Flirting with Models

The Research Library of Newfound Research

Tag: moving average

Why Trend Models Diverge

By

On March 9, 2020

In Risk & Style Premia, Trend, Weekly Commentary

This post is available as a PDF download here.

Summary

  • During the week of February 23rd, the S&P 500 fell more than 10%.
  • After a prolonged bullish period in equities, this tumultuous decline caused many trend-following signals to turn negative.
  • As we would expect, short-term signals across a variety of models turned negative. However, we also saw that price-minus-moving-average models turned negative across a broad horizon of lookbacks where the same was not true for other models.
  • In this brief research note, we aim to explain why common trend-following models are actually mathematically linked to one another and differ mainly in how they place weight on recent versus prior price changes.
  • We find that price-minus-moving-average models place the greatest weight on the most recent price changes, whereas models like time-series momentum place equal-weight across their lookback horizon.

In a market note we sent out last weekend, the following graphic was embedded:

What this table intends to capture is the percentage of trend signals that are on for a given model and lookback horizon (i.e. speed) on U.S. equities.  The point we were trying to establish was that despite a very bearish week, trend models remained largely mixed.  For frequent readers of our commentaries, it should come as no surprise that we were attempting to highlight the potential specification risks of selecting just one trend model to implement with (especially when coupled with timing luck!).

But there is a potentially interesting second lesson to learn here which is a bit more academic.  Why does it look like the price-minus (i.e. price-minus-moving-average) models turned off, the time series momentum models partially turned off, and the cross-over (i.e. dual-moving-average-cross) signals largely remained positive?

While this note will be short, it will be somewhat technical.  Therefore, we’ll spoil the ending: these signals are all mathematically linked.

They can all be decomposed into a weighted average of prior log-returns and the primary difference between the signals is the weighting concentration.  The price-minus model front-weights, the time-series model equal weights, and the cross-over model tends to back-weight (largely dependent upon the length of the two moving averages).  Thus, we would expect a price-minus model to react more quickly to large, recent changes.

If you want the gist of the results, just jump to the section The Weight of Prior Evidence, which provides graphical evidence of these weighting schemes.

Before we begin, we want to acknowledge that absolutely nothing in this note is novel.  We are, by in large, simply re-stating work pioneered by Bruder, Dao, Richard, and Roncalli (2011); Marshall, Nguyen and Visaltanachoti (2012); Levine and Pedersen (2015); Beekhuizen and Hallerbach (2015); and Zakamulin (2015).

Decomposing Time-Series Momentum

We will begin by decomposing a time-series momentum value, which we will define as:

We will begin with a simple substitution:

Which implies that:

Simply put, time-series momentum puts equal weight on all the past price changes1 that occur.

Decomposing Dual-Moving-Average-Crossover

We define the dual-moving-average-crossover as:

We assume m is less than n (i.e. the first moving average is “faster” than the second).  Then, re-writing:

Here, we can make a cheeky transformation where we add and subtract the current price, Pt:

What we find is that the double-moving-average-crossover value is the difference in two weighted averages of time-series momentum values.

Decomposing Price-Minus-Moving-Average

This decomposition is trivial given the dual-moving-average-crossover.  Simply,

The Weight of Prior Evidence

We have now shown that these decompositions are all mathematically related.  Just as importantly, we have shown that all three methods are simply re-weighting schemes of prior price changes.  To gain a sense of how past returns are weighted to generate a current signal, we can plot normalized weightings for different hypothetical models.

  • For TSMOM, we can easily see that shorter lookback models apply more weight on less data and therefore are likely to react faster to recent price changes.
  • PMAC models apply weight in a linear, declining fashion, with the most weight applied to the most recent price changes. What is interesting is that PMAC(50) puts far more weight on recent prices changes than the TSMOM(50) model does.  For equivalent lookback periods, then, we would expect PMAC to react much more quickly.  This is precisely why we saw PMAC models turn off in the most recent sell-off when other models did not: they are much more front-weighted.
  • DMAC models create a hump-shaped weighting profile, with increasing weight applied up until the length of the shorter lookback period, and then descending weight thereafter. If we wanted to, we could even create a back-weighted model, as we have with the DMAC(150, 200) example. In practice, it is common to see that m is approximately equal to n/4 (e.g. DMAC(50, 200)).  Such a model underweights the most recent information relative to slightly less recent information.

Conclusion

In this brief research note, we demonstrated that common trend-following signals – namely time-series momentum, price-minus-moving-average, and dual-moving-average-crossover – are mathematically linked to one another.  We find that prior price changes are the building blocks of each signal, with the primary differences being how those prior price changes are weighted.

Time-series momentum signals equally-weight prior price changes; price-minus-moving-average models tend to forward-weight prior price changes; and dual-moving-average-crossovers create a hump-like weighting function.  The choice of which model to employ, then, expresses a view as to the relative importance we want to place on recent versus past price changes.

These results align with the trend signal changes seen over the past week during the rapid sell-off in the S&P 500.  Price-minus-moving-average models appeared to turn negative much faster than time-series momentum or dual-moving-average-crossover signals.

By decomposing these models into their most basic and shared form, we again highlight the potential specification risks that can arise from electing to employ just one model.  This is particularly true if an investor selects just one of these models without realizing the implicit choice they have made about the relative importance they would like to place on recent versus past returns.

 

 

Diversifying the What, How, and When of Trend Following

By

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.

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% respective sector index / 50% U.S. risk-free rate.

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.

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.

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.

 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 assumes the reinvestment of all dividends. 

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.

 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 assumes the reinvestment of all dividends. 

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.

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 assumes the reinvestment of all dividends. 

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 assumes the reinvestment of all dividends. 

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:

  1. Our signals identify no change and we remain invested; the market sells off dramatically over the next month.
  2. 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.

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 assumes the reinvestment of all dividends. 

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 1st week of the month, another on the 2nd 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

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.

 

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.

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.

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.

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.

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.

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.

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.

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 50014.4%12.0%-52.3%
12-1 TS Momentum11.7%12.3%-10.9%
80/2012.3%9.4%-42.5%
60/4010.1%6.9%-32.0%
CBOE S&P 500 5% Put Protection Index10.2%10.1%-36.6%
Salient Trend Index (Managed Futures)1.2%10.3%-14.3%
Salient Risk Parity Index6.6%8.7%-30.8%
HFRX Global Hedge Fund Index1.5%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

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