*This post is available as a PDF download here.*

# Summary

- Trend following’s simple, systematic, and transparent approach does not make it any less frustrating to allocate to during periods of rapid market reversals.
- With most trend equity strategies exhibiting whipsaws in 2010, 2011, 2015-2016, and early 2018, it is tempting to ask, “is this something we can fix?”
- We argue that there are three historically-salient features that make trend following attractive: (1) positive skew, (2) convexity, and (3) a positive premium.
- We demonstrate that the convexity exhibited by trend equity strategies is both a function of the strategy itself (i.e. a fast- or slow-paced trend model) as well as the horizon we measure returns over.
- We suggest that it may be more consistent to think of convexity as an element than can provide
*crisis beta,*where the nature of the crisis is defined by the speed of the trend following system. - The failure of a long-term trend strategy to de-allocate in Q4 2018 or meaningfully re-allocate in Q1 2019 is not a glitch; it is encoded in the DNA of the strategy itself.

There’s an old saying in Tennessee – I know it’s in Texas, probably in Tennessee – that says, fool me once, shame on – shame on you. Fool me – you can’t get fooled again!— George W. Bush

It feels like we’ve seen this play before. It happened in 2010. Then again in 2011. More recently in 2015-2016. And who can forget early 2018? To quote Yogi Berra, “It’s déjà vu all over again.” We’re starting to think it is a glitch in the matrix.

Markets begin to deteriorate, losses begin to more rapidly accelerate, and then suddenly everything turns on a dime and market’s go on to recover almost all their losses within a few short weeks.

Trend following – like the trend equity mandates we manage here at Newfound – requires trends. If the market completely reverses course and regains almost all of its prior quarter’s losses within a few short weeks, it’s hard to argue that trend following should be successful. Indeed, it is the prototypical environment that we explicitly warn trend following will do quite poorly in.

That does not mean, however, that changing our approach in these environments would be a warranted course of action. We embrace a systematic approach to explicitly avoid contamination via emotion, particularly during these scenarios. Plus, as we like to say, “risk cannot be destroyed, only transformed.” Trying to eliminate the risk of whipsaw not only risks style pollution, but it likely introduces risk in unforeseen scenarios.

So, we have to scratch our heads a bit when clients ask us for an explanation as to our current positioning. After all, trend following is fairly transparent. You can probably pull up a chart, stand a few feet back, squint, and guess with a reasonable degree of accuracy as to how most trend models would be positioned.

When 12-month, 6-month, and 3-month returns for the S&P 500 were all negative at the end of December, it is a safe guess that we’re probably fairly defensively positioned in our domestic trend equity mandates. Despite January’s record-breaking returns, not a whole lot changed. 12-, 6-, and 3-month returns were negative, negative, and just slightly positive, respectively, entering February.

To be anything but defensively positioned would be a complete abandonment of trend following.

It is worth acknowledging that this may all just be Act I. Back when this show was screening in 2011 and 2015-2016, markets posted violent reversals – with the percent of stocks above their 50-day moving average climbing from less than 5% to more than 90% – only to roll over again and retest the lows.

Or this will be February 2018 part deux. We won’t know until well after the fact. And that can be frustrating depending upon your perspective of markets.

If you take a deterministic view, incorrect positioning implies an error in judgement. *You should have known to abandon trend following and buy the low on December 24 ^{th}. *If you take a probabilistic view, then it is possible to be correctly positioned for the higher probability event and still be wrong.

*The odds were tilted strongly towards continued negative market pressure and a defensive stance was warranted at the time.*

We would argue that there is a third model as well: *sustainability* (or, more morbidly, *survivability*). It does not matter if you have a 99% chance of success while playing Russian Roulette: play long enough and you’re eventually going to lose. Permanently. Sustainability argues that the low-probability bet may be the one worth taking if the payoff is sufficient enough or it protects us from ruin.

Thus, for investors for whom *failing fast *is a priority risk, a partially defensive allocation in January and February may be well warranted, even if the intrinsic probabilities have reversed course (which, based on trends, they largely had not).

But sustainability also needs to be a discussion about being able to stick with a strategy. It does not matter if the strategy survives over the long run if the investor does not participate.

That is why we believe transparency and continued education are so critical. If we do not know what we are invested in, we cannot set correct expectations. Without correct expectations, *everything *feels unexpected. And when everything feels unexpected, we have no way to determine if a strategy is behaving correctly or not.

Which brings us back to trend equity strategies in Q4 2018 and January 2019. Did trend equity behave as expected?

Trend following has empirically exhibited three attractive characteristics:

**Positive Skew:**The return distribution is asymmetric, with a larger right tail than left tail (i.e. greater frequency of larger, positive returns than large, negative returns).**Convex Payoff Profile:**As a function of the underlying asset the trend following strategy is applied on, upside potential tends to be greater than downside risk.**Positive Premium:**The strategy has a positive expected excess return.

While the first two features can be achieved by other means (e.g. option strategies), the third feature is downright anomalous, as we discussed in our recent commentary *Trend: Convexity & Premium*. Positive skew and convexity create and insurance-like payoff profile and therefore together tend to imply a *negative *premium.

The first two characteristics make trend following a potentially interesting portfolio diversifier. The last element, if it persists, makes it *very *interesting.

Yet while we may talk about these features as historically intrinsic properties of trend following, the nature of the trend-following strategy will significantly impact the horizon over which these features are observed. What is most important to acknowledge here is that skew and convexity are more akin to *beta *than they are *alpha*; they are byproducts of the trading strategy itself. While it can be hard to say things about alpha, we often can say quite a bit more about beta.

For example, a fast trend following system (typically characterized by a short lookback horizon) would be expected to rapidly adapt to changing market dynamics. This allows the system to quickly position itself for emerging trends, but also potentially makes the strategy more susceptible to losses from short-term reversals.

A slow trend following system (characterized by a long lookback period), on the other hand, would be less likely to change positioning due to short-term market noise, but is also therefore likely to adapt to changing trend dynamics more slowly.

Thus, we might suspect that a fast-paced trend system might be able to exhibit convexity over a shorter measurement period, whereas a slow-paced system will not be able to adapt rapidly. On the other hand, a fast trend following system may have less average exposure to the underlying asset over time and may compound trading losses due to whipsaw more frequently.

To get a better sense of these tradeoffs, we will construct prototype trend equity strategies which will invest either in broad U.S. equities or risk-free bonds. The strategies will be re-evaluated on a daily basis and are assumed to be traded at the close of the day following a signal change. Trend signals will be based upon prior total returns; e.g. a 252-day system will have a positive (negative) signal if prior 252-day total returns in U.S. equity markets are positive (negative).

Below we plot the monthly returns of a -short-term trend equity system (21 day)- and a -long-term trend equity system (252 day)- versus U.S. equity returns.

*Source: Kenneth French Data Library. Calculations by Newfound Research. Past performance is not a guarantee of future results. All returns are hypothetical and backtested. Returns are gross of all fees. For the avoidance of doubt, neither the Short-Term nor Long-Term Trend Equity strategy reflect any investment strategy offered or managed by Newfound Research and was constructed exclusively for the purposes of this commentary. It is not possible to invest in an index.*

We can see that the fast-paced system exhibits convexity over the monthly measurement horizon, while the slower system exhibits a more linear return profile.

As mentioned above, however, the more rapid adaptation in the short-term system might cause more frequent realization of whipsaw due to price reversals and therefore an erosion in long-term convexity. Furthermore, more frequent changes might also reduce long-term participation.

We now plot annual returns versus U.S. equities below.

*Source: Kenneth French Data Library. Calculations by Newfound Research. Past performance is not a guarantee of future results. All returns are hypothetical and backtested. Returns are gross of all fees. For the avoidance of doubt, neither the Short-Term nor Long-Term Trend Equity strategy reflect any investment strategy offered or managed by Newfound Research and was constructed exclusively for the purposes of this commentary. It is not possible to invest in an index.*

We can see that while the convexity of the short-term system remains intact, the long-term system exhibits greater upside participation.

To get a better sense of these trade-offs, we will follow Sepp (2018)^{1} and use the following model to deconstruct our prototype long/flat trend equity strategies:

By comparing daily, weekly, monthly, quarterly, and annual returns, we can extract the linear and convexity exposure fast- and slow-paced systems have historically exhibited over a given horizon.

Below we plot the regression coefficients (“betas”) for a fast-paced system.

*Source: Kenneth French Data Library. Calculations by Newfound Research. Past performance is not a guarantee of future results. All returns are hypothetical and backtested. Returns are gross of all fees. For the avoidance of doubt, the Short-Term Trend Equity strategy does not reflect any investment strategy offered or managed by Newfound Research and was constructed exclusively for the purposes of this commentary. It is not possible to invest in an index.*

We can see that the linear exposure remains fairly constant (and in line with decompositions we’ve performed in the past which demonstrate that long/flat trend equity can be thought of as a 50/50 stock/cash strategic portfolio plus a long/short overlay^{2}). The convexity profile, however, is most significant when measured over weekly or monthly horizons.

Long-term trend following systems, on the other hand, exhibit negative or insignificant convexity profiles over these horizons. Even over a quarterly horizon we see insignificant convexity. It is not until we evaluate returns on an annual horizon that a meaningful convexity profile is established.

*Source: Kenneth French Data Library. Calculations by Newfound Research. Past performance is not a guarantee of future results. All returns are hypothetical and backtested. Returns are gross of all fees. For the avoidance of doubt, the Long-Term Trend Equity strategy does not reflect any investment strategy offered or managed by Newfound Research and was constructed exclusively for the purposes of this commentary. It is not possible to invest in an index.** *

These results have very important implications for investors in trend following strategies.

We can see that long-term trend following, for example, is unlikely to be successful as a tail risk hedge for short-term events. Short-term trend following may have a higher probability of success in such a scenario, but only so long as the crisis occurs over a weekly or monthly horizon.^{3}

Short-term trend following, however, appears to exhibit *less *convexity with annual returns and has lower linear exposure. This implies less upside capture to the underlying asset.

Neither approach is likely to be particularly successful at hedging against daily crises (e.g. a 1987-type event), as the period is meaningfully shorter than the adaptation speed of either of the strategies.

These results are neither feature nor glitch. They are simply the characteristics we select when we choose either a fast or slow trend-following strategy. While trend-following strategies are often pitched as *crisis alpha*, we believe that skew and convexity components are more akin to *crisis beta. *And this is a good thing. While alpha is often ephemeral and unpredictable, we can more consistently plan around beta.

Thus, when we look back on Q4 2018 and January 2019, we need to acknowledge that we are evaluating results over a monthly / quarterly horizon. This is fine if we are evaluating the results of fast-paced trend-following strategies, but we certainly should not expect any convexity benefits from slower trend models. Quite simply, it all happened too fast.

**Conclusion**

When markets rapidly reverse course, trend following can be a frustrating style to allocate to. With trend equity styles exhibiting whipsaws in 2010, 2011, 2015-2016, and early 2018, the most recent bout of volatility may have investors rolling their eyes and thinking, “again?”

“Where’s the crisis alpha?” investors cry. “Where’s the crisis?” managers respond back.

Yet as we demonstrated in our last commentary, two of the three salient features of trend following – namely positive skew and positive convexity – may be byproducts of the trading strategy and not an anomaly. Rather, the historically positive premium that trend following has generated has been the anomaly.

While the potential to harvest alpha is all well and good, we should probably think more in the context of *crisis beta* than *crisis alpha *when setting expectations. And that beta will be largely defined by the speed of the trend following strategy.

But it will also be defined by the period we are measuring the crisis over.

For example, we found that fast-paced trend equity strategies exhibit positive convexity when measured over weekly and monthly time horizons, but that the convexity decays when measured over annual horizons.

Strategies that employ longer-term trend models, on the other hand, fail to exhibit positive convexity over shorter time horizons, but exhibit meaningful convexity over longer-horizons. The failure of long-term trend strategies to meaningfully de-allocate in Q4 2018 or rapidly re-allocate in Q1 2019 is not a glitch: it is encoded into the DNA of the strategy.

Put more simply: if we expect long-term trend models to protect against short-term sell-offs, we should prepare to be disappointed. On the other hand, the rapid adaptation of short-term models comes at a cost, which can materialize as lower up-capture over longer horizons.

Thus, when it comes to these types of models, we have to ask ourselves about the risks we are trying to manage and the trade-offs we are willing to make. After all, “risk cannot be destroyed, only transformed.”

## The Speed Limit of Trend

By Corey Hoffstein

On April 15, 2019

In Trend, Weekly Commentary

This post is available as a PDF download here.## Summary

We like to use the phrase “mechanically convex” when it comes to trend following. It implies a transparent and deterministic “if-this-then-that” relationship between the price dynamics of an asset, the rules of a trend following, and the performance achieved by a strategy.

Of course, nobody knows how an asset’s future price dynamics will play out. Nevertheless, the deterministic nature of the rules with trend following should, at least, allow us to set semi-reasonable expectations about the outcomes we are trying to achieve.

A January 2018 paper from OneRiver Asset Management titled

The Interplay Between Trend Following and Volatility in an Evolving “Crisis Alpha” Industrytouches precisely upon this mechanical nature. Rather than trying to draw conclusions analytically, the paper employs numerical simulation to explore how certain trend speeds react to different drawdown profiles.Specifically, the authors simulate 5-years of daily equity returns by assuming a geometric Brownian motion with 13% drift and 13% volatility. They then simulate drawdowns of different magnitudes occurring over different time horizons by assuming a Brownian bridge process with 35% volatility.

The authors then construct trend following strategies of varying speeds to be run on these simulations and calculate the median performance.

Below we re-create this test. Specifically,

By varying T and the NxM models, we can attempt to get a sense as to how different trend speeds should behave in different drawdown profiles.

Note that the generated tables report on the median performance of the trend following strategy over only the drawdown period. The initial five years of positive expected returns are essentially treated as a burn-in period for the trend signal. Thus, if we are looking at a drawdown of 20% and an entry in the table reads -20%, it implies that the trend model was exposed to the full drawdown without regard to what happened in the years prior to the drawdown. The return of the trend following strategies over the drawdown period can be larger than the drawdown because of whipsaw and the fact that the underlying equity can be down more than 20% at points during the period.

Furthermore, these results are for

long/shortimplementations. Recall that a long/flat strategy can be thought of as 50% explore to equity plus 50% exposure to a long/short strategy. Thus, the results of long/flat implementations can be approximated by halving the reported result and adding half the drawdown profile. For example, in the table below, the 20×60 trend system on the 6-month drawdown horizon is reported to have a drawdown of -4.3%. This would imply that a long/flat implementation of this strategy would have a drawdown of approximately -12.2%.Calculations by Newfound Research. Results are hypothetical. Returns are gross of all fees, including manager fees, transaction costs, and taxes.There are several potential conclusions we can draw from this table:

Note that these results align with results found in earlier research commentaries about the relationship between measured convexity and trend speed. Namely, faster trends appear to exhibit convexity when measured over shorter horizons, whereas slower trend speeds require longer measurement horizons.

But what happens if we change the drawdown profile from 20%?

Varying Drawdown SizeCalculations by Newfound Research. Results are hypothetical. Returns are gross of all fees, including manager fees, transaction costs, and taxes.We can see some interesting patterns emerge.

First, for more shallow drawdowns, slower trend models struggle over almost all drawdown horizons. On the one hand, a 10% drawdown occurring over a month will be too fast to capture. On the other hand, a 10% drawdown occurring over several years will be swamped by the 35% volatility profile we simulated; there is too much noise and too little signal.

We can see that as the drawdowns become larger and the duration of the drawdown is extended, slower models begin to perform much better and faster models begin to degrade in relative performance.

Thus, if our goal is to protect against large losses over sustained periods (e.g. 20%+ over 6+ months), intermediate-to-slow trend models may be better suited our needs.

However, if we want to try to avoid more rapid, but shallow drawdowns (e.g. Q4 2018), faster trend models will likely have to be employed.

Varying VolatilityIn our test, we specified that the drawdown periods would be simulated with an intrinsic volatility of 35%. As we have explored briefly in the past, we expect that the optimal trend speed would be a function of both the dynamics of the trend process and the dynamics of the price process. In simplified models (i.e. constant trend), we might assume the model speed is proportional to the trend speed relative to the price volatility. For a more complex model, others have proposed that model speed should be proportional to the volatility of the trend process relative to the volatility of the price process.

Therefore, we also want to ask the question, “what happens if the volatility profile changes?” Below, we re-create tables for a 20% and 40% drawdown, but now assume a 20% volatility level, about half of what was previously used.

Calculations by Newfound Research. Results are hypothetical. Returns are gross of all fees, including manager fees, transaction costs, and taxes.We can see that results are improved almost without exception.

^{1}Not only do faster models now perform better over longer drawdown horizons, but intermediate and slow models are now much more effective at horizons where they had previously not been. For example, the classic 50×200 model saw an increase in its median return from -23.1% to -5.3% for 20% drawdowns occurring over 1.5 years.

It is worth acknowledging, however, that even with a reduced volatility profile, a shallower drawdown over a long horizon is still difficult for trend models to exploit. We can see this in the last three rows of the 20% drawdown / 20% volatility table where none of the trend models exhibit a positive median return, despite having the ability to profit from shorting during a negative trend.

ConclusionThe transparent, “if-this-then-that” nature of trend following makes it well suited for scenario analysis. However, the uncertainty of how price dynamics may evolve can make it difficult to say anything about the future with a high degree of precision.

In this commentary, we sought to evaluate the relationship between trend speed, drawdown size, drawdown speed, and asset volatility and a trend following systems ability to perform in drawdown scenarios. We generally find that:

From peak-to-trough, the dot-com bubble imploded over about 2.5 years, with a drawdown of about -50% and a volatility of 24%. The market meltdown in 2008, on the other hand, unraveled in 1.4 years, but had a -55% drawdown with 37% volatility. Knowing this, we might expect a slower model to have performed better in early 2000, while an intermediate model might have performed best in 2008.

If only reality were that simple!

While our tests may have told us something about the

expectedperformance, we only live through one realization. The precise and idiosyncratic nature of how each drawdown unfolds will ultimately determine which trend models are successful and which are not. Nevertheless, evaluating the historical periods of large U.S. equity drawdowns, we do see some common patterns emerge.The sudden drawdown of 1987, for example, remains elusive for most of the models. The dot-com and Great Recession were periods where intermediate-to-slow models did best. But we can also see that trend is not a panacea: the 1946-1949 drawdown was very difficult for most trend models to navigate successfully.

Our conclusion is two-fold. First, we should ensure that the trend model we select is in-line with the sorts of drawdown profiles we are looking to create convexity against. Second, given the unknown nature of how drawdowns might evolve, it may be prudent to employ a variety of trend following models.