, and moving-average-change-of-direction technical trading rules and found that they can be interpreted as the computation of a weighted moving average of momentum rules with different lookback periods.[5]

These studies are important because they help validate the approach of traditional price-based systems (e.g. moving averages) with the growing body of academic literature on time-series momentum.

The other interpretation, however, is that all of the approaches are simply a different way of trying to tap into the same underlying factor. The realized difference in their results, then, will likely have to do more with the inefficiencies in capturing that factor and which specific environments a given approach may underperform. For example, below we plot the maximum return difference over rolling 5-year periods between four different trend following approaches: (1) moving-average change-in-direction (12-month), (2) moving-average double-crossover (3-month / 12-month), (3) price-minus-moving-average (12-month), and (4) time-series momentum (12-1 month).

We can see that during certain periods, the spread between approaches can exceed several hundred basis points. In fact, the long-term average spread was 348 basis points (“bps”) and the median was 306 bps. What is perhaps more astounding is that no approach was a consistent winner or loser: relative performance was highly time-varying. In fact, when ranked 1-to-4 based on prior 5-year realized returns, the average long-term ranks of the strategies were 2.09, 2.67, 2.4, and 2.79 respectively, indicating that no strategy was a clear perpetual winner or loser.

Without the ability to forecast which model will do best and when, model choice represents an uncompensated risk that we bear as a manager. Using multiple methods, then, is likely a prudent course of action.

Identifying the Magic Parameter

The academic and empirical evidence for trend following (and, generally, momentum) tends to support a formation (“lookback”) period of 6-to-12 months. Often we see moving averages used that align with this time horizon as well.

Intuition is that shorter horizons tend to react to market changes more quickly since new information represents a larger proportion of the data used to derive the signal. For example, in a 6-month momentum measure a new monthly data point represents 16.6% of the data, whereas it only represents 8.3% of a 12-month moving average.

A longer horizon, therefore, is likely to be more “stable” and therefore less susceptible to whipsaw.

Which particular horizon achieves the best performance, then, will likely be highly regime dependent. To get a sense of this, we ran six time-series momentum strategies, with look-back periods ranging from 6-months to 12-months. Again, we plot the spread between the best and worst performing strategies over rolling 5-year periods.

Ignoring the Great Depression for a moment, we can see that 5-year annualized returns between parameterizations frequently deviate by more than 500 bps. If we dig under the hood, we again see that the optimal parameterization is highly regime dependent.

For example, coming out of the Great Depression, the longer-length strategies seemed to perform best. From 8/1927 to 12/1934, an 11-1 time-series momentum strategy returned 136% while a 6-1 time-series momentum strategy returned -25%. Same philosophy; very different performance.

Conversely, from 12/1951 to 12/1971, the 6-1 strategy returned 723% while the 11-1 strategy returned 361%.

Once again, without evidence that we can time our parameter choice, we end up bearing unnecessary parameterization risk, and diversification is a prudent action.

**The When: Timing Luck**

Long-time readers of our commentary will be familiar with this topic. For those unfamiliar, we recommend a quick glance over our commentary Quantifying Timing Luck (specifically, the section What is “Timing Luck”?).

The simple description of the problem is that investment strategies can be affected by the investment opportunities they see at the point at which they rebalance. For example, if we rebalance our tactical strategies at the end of each month, our results will be subject to what our signals say at that point. We can easily imagine two scenarios where this might work against us:

Our signals identify no change and we remain invested; the market sells off dramatically over the next month.
The market sells off dramatically prior to our rebalance, causing us to move to cash. After we trade, the market rebounds significantly, causing us to miss out on potential gains.

As it turns out, these are not insignificant risks. Below we plot four identically managed tactical strategies that each rebalance on a different week of the month. While one of the strategies turned $1 into $4,139 another turned it into $6,797. That is not an insignificant difference.

Fortunately, the cure for this problem is simple: diversification. Instead of picking a week to rebalance on, we can allocate to multiple variations of the strategy, each rebalancing at a different point in time. One variation may rebalance on the 1^st week of the month, another on the 2^nd week, et cetera. This technique is called “overlapping portfolios” or “tranching” and we have proven in past commentaries that it can dramatically reduce the impact that timing luck can have on realized results.

Conclusion

Basic, naïve implementations of long/flat trend following exhibit considerable robustness and consistency over the long run when applied to U.S. equities. The short run, however, is a different story. While simple implementations can help ensure that we avoid overfitting our models to historical data, it can also leave us exposed to a number of unintended bets and uncompensated risks.

Instead of adding more complexity, we believe that the simple solution to combat these risks is diversification.

Specifically, we explore diversification across three axes.

The first axis is “what” and represents “what we invest across.” We saw that while trend following worked well on U.S. equities, the approach had less consistency when applied to international indices. Instead of presuming that the U.S. represents a unique candidate for this type of strategy, we explored a sector-based implementation that may allow for greater internal diversification.

The second axis is “how” and captures “how we implement the strategy.” There are a variety of approaches practitioners use to measure and identify trends, and each comes with its own pros and cons. We explore four popular methods and find that none consistently reigns supreme, indicating once again that diversification of process is likely a prudent approach.

Similarly, when it comes to parameterizing these models, we find that a range of lookback periods are successful in the long run, but have varying performance in the short run. A prudent solution once again, is diversification.

The final axis is “when” and represents “when we rebalance our portfolio.” Long-time readers recognize this topic as one we frequently write about: timing luck. We demonstrate that merely shifting what week of the month we rebalance on can have considerable long-term effects. Again, as an uncompensated risk, we would argue that it is best diversified away.

While a naïve trend following process is easy to implement, we believe that a robust one requires thinking along the many dimensions of risk and asking ourselves which risks are worth bearing (hopefully those that are compensated) and which risks we should seek to hedge or diversify away.

[1] Bruder, Benjamin and Dao, Tung-Lam and Richard, Jean-Charles and Roncalli, Thierry, Trend Filtering Methods for Momentum Strategies (December 1, 2011). Available at SSRN: http://ssrn.com/abstract=2289097

[2] Marshall, Ben R. and Nguyen, Nhut H. and Visaltanachoti, Nuttawat, Time-Series Momentum versus Moving Average Trading Rules (December 22, 2014). Available at SSRN: http://ssrn.com/abstract=2225551

[3] Levine, Ari and Pedersen, Lasse Heje, Which Trend Is Your Friend? (May 7, 2015). Financial Analysts Journal, vol. 72, no. 3 (May/June 2016). Available at SSRN: https://ssrn.com/abstract=2603731

[4] Beekhuizen, Paul and Hallerbach, Winfried G., Uncovering Trend Rules (May 11, 2015). Available at SSRN: http://ssrn.com/abstract=2604942

[5] Zakamulin, Valeriy, Market Timing with Moving Averages: Anatomy and Performance of Trading Rules (May 13, 2015). Available at SSRN: http://ssrn.com/abstract=2585056

Protect & Participate: Managing Drawdowns with Trend Following

By Corey Hoffstein

On March 26, 2018

In Risk & Style Premia, Risk Management, Trend, Weekly Commentary

This post is available as PDF download here.

Summary

Trend following is an investment strategy that buys assets exhibiting strong absolute performance and sells assets exhibiting negative absolute performance.
Despite its simplistic description, trend following has exhibited considerable empirical robustness as a strategy, having been found to work in equity indices, bonds, commodities, and currencies.
A particularly interesting feature about trend following is its potential ability to avoid significant losses. Evidence suggests that trend following approaches can be used as alternative risk management techniques.
However, if investors expect to fully participate with asset growth while receiving significant protection, they are likely to be disappointed.
Relative to other risk management techniques, even very simple trend following strategies have exhibited very attractive return profiles.

What is Trend Following?

At its core, trend following – also called “absolute” or “time-series” momentum – is a very basic investment thesis: investments exhibiting positive returns tend to keep exhibiting positive returns and those exhibiting negative returns tend to keep exhibiting negative returns.

While the approach may sound woefully simplistic, the empirical and academic evidence that supports it extends back nearly two centuries. Lempérière, Deremble, Seager, Potters, and Bouchard (2014), for example, test trend following approaches on commodities, currencies, stock indices, and bonds going back to 1800 and find that “the existence of trends [is] one of the most statistically significant anomalies in financial markets.”[1]

While LDSPB (2014) may have one of the longest backtests to date, a variety of other authors have demonstrated the existence of trends, and the success of trend following, in a variety of environments and markets. We won’t list them here, but for those interested, a more thorough history can be found in our own paper Two Centuries of Momentum.

The driving theory behind trend following is that investor (mis-)behavior causes the emergence of trends. When new information enters the market, investors underreact due to an anchoring bias that causes them to overweight prior information. As price begins to drift towards fair value, herding takes over and causes investors to overreact. This under and subsequent over-reaction is what causes a trend to emerge.

While somewhat contradictory to the notion that investors should not “chase performance” or “time markets,” evidence suggests that when systematically applied, trend following approaches can create a potentially significant return premium and potentially help investors avoid significant losses.

The Basic Trend Following Setup

In our experience, the two most popular methods of implementing a trend following signal are (1) a simple moving average cross-over system and (2) a measure of trailing total return.

In a simple moving average system cross-over system, when price is above the simple moving average, the system stays invested. When price falls below, the strategy divests (usually into a risk-free asset, like U.S. Treasury Bills). This sort of “in-or-out” system is often called “long/flat.” For example, below we show a 12-month simple moving average and highlight when the system would buy and sell based upon when price crosses over.

The second form of trend following is more commonly referred to as “time-series momentum.” In this approach, prior realized returns are calculated and the signal is generated depending upon whether returns were positive or negative. For example, a popular academic approach is to use a “12-1” model, which takes the prior 12-month returns and subtracts the most recent month’s return (to avoid short-term mean reversion effects). If this value is positive, the system invests and if the value is negative, it divests.

By looking at the example graphs, we can see that while these systems are similar, they are not exactly equal. Nor are they the only way trend following approaches are implemented by practitioners. What is important here is not the specific methodology, but that these methodologies attempt to capture the same underlying dynamics.

Empirical Evidence: Trend Following in a Crisis

To explore how a simple 12-1 time-series momentum system has worked in the past, we will apply the process to a broad U.S. equity index. At the end of each month, we will calculate the trend following signal. If the signal is positive, we will remain invested in the index (i.e. we are “long”). If the signal is negative, we will divest into U.S. Treasury Bills (i.e. we are “flat”).

To explore the potential risk management capabilities of trend following, we will define a “crisis” as any period over which the broad U.S. equity market suffers a drawdown exceeding 25% from a recent market high. We will then measure the maximum peak-to-trough drawdown of U.S. equities over the period and compare it to the maximum peak-to-trough drawdown of the 12-1 time series momentum strategy.

Since the early 1900s, we identify eight such scenarios.

Source: Kenneth French Data Library. Calculations by Newfound Research. Past performance is not indicative of future returns. All performance is hypothetical and backtested. Performance assumes the reinvestment of all distributions. Returns are gross of all fees, including management fees, transaction costs, and taxes.

A few important takeaways:

Trend following is not a risk panacea. Even with trend following applied, drawdowns in excess of 15% occurred in each of these cases. This is the cost of market participation, which will address a bit later.
Trend following did not limit losses in all cases. The market sell-off in October 1987 was so rapid that there was not sufficient time for trends to emerge and the system to be able to exit. When trend following ends up protecting from quick sell-offs, it is more likely a function of luck than skill.
In many cases, trend following did help cut losses significantly. In the bear markets of the 1970s and 2000s, trend following helped reduce realized losses by over 50%.

Of course, the experience of these losses is very different than the summary numbers. Below we plot the actual returns of equities versus a trend following overlay for several of the scenarios.

We can see that the in many cases, when the trend following system got out, the market subsequently rallied, meaning that a trend follower would have a larger drawdown. For example, in the Great Depression after the trend following system divested into U.S. Treasury Bills, the equity market rallied significantly. This left the trend follower with a realized loss of -32% while a buy-and-hold investor would only be down -19%.

It is only with the benefit of hindsight that we can see that markets continued to fall and the patient trend follower was rewarded.

Ex-Ante Expectations About Participation

Of course, protecting capital is only half of the equation. If we only cared about capital preservation, we could invest in short-term inflation-protected Treasuries and, barring a default by the U.S. government, sleep very well at night.

Before we demonstrate any empirical evidence about trend following’s ability to participate in growth, we want to use one of our favorite exercises – a coin flip game – to help establish reasonable expectations.

Imagine that we approach you with the offer to play a game. We are going to flip a coin and you are going to try to guess how it lands. If the coin lands on heads and you guess heads, the game is a push. If it lands on tails and you guess tails, we give you $1. If you guess wrong, you give us $1.

Does this sound like a game you would want to play? Our guess is “no.”

Yet when we talk to many investors about their expectations for trend following strategies, this is the game they have created by choosing the U.S. equity market as a benchmark.

Consider the four scenarios that can happen:

The market goes up and trend following participates.
The market goes down and trend following goes down.
The market goes up and trend following is in cash.
The market goes down and trend following is in cash.

In the first scenario, even though trend following got the call right, we created a mental “push.” In the middle two scenarios, trend following was incorrect and either participates on the downside or fails to participate on the upside (i.e. we “lose”). It is only in the last scenario that trend following adds value.

In other words, by choosing U.S. equities as our benchmark for a long/flat trend following strategy, the strategy can only add value when the market is going down. If we believe that the market will go up over the long run, that leaves very few scenarios for trend following to add value and plenty of scenarios for it to be a detractor.

Which is, unsurprisingly, exactly what you see if you plot the growth of a buy-and-hold investor versus a time-series momentum strategy: success in periods of significant market drawdown and relative underperformance in other periods.

We can see, for example, that the trend following strategy lost its entire lead to the buy-and-hold investor from 1942 to 1962. That is a frustratingly long period of underperformance for any investor to weather.

Determining the appropriate benchmark, however, is often a matter of preference. We believe the appropriate way to address the problem is by asking whether trend following materially outperforms U.S. equities on a risk-adjusted basis.

To answer this question, we calculate the strategy’s full-period sensitivity to the U.S. equity index (i.e. its “beta”) and then re-create a new index that is comprised of a mixture U.S. equities and U.S. Treasury Bills that shares the same beta. In this case, that index is 50% U.S. equities and 50% U.S. Treasury Bills.

We can see that compared to a risk-adjusted benchmark, trend following exhibits a significant return premium without necessarily materializing significant excess downside risk.

Our take away from this is simple: investors who expect long/flat trend following strategies to keep up with equities are sure to be disappointed eventually. However, if we use a benchmark that allows both “in” and “flat” decisions to add value (e.g. a 50% U.S. equity index + 50% U.S. Treasury Bill portfolio), trend following has historically added significant value.

One interpretation may be that trend following may be best suited as a “risk pivot” within the portfolio, rather than as an outright replacement for U.S. equity. For example, if an investor has a 60% equity and 40% bond portfolio, rather than replacing equity with a trend strategy, the investor could replace a mix of both stocks and bonds. By taking 10% from stocks and 10% from bonds to give to the trend allocation, the portfolio now has the ability to pivot between a 70/30 and a 50/50. You can read more about this idea in our whitepaper Achieving Risk Ignition.

Another potential interpretation of this data is that long/flat trend following is a risk management technique and should be compared in light of alternative means of managing risk.

Pre-2008 versus Post-2008 Experience

Unfortunately, many investors have had their expectations for long/flat trend following strategies set by the period leading up to the 2008 financial crisis as well as the crisis itself, only to find themselves disappointed by subsequent performance.

Several years of whipsaws (including 2011, 2015 and 2016) leading to relative underperformance have caused many to ask, “is trend following broken?”

When we evaluate the data, however, we see that it is not the post-2008 period that is unique, but rather the pre-2008 period.

In fact, the pre-2008 period is unique in how calm a market environment it was, with drawdowns rarely eclipsing 10%. While the post-2008 period has had its calm years (e.g. 2013 and 2017), it has also been punctuated by periods of volatility. We can see the difference by plotting the drawdowns over the two periods.

Source: Kenneth French Data Library. Calculations by Newfound Research.

The unfortunate reality is that the calm period of pre-2008 and the strong performance of trend following in 2008 gave investors the false confidence that trend following had the ability to nearly fully participate on the upside and protect almost entirely on the downside.

Unfortunately, this simply is not true. As we have said many times in the past, “risk cannot be destroyed, only transformed.” While trend following tends to do well in environments where trends persist, it does poorly in those periods that exhibit sharp and sudden price reversals.

However, if we compare our trend following system against the more appropriate long-term risk-adjusted benchmark, we still see a significant return premium earned.

One question we may ask ourselves is, “if we are using trend following to manage risk, how did other risk management techniques perform over the same period?”

	Annualized Return (2009 – 2017)	Annualized Volatility (2009 – 2017)	Maximum Drawdown (2007 – 2009)
S&P 500	14.4%	12.0%	-52.3%
12-1 TS Momentum	11.7%	12.3%	-10.9%
80/20	12.3%	9.4%	-42.5%
60/40	10.1%	6.9%	-32.0%
CBOE S&P 500 5% Put Protection Index	10.2%	10.1%	-36.6%
Salient Trend Index (Managed Futures)	1.2%	10.3%	-14.3%
Salient Risk Parity Index	6.6%	8.7%	-30.8%
HFRX Global Hedge Fund Index	1.5%	4.0%	-23.4%

Source: Kenneth French Data Library, CSI, Salient, HFRI, CBOE. Calculations by Newfound Research. Past performance is not indicative of future returns. Performance assumes the reinvestment of all distributions. Returns are gross of all fees, including management fees, transaction costs, and taxes. 60/40 and 80/20 portfolios are mixtures of the SPDR S&P 500 ETF (“SPY”) and iShares Core U.S. Bond ETF (“AGG”) in 60%/40% and 80%/20% proportional allocations, rebalanced annually.

We can see that while trend following has failed to keep up with U.S. equities in the post-crisis period (again, we would expect this), it has kept up much better than other potential risk management alternatives while providing significantly more protection during the crisis period.

Another important takeaway is that during the post crisis period, the trend following strategy had the highest volatility of any of the strategies measured. In other words, while we might be able to rely on trend following for crisis risk management (i.e. avoiding the large left tail of returns), it is not necessarily going to reduce volatility during a bull market.

Conclusion

As an investment strategy, trend following has a long history of academic and empirical support. Evidence suggests that trend following can be an effective means of avoiding large negative returns that coincide with traditional bear markets.

However, trend following is not a panacea. In line with our philosophy that “risk cannot be destroyed, only transformed,” the risk management benefit often seen in trend following strategies comes with higher risks in other environments (i.e. “whipsaw”).

Investors who have relied upon the realized participation of trend following strategies during the pre-crisis period (2003-2007), as well as the protection afforded during the 2008 crisis itself, may have unrealistic expectations for forward performance. Simply put: long/flat trend following strategies are very likely to underperform the underlying asset during strong bull markets. In this case, replacing traditional equity exposure with a long/flat trend following strategy will likely lead to long-term underperformance.

However, when compared against other means of risk management, trend following has historically exhibited considerable downside protection for the upside participation it has realized. Compared to a risk-adjusted benchmark, a long/flat U.S. equity trend following strategy exhibits an annualized excess return of 2.89%.

For investors looking to diversify how they manage risk, we believe the trend following represents a high transparent, and historically effective, alternative.

[1] https://arxiv.org/pdf/1404.3274.pdf

Two Centuries of Momentum

By Corey Hoffstein

On March 23, 2018

This post is available as a PDF download here.

A momentum-based investing approach can be confusing to investors who are often told that “chasing performance” is a massive mistake and “timing the market” is impossible.

Yet as a systematized strategy, momentum sits upon nearly a quarter century of positive academic evidence and a century of successful empirical results.

Our firm, Newfound Research, was founded in August 2008 to offer research derived from our volatility-adjusted momentum models. Today, we provide tactically risk-managed investment portfolios using those same models.

Momentum, and particularly time-series momentum, has been in our DNA since day one.

In this Foundational Series piece, we want to explore momentum’s rich history and the academic evidence demonstrating its robustness across asset classes, geographies, and market cycles.

1. What is momentum?

Momentum is a system of investing that buys and sells based upon recent returns. Momentum investors buy outperforming securities and avoid – or sell short – underperforming ones.

The notion is closely tied to physics. In physics, momentum is the product of the mass and velocity of an object. For example, a heavy truck moving at a high speed has large momentum. To stop the truck, we must apply either a large or a prolonged force against it.

Momentum investors apply a similar notion. They assume outperforming securities will continue to outperform in absence of significant headwinds.

2. The Two Faces & Many Names of Momentum

2.1 Relative Momentum

The phenomenon of relative momentum is also called cross-sectional momentum and relative strength.

Relative momentum investors compare securities against each other’s performance. They favor buying outperforming securities and avoiding – or short-selling – underperforming securities.

Long-only relative momentum investors rotate between a subset of holdings within their investable universe. For example, a simple long-only relative strength system example is “best N of.” At rebalance, this system sells its current holdings and buys the top N performing securities of a basket. In doing so, the strategy seeks to align the portfolio with the best performing securities in hopes they continue to outperform.

2.2 Absolute Momentum

Absolute momentum is also referred to as time-series momentum or trend following.

Absolute momentum investors compare a security against its own historical performance. The system buys positive returning securities and avoids, or sells short, negative returning securities.

The primary difference is that relative momentum makes no distinction about return direction. If all securities are losing value, relative momentum will seek to invest in those assets that are going down least. Absolute momentum will seek to avoid negative returning assets.

3. A Brief History of Momentum

3.1 Early Practitioners

Momentum is one of Wall Street’s oldest investment strategies.

In 1838, James Grant published The Great Metroplis, Volume 2. Within, he spoke of David Ricardo, an English political economist who was active in the London markets in the late 1700s and early 1800s. Ricardo amassed a large fortune trading both bonds and stocks.

According to Grant, Ricardo’s success was attributed to three golden rules:

As I have mentioned the name of Mr. Ricardo, I may observe that he amassed his immense fortune by a scrupulous attention to what he called his own three golden rules, the observance of which he used to press on his private friends. These were, “Never refuse an option* when you can get it,”—”Cut short your losses,”—”Let your profits run on.” By cutting short one’s losses, Mr. Ricardo meant that when a member had made a purchase of stock, and prices were falling, he ought to resell immediately. And by letting one’s profits run on he meant, that when a member possessed stock, and prices were raising, he ought not to sell until prices had reached their highest, and were beginning again to fall. These are, indeed, golden rules, and may be applied with advantage to innumerable other transactions than those connected with the Stock Exchange.

The rules “cut short your losses” and “let your profits run on” are foundational philosophies of momentum.

Following in Ricardo’s footsteps are some of Wall Street’s greatest legends who implemented momentum and trend-following techniques.

Charles H. Dow (1851 – 1902) was the founder and first editor of the Wall Street Journal as well as the co-founder of Dow Jones and Company. In his Wall Street Journal column, he published his market trend analysis, which eventually developed into a body of research called Dow theory. Dow theory primarily focuses on the identification of trends as being the key signal for investing.

Jesse Livermore (1877 – 1940) was a stock market speculator in the early 1900s who famously made – and subsequently lost – two massive fortunes during the market panic of 1907 and crash of 1929. He is attributed (by Edwin Lefèvre, in Reminiscences of a Stock Operator) to saying,

[T]he big money was not in the individual fluctuations but in the main movements … sizing up the entire market and its trend.

Livermore claimed that his lack of adherence to his own rules was the main reason he lost his wealth.

In the same era of Livermore, Richard Wyckoff (1873 – 1934) noted that stocks tended to trend together. Thus he focused on entering long positions only when the broad market was trending up. When the market was in decline, he focused on shorting. He also emphasized the placement of stop-losses to help control risk.

He was personally so successful with his techniques, he eventually owned nine and a half acres in the Hamptons.

Starting in the 1930s, George Chestnutt successfully ran the American Investors Fund for nearly 30 years using relative strength techniques. He also published market letters with stock and industry group rankings based on his methods. He wrote,

[I]t is better to buy the leaders and leave the laggards alone. In the market, as in many other phases of life, ‘the strong get stronger, and the weak get weaker.’

In the late 1940s and early 1950s, Richard Donchian developed a rules based technical system that became the foundation for his firm Futures, Inc. Futures, Inc. was one of the first publicly held commodity funds. The investment philosophy was based upon Donchian’s belief that commodity prices moved in long, sweeping bull and bear markets. Using moving averages, Donchian built one of the first systematic trend-following methods, earning him the title of the father of trend-following.

In the late 1950s, Nicholas Darvas (1920 – 1977), trained economist and touring dancer, invented “BOX theory.” He modeled stock prices as a series of boxes. If a stock price remained in a box, he waited. As a stock price broke out of a box to new highs, he bought and placed a tight stop loss. He is quoted as saying,

I keep out in a bear market and leave such exceptional stocks to those who don’t mind risking their money against the market trend.

Also during the 1950s and 1960s was Jack Dreyfus, who Barron’s named the second most significant money manager of the last century. From 1953 to 1964, his Dreyfus Fund returned 604% compared to 346% for the Dow index. Studies performed by William O’Neil showed that Dreyfus tended to buy stocks making new 52-week highs. It wouldn’t be until 2004 that academic studies would confirm this method of investing.

Richard Driehaus took the momentum torch during the 1980s. In his interview in Jack Schwager’s The New Market Wizards, he said he believed that money was made buying high and selling higher.

That means buying stocks that have already had good moves and have high relative strength – that is, stocks in demand by other investors. I would much rather invest in a stock that’s increasing in price and take the risk that it may begin to decline than invest in a stock that’s already in a decline and try to guess when it will turn around.

3.2 Earliest Academic Studies

In 1933, Alfred Cowles III and Herbert Jones released a research paper titled Some A Posteriori Probabilities in Stock Market Action. Within it they specifically focused on “inertia” at the “microscopic” – or stock – level.

They focused on counting the ratio of sequences – times when positive returns were followed by positive returns, or negative returns were followed by negative returns – to reversals – times when positive returns were followed by negative returns, and vice versa.

Their results:

It was found that, for every series with intervals between observations of from 20 minutes up to and including 3 years, the sequences out-numbered the reversals. For example, in the case of the monthly series from 1835 to 1935, a total of 1200 observations, there were 748 sequences and 450 reversals. That is, the probability appeared to be .625 that, if the market had risen in a given month, it would rise in the succeeding month, or, if it had fallen, that it would continue to decline for another month. The standard deviation for such a long series constructed by random penny tossing would be 17.3; therefore the deviation of 149 from the expected value of 599 is in excess of eight times the standard deviation. The probability of obtaining such a result in a penny-tossing series is infinitesimal.

Despite the success of their research on the statistical significance of sequences, the next academic study on momentum was not released for 30 years.

In 1967, Robert Levy published Relative Strength as a Criterion for Investment Selection. Levy found that there was “good correlation between past performance groups and future … performance groups” over 26-week periods. He states:

[…] the [26-week] average ranks and ratios clearly support the concept of continuation of relative strength. The stocks which historically were among the 10 per cent strongest (lowest ranked) appreciated in price by an average of 9.6 per cent over a 26-week future period. On the other hand, the stocks which historically were among the 10 per cent weakest (highest ranked) appreciated in price an average of only 2.9 per cent over a 26-week future period.

Unfortunately, the scope of the study was limited. The period used in the analysis was only from 1960 to 1965. Thus, of the 26-week periods tested, only 8 were independent. In Levy’s words, “the results were extensively intercorrelated; and the use of standard statistical measures becomes suspect.” Therefore, Levy omitted these statistics.

Despite its promise, momentum research went dark for the next 25 years.

4. The Dark Days of Momentum Research

Despite the success of practitioners and promising results of early studies, momentum would go largely ignored by academics until the 1990s.

Exactly why is unknown, but we have a theory: fundamental investing, modern portfolio theory, and the efficient market hypothesis.

4.1 The Rise of Fundamental Investing

In 1934, Benjamin Graham and David Dodd published Security Analysis. Later, in 1949, they published The Intelligent Investor. In these tomes, they outline their methods for successful investing.

For Graham and Dodd, a purchase of stock was a purchase of partial ownership of a business. Therefore, it was important that investors evaluate the financial state of the underlying business they were buying.

They also defined a strong delineation between investing and speculating. To quote,

An investment operation is one which, upon thorough analysis, promises safety of principal and an adequate return. Operations not meeting these requirements are speculative.

Speculative was a pejorative term. Even the title of The Intelligent Investor implied that any investors not performing security analysis were not intelligent.

The intelligent investor began her process by computing a firm’s intrinsic value. In other words, “what is the business truly worth?” This value was either objectively right or wrong based on the investor’s analysis. Whether the market agreed or not was irrelevant.

Once an intrinsic value was determined, Graham and Dodd advocated investors buy with a margin of safety. This meant waiting for the market to offer stock prices at a deep discount to intrinsic value.

These methods of analysis became the foundation of value investing.

To disciples of Graham and Dodd, momentum is speculative nonsense. To quote Warren Buffett in The Superinvestors of Graham-and-Doddsville:

I always find it extraordinary that so many studies are made of price and volume behavior, the stuff of chartists. Can you imagine buying an entire business simply because the price of the business had been marked up substantially last week and the week before?

4.2 Modern Portfolio Theory and the Efficient Market Hypothesis

In his 1952 article “Portfolio Selection,” Harry Markowitz outlined the foundations of Modern Portfolio Theory (MPT). The biggest breakthrough of MPT was that it provided a mathematical formulation for diversification.

While the concept of diversification has existed since pre-Biblical eras, it had never before been quantified. With MPT, practitioners could now derive portfolios that optimally balanced risk and reward. For example, by combining assets together, Markowitz created the efficient frontier: those combinations for which there is the lowest risk for a given level of expected return.

By introducing a risk-free asset, the expected return of any portfolio constructed can be linearly changed by varying the allocation to the risk-free asset. In a graph like the one on the left, this can be visualized by constructing a line that passes through the risk-free asset and the risky portfolio (called a Capital Allocation Line or CAL). The CAL that is tangent to the efficient frontier is called the capital market line (CML). The point of tangency along the efficient frontier is the portfolio with the highest Sharpe ratio (excess expected return divided by volatility).

According to MPT, in which all investors seek to maximize their Sharpe ratio, an investor should only hold a mixture of this portfolio and the risk free asset. Increasing the allocation to the risk-free asset decreases risk while introducing leverage increases risk.

The fact that any investor should only hold one portfolio has a very important implication: given all the assets available in the market, all investors should hold, in equal relative proportion, the same portfolio of global asset classes. Additionally, if all investors are holding the same mix of assets, in market equilibrium, the prices of asset classes – and therefore their expected returns – must adjust such that the allocation ratios of the assets in the tangency portfolio will match the ratio in which risky assets are supplied to the market.

Holding anything but a combination of the tangency portfolio and the risk-free asset is considered sub-optimal.

From this foundation, concepts for the Capital Asset Pricing Model (CAPM) are derived. CAPM was introduced independently by Jack Treynor, William Sharpe, John Lintner, and Jan Mossin from 1961-1966.

CAPM defines a “single-factor model” for pricing securities. The expected return of a security is defined in relation to a risk-free rate, the security’s “systematic” risk (sensitivity to the tangency portfolio), and the expected market return. All other potentially influencing factors are considered to be superfluous.

While its origins trace back to the 1800s, the efficient market hypothesis (EMH) was officially developed by Eugene Fama in his 1962 Ph.D. thesis.

EMH states that stock prices reflect all known and relevant information and always trade at fair value. If stocks could not trade above or below fair value, investors would never be able to buy them at discounts or sell them at premiums. Therefore, “beating the market” on a risk-adjusted basis is impossible.

Technically, MPT and EMH are independent theories. MPT tells us we want to behave optimally, and gives us a framework to do so. EMH tells us that even optimal behavior will not generate any return in excess of returns predicted by asset pricing models like CAPM.

Markowitz, Fama, and Sharpe all went on to win Nobel prizes for their work.

4.3 Growing Skepticism Towards Technical Analysis

Technical analysis is a category of investing methods that use past market data – primarily price and volume – to make forward forecasts.

As a category, technical analysis is quite broad. Some technicians look for defined patterns in price charts. Others look for lines of support or resistance. A variety of indicators may be calculated and used. Some technicians follow specific techniques – like Dow theory or Elliot Wave theory.

Unfortunately, the broad nature of technical analysis makes it difficult to evaluate academically. Methods vary widely and different technical analysts can make contradictory predictions using the same data.

Thus, during the rise of EMH through the 1960s and 1970s, technical analysis was largely dismissed by academics.

Since momentum relies only on past prices, and many practitioners used tools like moving averages to identify trends, it was categorized as a form of technical analysis. As academics dismissed the field, momentum went overlooked.

4.4 But Value Research Went On

Despite CAPM, EMH, and growing skepticism towards technical analysis, academic research for fundamental investing continued. Focus was especially strong on value investing.

For example, in 1977, S. Basu authored a comprehensive study on value investing, titled Investment Performance of Common Stocks in Relation to their Price-Earnings Ratios: A Test of the Efficient Market Hypothesis. Within, Basu finds that the return relationship strictly increases for stocks sorted on their price-earnings ratio. Put more simply, cheap stocks outperform expensive ones.

Unfortunately, in many of these studies, the opposite of value was labeled growth or glamor. This became synonymous with high flying, over-priced stocks. Of course, not value is not the same as growth. And not value is certainly not the same as momentum. It is entirely possible that a stock can be in the middle of a positive trend, yet still be undervalued. Nevertheless, it is easy to see how relatively outperforming and over-priced may be conflated.

It is possible that the success of value research in demonstrating the success of buying cheap stocks dampened the enthusiasm for momentum research.

5. The Return of Momentum

Fortunately, decades of value-based evidence against market efficiency finally piled up.

In February 1993, Eugene Fama and Kenneth French released Common Risk Factors in the Returns on Stocks and Bonds. Fama and French extended the single-factor model of CAPM into a three-factor model. Beyond the “market factor,” factors for “value” and “size” were added, acknowledging these distinct drivers of return.

Momentum was still nowhere to be found.

But a mere month later, Narasimhan Jegadeesh and Sheridan Titman published their seminal work on momentum, titled Returns to Buying Winners and Selling Losers: Implication for Stock Market Efficiency. Within they demonstrated:

Strategies which buy stocks that have performed well in the past and sell stocks that have performed poorly in the past generate significant positive returns over 3- to 12-month holding periods.

The results of the paper could not be explained by systematic risk or delayed reactions to other common factors, echoing the results of Cowles and Jones some 60 years prior.

In 1996, Fama and French authored Multifactor Explanations of Asset Pricing Anomalies. Armed with their new three-factor model, they explored whether recently discovered market phenomena – including Jegadeesh and Titman’s momentum – could be rationally explained away.

While most anomalies disappeared under scrutiny, the momentum results remained robust. In fact, in the paper Fama and French admitted that,

“[momentum is the] main embarrassment of the three-factor model.”

6. The Overwhelming Evidence for Momentum

With its rediscovery and robustness against prevailing rational pricing models, momentum research exploded over the next two decades. It was applied across asset classes, geographies, and time periods. In chronological order:

Asness, Liew, and Stevens (1997) shows that momentum investing is a profitable strategy for country indices.

Carhart (1997) finds that portfolios of mutual funds, constructed by sorting on trailing one-year returns, decrease in monthly excess return nearly monotonically, inline with momentum expectations.

Rouwenhorst (1998) demonstrates that stocks in international equity markets exhibit medium-term return continuations. The study covered stocks from Austria, Belgium, Denmark, France, Germany, Italy, the Netherlands, Norway, Spain, Sweden, Switzerland, and the United Kingdom.

LeBaron (1999) finds that a simple momentum model creates unusually large profits in foreign exchange series.

Moskowitz and Grinblatt (1999) finds evidence for a strong and persistent industry momentum effect.

Rouwenhorst (1999), in a study of 1700 firms across 20 countries, demonstrates that emerging market stocks exhibit momentum.

Liew and Vassalou (2000) shows that momentum returns are significantly positive in foreign developed countries but there is little evidence to explain them by economic developments.

Griffin, Ji, and Martin (2003) demonstrates momentum’s robustness, finding it to be large and statistically reliable in periods of both negative and positive economic growth. The study finds no evidence for macroeconomic or risk-based explanations to momentum returns.

Erb and Harvey (2006) shows evidence of success for momentum investing in commodity futures.

Gorton, Hayashi, and Rouwenhorst (2008) extends momentum research on commodities, confirming its existence in futures but also identifying its existence in spot prices.

Jostova, Niklova Philopov, and Stahel (2012) shows that momentum profits are significant for non-investment grade corporate bonds.

Luu and Yu (2012) identifies that for liquid fixed-income assets, such as government bonds, momentum strategies may provide a good risk-return trade-off and a hedge for credit exposure.

7. Academic Explanations for Momentum

While academia has accepted momentum as a distinct driver of return premia in many asset classes around the world, the root cause is still debated.

So far, the theory for rational markets has failed to account for momentum’s significant and robust returns. It is not correlated with macroeconomic variables and does not seem to reflect exposure to other known risk factors.

But there are several hypotheses that might explain how irrational behavior may lead to momentum.

7.1 The Behavioral Thesis

The most commonly accepted argument for why momentum exists and persists comes from behavioral finance. Behavioral finance is a field that seeks to link psychological theory with economics and finance to explain irrational decisions.

Some of the popular behavioral finance explanations for momentum include:

Herding: Also known as the “bandwagon effect,” herding is the tendency for individuals to mimic the actions of a larger group.

Anchoring Bias: The tendency to rely too heavily on the first piece of information received.

Confirmation Bias: The tendency to ignore information contradictory to prior beliefs.

Disposition Effect: Investors tend to sell winners too early and hold on to losers too long. This occurs because investors like to realize their gains but not their losses, hoping to “make back” what has been lost.

Together, these biases cause investors to either under- or over-react to information, causing pricing inefficiencies and irrational behavior.

7.1.1 Cumulative Advantage & Momentum Beyond Markets

There is strong evidence for momentum being a behavioral and social phenomenon beyond stock markets.

Matthew Salganik, Peter Dodds, and Duncan Watts ran a 14,000 participant, web-based study designed to establish independence of taste and preference in music.

Participants were asked to explore, listen to, and rate music. One group of participants would be able to see how many times a song was downloaded and how other participants rated it; the other group would not be able to see downloads or ratings. The group that could see the number of downloads (“social influence”) was then sub-divided into 8 distinct, random groups where members of each sub-group could only see the download and ratings statistics of their sub-group peers.

The hypothesis of the study was that “good music” should garner the same amount of market share regardless of the existence of social influence: hits should be hits. Secondly, the same hits should be hits across all independent social influence groups.

What the study found was dramatically different. Each social-influence group had its own hit songs, and those songs commanded a much larger market share of downloads than songs did in the socially-independent group.

Introducing social-influence did two things: it made hits bigger and it made hits more unpredictable. The authors called this effect “cumulative advantage.” The consequences are profound. To quote an article in the New York Times by Watts,

It’s a simple result to state, but it has a surprisingly deep consequence. Because the long-run success of a song depends so sensitively on the decisions of a few early-arriving individuals, whose choices are subsequently amplified and eventually locked in by the cumulative-advantage process, and because the particular individuals who play this important role are chosen randomly and may make different decisions from one moment to the next, the resulting unpredictability is inherent to the nature of the market. It cannot be eliminated either by accumulating more information — about people or songs — or by developing fancier prediction algorithms, any more than you can repeatedly roll sixes no matter how carefully you try to throw the die.

7.2 The Limits to Arbitrage Thesis

EMH assumes that any mis-pricing in public markets will be immediately arbitraged away by rational market participants. The limits to arbitrage theory recognizes that there are often restrictions – both regulatory and capital based – that may limit rational traders from fully arbitraging away these price inefficiencies.

In support of this thesis is Chabot, Ghysels, and Jagannathan (2009), which finds that when arbitrage capital is in short supply, momentum cycles last longer.

Similarly, those investors bringing good news to the market may lack the capital to take full advantage of that information. So if there has been good news in the past, there may be good news not yet incorporated into the price.

7.3 The Rational Inattention Thesis

Humans possess a finite capacity to process the large amounts of information they are confronted with. Time is a scarce resource for decision makers.

The rational inattention theory argues that some information may be evaluated less carefully, or even outright ignored. Or, alternatively, it may be optimal for investors to obtain news with limited frequency or limited accuracy. This can cause investors to over- or under-invest and could cause the persistence of trends.

Chen and Yu (2014) found that portfolios constructed from stocks “more likely to grab attention” based on visual patterns induces investor over-reaction. They provide evidence that momentum continuation is induced by visually-based psychological biases.

8. Advances in Cross-Sectional Research

Much like there are many ways to identify value, there are many ways to identify momentum. Recent research has identified methods that may improve upon traditional total return momentum.

52-Week Highs: Hwang and George (2004) shows that nearness to a 52-week high price dominates and improves upon the forecasting power of past returns (i.e. momentum). Perhaps most interestingly, future returns forecast using a 52-week high do not mean-revert in the long run, like traditional momentum.

Liu, Liu, and Ma (2010) tests the 52-week high strategy in 20 international markets and finds that it is profitable in 18 and significant in 10.

Residual Momentum: Using a universe of domestic equities, covering the period of January 1926 to December 2009, Blitz, Huij, and Martens (2009) decomposes stock returns using the Fama-French three-factor model. Returns unexplained by the market, value, and size factors are considered to be residual. The study finds that momentum strategies built from residual returns exhibit risk-adjusted profits that are twice as large as those associated with total return momentum.

Idiosyncratic Momentum: Similar to Blitz, Huij, and Martens, Chaves (2012) uses the CAPM model to correct stocks for market returns and identify idiosyncratic returns. Idiosyncratic momentum is found to work better than momentum in a sample of 21 developed countries. Perhaps most importantly, idiosyncratic momentum is successful in Japan, where most traditional momentum strategies have failed.

9. Using Momentum to Manage Risk

While most research in the late 1990s and early 2000s focused on relative momentum, research after 2008 has been heavily focused on time-series momentum for its risk-mitigating and diversification properties.

Some of the earliest, most popular research was done by Faber (2006), in which a simple price-minus-moving-average approach was used to drive a portfolio of U.S. equities, foreign developed equities, commodities, U.S. REITs, and U.S. government bonds. The resulting portfolio demonstrates “equity-like returns with bond-like volatility.”

Hurst, Ooi, and Pedersen (2010) identifies that trend-following, or time-series momentum, is a significant component of returns for managed futures strategies. In doing so, the research demonstrates the consistency of trend-following approaches in generating returns in both bull and bear markets.

Going beyond managed futures specifically, Moskowitz, Ooi, Hua, and Pedersen (2011) documents significant time-series momentum in equity index, currency, commodity, and bond futures covering 58 liquid instruments over a 25-year period.

Perhaps some of the most conclusive evidence comes from Hurst, Ooi, Pedersen (2012), which explores time-series momentum going back to 1903 and through 2011.

The study constructs a portfolio of an equal-weight combination of 1-month, 3-month, and 12-month time-series momentum strategies for 59 markets across 4 major asset classes, including commodities, equity indices, and currency pairs. The approach is consistently profitable across decades. The research also shows that incorporating a time-series momentum approach into a traditional 60/40 stock/bond portfolio increases returns, reduces volatility, and reduces maximum drawdown.

Finally, Lempérière, Deremble, Seager, Potters, and Bouchard (2014) extends the tests even further, using both futures and spot prices to go back to 1800 for commodity and stock indices. It finds that excess returns driven by trend-following is both significant and stable across time and asset classes.

10. Evidence & Advances in Time-Series Momentum

While the evidence for time-series momentum was significantly advanced by the papers and teams cited above, there were other, more focused contributions throughout the years that helped establish it in more specific asset classes.

Wilcox and Crittenden (2005) demonstrates that buying stocks when they make new 52-week highs and selling after a prescribed stop-loss is broken materially outperforms the S&P 500 even after accounting for trading slippage.

ap Gwilym, Clare, Seaton, and Thomas (2009) explores whether trend-following can be used as an allocation tool for international equity markets. Similar to Faber (2006), it utilizes a 10-month price-minus-moving-average model. Such an approach delivers a similar compound annual growth rate to buy and hold, but with significantly lower volatility, increasing the Sharpe ratio from 0.41 to 0.75.

Szakmary, Shen, and Sharma (2010) explores trend-following strategies on commodity futures markets covering 48 years and 28 markets. After deducting reasonable transaction costs, it finds that both a dual moving-average-double-crossover strategy and a channel strategy yield significant profit over the full sample period.

Antonacci (2012) explores a global tactical asset allocation approach utilizing both relative and absolute momentum techniques in an approach called “dual momentum.” Dual momentum increases annualized return, reduces volatility, and reduces maximum drawdown for equities, high yield & credit bonds, equity & mortgage REITs, and gold & treasury bonds.

Dudler, Gmuer, and Malamud (2015) demonstrates that risk-adjusted time series momentum – returns normalized by volatility – outperforms time series momentum on a universe of 64 liquid futures contracts for almost all combinations of holdings and look-back periods.

Levine and Pedersen (2015) uses smoothed past prices and smoothed current prices in their calculation of time-series momentum to reduce random noise in data that might occur from focusing on a single past or current price.

Clare, Seaton, Smith and Thomas (2014) finds that trend following “is observed to be a very effective strategy over the study period delivering superior risk-adjusted returns across a range of size categories in both developed and emerging markets.”

11. Unifying Momentum & Technical Analysis

Despite their similarities, trend-following moving average rules are often still considered to be technical trading rules versus the quantitative approach of time-series momentum. Perhaps the biggest difference is that the trend-following camp tended to focus on prices while the momentum camp focused on returns.

However, research over the last half-decade actually shows that they are highly related strategies.

Bruder, Dao, Richard, and Roncalli (2011) unites moving-average-double-crossover strategies and time-series momentum by showing that cross-overs were really just an alternative weighting scheme for returns in time-series momentum. To quote,

The weighting of each return … forms a triangle, and the biggest weighting is given at the horizon of the smallest moving average. Therefore, depending on the horizon n2 of the shortest moving average, the indicator can be focused toward the current trend (if n2 is small) or toward past trends (if n2 is as large as n1/2 for instance).

We can see, above, this effect in play. When n2 << n1 (e.g. n2=10, n1=100), returns are heavily back-weighted in the calculation. As n2 approaches half of n1, we can see that returns are most heavily weighted at the middle point.

Marshall, Nguyen and Visaltanachoti (2012) proves that time-series momentum is related to moving-average-change-in-direction. In fact, time-series momentum signals will not occur until the moving average changes direction. Therefore, signals from a price-minus-moving-average strategy are likely to occur before a change in signal from time-series momentum.

Levine and Pedersen (2015) shows that time-series momentum and moving average cross-overs are highly related. It also find that time-series momentum and moving-average cross-over strategies perform similarly across 58 liquid futures and forward contracts.

Beekhuizen and Hallerbach (2015) also links moving averages with returns, but further explores trend rules with skip periods and the popular MACD rule. Using the implied link of moving averages and returns, it shows that the MACD is as much trend following as it is mean-reversion.

Zakamulin (2015) explores price-minus-moving-average, moving-average-double-crossover, and moving-average-change-of-direction technical trading rules and finds that they can be interpreted as the computation of a weighted moving average of momentum rules with different lookback periods.

These studies are important because they help validate the approach of price-based systems. Being mathematically linked, technical approaches like moving averages can now be tied to the same theoretical basis as the growing body of work in time-series momentum.

12. Conclusion

As an investment strategy, momentum has a deep and rich history.

Its foundational principles can be traced back nearly two centuries and the 1900s were filled with its successful practitioners.

But momentum went long misunderstood and ignored by academics.

In 1993, Jegadeesh and Titman published “Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency.” Prevailing academic theories were unable to account for cross-sectional momentum in rational pricing models and the premier market anomaly was born.

While momentum’s philosophy of “buy high, sell higher” may seem counterintuitive, prevailing explanations identify its systemized process as taking advantage of the irrational behavior exhibited by investors.

Over the two decades following momentum’s (re)introduction, academics and practitioners identified the phenomenon as being robust in different asset classes and geographies around the globe.

After the financial crisis of 2008, a focus on using time-series momentum emerged as a means to manage risk. Much like cross-sectional momentum, time-series momentum was found to be robust, offering significant risk-management opportunities.

While new studies on momentum are consistently published, the current evidence is clear: momentum is the premier market anomaly.

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