*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.”

## How Much Accuracy Is Enough?

By Nathan Faber

On March 4, 2019

In Craftsmanship, Portfolio Construction, Trend, Weekly Commentary

Available as a PDF download here.## Summary

The distinction between luck and skill in investing can be extremely difficult to measure. Seemingly good or bad strategies can be attributable to either luck or skill, and the truth has important implications for the future prospects of the strategy.

Source: Grinold and Kahn, Active Portfolio Management. (New York: McGraw-Hill, 1999).Time is one of the surest ways to weed out lucky strategies, but the amount of time needed to make this decision with a high degree of confidence can be longer than we are willing to wait. Or, sometimes, even longer than the data we have.

For example, in order to be 95% confident that a strategy with a 7% historical return and a volatility of 15% has a true expected return that is greater than a 2% risk-free rate, we would need 27 years of data. While this is possible for equity and bond strategies, we would have a long time to wait in order to be confident in a Bitcoin strategy with these specifications.

Even after passing that test, however, that same strategy could easily return less than the risk-free rate over the

next5 years(the probability is 25%).Regardless of the skill, would you continue to hold a strategy that underperformed for that long?

In this commentary, we will use a sample U.S. sector strategy that isolates luck and skill to explore the impacts of varying accuracy and how even increased accuracy may only be an idealized goal.

The (In)Accurate InvestorTo investigate the historical impact of luck and skill in the arena of U.S. equity investing, we will consider a strategy that invests in the 30 industries from the Kenneth French Data Library.

Each month, the strategy independently evaluates each sector and either holds it or invests the capital at the risk-free rate. The term “evaluates” is used loosely here; the evaluation can be as simple as flipping a (potentially biased) coin.

The allocation allotted to each sector is 1/30

^{th}of the portfolio (3.33%). We are purposely not reallocating capital among the sectors chosen so that the sector calls based on the accuracy straightforwardly determine the performance.To get an idea for the bounds of how well – or poorly – this strategy would have performed over time, we can consider three investors:

The Plain Investor– This investor simply holds all 30 sectors, equally weighted, all the time.The Perfect Investor– This investor allocates with 100% accuracy. Using a crystal ball to look into the future, if a sector will go up in the subsequent month, this investor will allocate to it. If the sector will go down, this investor will invest the capital in cash.The Anti-Perfect Investor– This investor not merely imperfect, they are the complete opposite of the Perfect Investor. They make the wrong calls to invest or not without fail. Their accuracy is 0%. They are so reliably bad that if you could short their strategy, you would be the Perfect Investor.The Perfect and Anti-Perfect investors set the bounds for what performance is possible within this framework, and the Plain Investor denotes the performance of not making any decisions.

The growth of each boundary strategy over the entire time period is a little outrageous.

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. This 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.A more informative illustration is the rolling annualized 5-year return for each strategy.

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. This 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.While the spread between the Perfect and Anti-Perfect investors ebbs and flows, its median value Is 59,000 basis points (“bps”). Between the Perfect and Plain investors, there is still 29,000 bps of annualized outperformance to be had. A natural wish is to make calls that harvest some of this spread.

Accounting for AccuracyNow we will look at a set of investors who are able to evaluate each sector with some known degree of accuracy.

For each accuracy level between 0% and 100% (i.e. our Anti-Perfect and Perfect investors, respectively), we simulate 1,000 trials and look at how the historical results have played out.

A natural starting point is the investor who merely flips a fair coin for each sector. Their accuracy is 50%.

The chart below shows the rolling 5-year performance range of the simulated trials for the 50% Accurate Investor.

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. This 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.In 59% of the rolling periods, the buy-and-hold Plain Investor beat even the best 50% Accurate Investor. The Plain Investor was only worse than the worst performing coin flip strategy in 6% of rolling periods.

Beating buy-and-hold is hard to do reliably if you rely only on luck.

In this case, having a neutral hit rate with the negative skew of the sector equity returns leads to negative information coefficients. Taking more bets over time and across sectors did not help offset this distributional disadvantage.

So, let’s improve the accuracy slightly to see if the rolling results improve. Even with negative skew (-0.42 median value for the 30 sectors), an improvement in the accuracy to 60% is enough to bring the theoretical information coefficient back into the positive realm.

The worst of these more skilled investors is now beating the Plain Investor in 41% of the rolling periods, and the best is losing to the buy-and-hold investor in 13% of the periods.

Going the other way, to a 40% accurate investor, we find that the best one was beaten by the Plain investor 93% of the time, and the worst one never beats the buy-and-hold investor.

If we only require a modest increase in our accuracy to beat buy-and-hold strategies over shorter time horizons, why isn’t diligently focusing on increasing our accuracy an easy approach to success?

In order to increase our accuracy, we must first find a reliable way to do so: a task easier said than done due to the inherent nature of probability. Something having a 60% probability of being right does not preclude it from being wrong for a long time. The Law of Large Numbers can require larger numbers than our portfolios can stand.

Thus, even if we have found a way that will reliably lead to a 60% accuracy, we may not be able to establish confidence in that accuracy rate. This uncertainty in the accuracy can be unnerving. And it can cut both ways.

A strategy with a hit rate of less than 50% can masquerade as a more accurate strategy simply for lack of sufficient data to sniff out the true probability.

You may think you have an edge when you do not. And if you do not have an edge, repeatedly applying it will lead to worse and worse outcomes.

^{2}Accuracy SchmaccuracyOur preference is to rely on systematic bets, which generally fall under the umbrella of factor investing. Even slight improvements to the accuracy can lead to better results when applied over a sufficient breadth of investments. Some of these factors also alter the distribution of returns (i.e. the skew) so that accuracy improvements have a larger impact.

Consider two popular measures of trend, used as the signals to determine the allocations in our 30 sector US equity strategy from the previous sections:

12-1 Momentum:We calculate the return over an 11-month period, starting one month ago to account for mean reversionary effects. If this number is positive, we hold the sector; if it is negative, we invest that capital at the risk-free rate.10-month Simple Moving Average (SMA):We average the prices over the prior 10 months and compare that value to the current price. If the current price is greater than or equal to the average, we hold the sector; if it is less than, we invest that capital at the risk-free rate.These strategies have volatilities in line with the Perfect and Anti-Perfect Investors and returns similar to the Plain Investor.

Using our measure of accuracy as correctly calling the direction of the sector returns over the subsequent month, it might come as a surprise that the accuracies for the 12-1 Momentum and 10-month SMA signals are only 42% and 41%, respectively.

Even with this low accuracy, the following chart shows that over the entire time period, the returns of these strategies more closely resemble those of the 55% Accurate Investor and have even looked like those of the 70% Accurate Investor over some time periods. What gives?

This is an example of how addressing the negative skew in the underlying asset returns can offset a sacrifice in accuracy. These trend following strategies may have overall accuracy of less than 50%, but they have been historically right when it counts.

Consistently removing large negative returns – at the expense of giving up some large positive returns – is enough to generate a return profile that looks much like a strategy that picks sectors with above average accuracy.

Whether investors can stick with a strategy that exhibits below 50% accuracy, however, is another question entirely.

ConclusionWhile most investors expect the proof to be in the eating of the pudding, in this commentary we demonstrate how luck can have a meaningful impact in the determination of whether skill exists. While skill should eventually differentiate itself from luck, the horizon over which it will do so may be far, far longer than most investors suspect.

To explore this idea, we construct portfolios comprised of all thirty industry groups. We then simulate the results of investors with known accuracy rates, comparing their outcomes to 100% Accuracy, 100% Inaccurate, and Buy-and-Hold benchmarks.

Perhaps somewhat counter-intuitively, we find that an investor exhibiting 50% accuracy would have fairly reliably underperformed a Buy-and-Hold Investor. This seems somewhat counter-intuitive until we acknowledge that equity returns have historically exhibit negative skew, with the left tail of their return distribution (“losses”) being longer and fatter than the right (“gains”). Combining a neutral hit rate with negative skew creates negative information coefficients.

To offset this negative skew, we require increased accuracy. Unfortunately, even in the case where an investor exhibits 60% accuracy, there are a significant number of 5-year periods where it might masquerade as a strategy with a much higher or lower hit-rate, inviting false conclusions.

This is all made somewhat more confusing when we consider that a strategy can have an accuracy rate

below50% and still be successful. Trend following strategies are a perfect example of this phenomenon. The positive skew that has been historically exhibited by these strategies means that frequently inaccurate trades of small magnitude are offset by infrequent, by very large accurate trades.Yet if we measure success by short-term accuracy rates, we will almost certainly dismiss this type of strategy as one with no skill.

When taken together, this evidence suggests that not only might it be difficult for investors to meaningfully determine the difference between skill and luck over seemingly meaningful time horizons (e.g. 5 years), but also that short-term perceptions of accuracy can be woefully misleading for long-term success. Highly accurate strategies can still lead to catastrophe if there is significant negative skew lurking in the shadows (e.g. an ETF like XIV), while inaccurate strategies can be successful with enough positive skew (e.g. trend following).