Flirting with Models

The Research Library of Newfound Research

Author: Corey Hoffstein Page 8 of 18

Corey is co-founder and Chief Investment Officer of Newfound Research.

Corey holds a Master of Science in Computational Finance from Carnegie Mellon University and a Bachelor of Science in Computer Science, cum laude, from Cornell University.

You can connect with Corey on LinkedIn or Twitter.

The Speed Limit of Trend

By

On April 15, 2019

In Trend, Weekly Commentary

This post is available as a PDF download here.

Summary­

  • Trend following is “mechanically convex,” meaning that the convexity profile it generates is driven by the rules that govern the strategy.
  • While the convexity can be measured analytically, the unknown nature of future price dynamics makes it difficult to say anything specific about expected behavior.
  • Using simulation techniques, we aim to explore how different trend speed models behave for different drawdown sizes, durations, and volatility levels.
  • We find that shallow drawdowns are difficult for almost all models to exploit, that faster drawdowns generally require faster models, and that lower levels of price volatility tend to make all models more effective.
  • Finally, we perform historical scenario analysis on U.S. equities to determine if our derived expectations align with historical performance.

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” Industry touches 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,

  • We generate 10,000 5-year simulations assuming a geometric Brownian motion with 13% drift and 13% volatility.
  • To the end of each simulation, we attach a 20% drawdown simulation, occurring over T days, assuming a geometric Brownian bridge with 35% volatility.
  • We then calculate the performance of different NxM moving-average-cross-over strategies, assuming all trades are executed at the next day’s closing price. When the short moving average (N periods) is above the long moving average (M periods), the strategy is long, and when the short moving average is below the long moving average, the strategy is short.
  • For a given T-day drawdown period and NxM trend strategy, we report the median performance across the 10,000 simulations over the drawdown period.

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/short implementations.  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:

  1. None of the trend models are able to avoid an immediate 1-day loss.
  2. Very-fast (10×30 to 10×50) and fast (20×60 and 20×100) trend models are able to limit losses for week-long drawdowns, and several are even able to profit during month-long drawdowns but begin to degrade for drawdowns that take over a year.
  3. Intermediate (50×150 to 50×250) and slow (75×225 to 75×375) trend models appear to do best for drawdowns in the 3-month to 1-year range.
  4. Very slow (100×300 to 200×400) trend models do very little at all for drawdowns over any timeframe.

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 Size

Calculations 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 Volatility

In 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.

Conclusion

The 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:

  • The effectiveness of trend speed appears to be positively correlated with drawdown speed. Intuitively, faster drawdowns require faster trend models.
  • Trend models struggle to capture shallow drawdowns (e.g. 10%). Faster trend models appear to be effective in capturing relatively shallow drawdowns (~20%), so long as they happen with sufficient speed (<6 months).  Slower models appear relatively ineffective against this class of drawdowns over all horizons, unless they occur with very little volatility.
  • Intermediate-to-slow trend models are most effective for larger, more prolonged drawdowns (e.g. 30%+ over 6+ months).
  • Lower intrinsic asset volatility appears to make trend models effective over longer drawdown horizons.

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 expected performance, 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.

Calculations by Newfound Research.  Results are hypothetical.  Returns are gross of all fees, including manager fees, transaction costs, and taxes.

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.

 

Time Dilation

By

On March 25, 2019

In Portfolio Construction, Weekly Commentary

This post is available as a PDF download here.

Summary

  • Information does not flow into the market at a constant frequency or with constant magnitude.
  • By sampling data using a constant time horizon (e.g. “200-day simple moving average”), we may over-sample during calm market environments and under-sample in chaotic ones.
  • As an example, we introduce a highly simplified price model and demonstrate that trend following lookback periods should be a dynamic function of trend and volatility in the time domain.
  • By changing the sampling domain slightly, we are able to completely eliminate the need for the dynamic lookback period.
  • Finally, we demonstrate a more complicated model that samples market prices based upon cumulative log differences, creating a dynamic moving average in the time domain.
  • We believe that there are other interesting applications of this line of thinking, many of which may already be in use today by investors who may not be aware of it (e.g. tracking-error-based rebalancing techniques).

In the 2014 film Interstellar, Earth has been plagued by crop blights and dust storms that threaten the survival of mankind. Unknown, interstellar beings have opened a wormhole near Saturn, creating a path to a distant galaxy and the potential of a new home for humanity.

Twelve volunteers travel into the wormhole to explore twelve potentially hospitable planets, all located near a massive black hole named Gargantua. Of the twelve, only three reported back positive results.

With confirmation in hand, the crew of the spaceship Endurance sets out from Earth with 5,000 frozen human embryos, intent on colonizing the new planets.

After traversing the wormhole, the crew sets down upon the first planet – an ocean world – and quickly discovers that it is actually inhospitable. A gigantic tidal wave kills one member of the crew and severely delays the lander’s departure.

The close proximity of the planet to the gravitational forces of the supermassive black hole invites exponential time dilation effects. The positive beacon that had been tracked had perhaps been triggered just minutes prior on the planet. For the crew, the three hours spent on the planet amounted to over 23 years on Earth. The crew can only watch, devastated, as their loved ones age before their eyes in the video messages received – and never responded to – in their multi-decade absence.

Our lives revolve around the clock, though we do not often stop to reflect upon the nature of time.

Some aspects of time tie to corresponding natural events. A day is simply reckoned from one midnight to the next, reflecting the Earth’s full rotation about its axis. A year, which reflects the length of time it takes for the Earth to make a full revolution around the Sun, will also correspond to a full set of a seasons.

Others, however, are seemingly more arbitrary. The twenty-four-hour day is derived from ancient Egyptians, who divided day-time into 10 hours, bookended by twilight hours. The division of an hour into sixty minutes comes from the Babylonians, who used a sexagesimal counting system.

We impose the governance of the clock upon our financial system as well. Public companies prepare quarterly and annual reports. Economic data is released at a scheduled monthly or quarterly pace. Trading days for U.S. equity markets are defined as between the hours of 9:30am and 4:00pm ET.

In many ways, our imposition of the clock upon markets creates a natural cadence for the flow of information.

Yet, despite our best efforts to impose order, information most certainly does not flow into the market in a constant or steady manner.

New innovations, geopolitical frictions, and errant tweets all represent idiosyncratic events that can reshape our views in an instant. A single event can be of greater import than all the cumulative economic news that came before it; just consider the collapse of Lehman Brothers.

And much like the time dilation experienced by the crew of Endurance, a few, harrowing days of 2008 may have felt longer than the entirety of a tranquil year like 2017.

One way of trying to visualize this concept is by looking at the cumulative variance of returns. Given the clustered nature of volatility, we would expect to see periods where the variance accumulates slowly (“calm markets”) and periods where the variance accumulates rapidly (“chaotic markets”).

When we perform this exercise – by simply summing squared daily returns for the S&P 500 over time – we see precisely this. During market environments that exhibit stable economic growth and little market uncertainty, we see very slow and steady accumulation of variance. During periods when markets are seeking to rapidly reprice risk (e.g. 2008), we see rapid jumps.

Source: CSI Data. Calculations by Newfound Research.

If we believe that information flow is not static and constant, then sampling data on a constant, fixed interval will mean that during calm markets we might be over-sampling our data and during chaotic markets we might be under-sampling.

Let’s make this a bit more concrete.

Below we plot the –adjusted closing price of the S&P 500– and its –200-day simple moving average–. Here, the simple moving average aims to estimate the trend component of price. We can see that during the 2005-2007 period, it estimates the underlying trend well, while in 2008 it dramatically lags price decline.

Source: CSI Data. Calculations by Newfound Research.

The question we might want to ask ourselves is, why are looking at the prior 200 days? Or, more specifically, why is a day a meaningful unit of measure? We already demonstrated above that it very well may not be: one day might be packed with economically-relevant information and another entirely devoid.

Perhaps there are other ways in which we might think about sampling data. We could, for example, sample data based upon cumulative volume intervals. Another might be on a fixed number of cumulative ticks or trades. Yet another might be on a fixed cumulative volatility or variance.

As a firm which makes heavy use of trend-following techniques, we are particularly partial to the latter approach, as the volatility of an asset’s trend versus its price should inform the trend lookback horizon. If we think of trend following as being the trading strategy that replicates the payoff profile of a straddle, increased volatility levels will decrease the delta of the option positions, and therefore decrease our position size. An interpretation of this effect is that the increased volatility decreases our certainty of where price will fall at expiration, and therefore we need to decrease our sensitivity to price movements.

If that all sounds like Greek, consider this simple example. Assume that price follows a highly simplified model as a function of time:

There are two components of this model: the linear trend and the noise.

Now let’s assume we are attempting to identify whether the linear trend is positive or negative by using a simple moving average (“SMA”) of price:

To determine if there is a positive or a negative trend, we simply ask if our current SMA value is greater or less than the prior SMA value. For a positive trend, we require:

Substituting our above definition of the simple moving average:

When we recognize that most of the terms on the left also appear on the right, we can re-write the whole comparison as the new price in the SMA being greater than the old price dropping out of the SMA:

Which, through substitution of our original definition, leaves us with:

Re-arranging a bit, we get:

Here we use the fact that sin(x) is bounded between -1 and 1, meaning that:

Assuming a positive trend (m > 0), we can replace with our worst-case scenario,

To quickly test this result, we can construct a simple time series where we assume a=3 and m=0.5, which implies that our SMA length should be greater than 11. We plot the –time series– and –SMA– below. Note that the –SMA– is always increasing.

Despite being a highly simplified model, it illuminates that our lookback length should be a function of noise versus trend strength. The higher the ratio of noise to trend, the longer the lookback required to smooth out the noise. On the other hand, when the trend is very strong and the noise is weak, the lookback can be quite short.1

Thus, if trend and noise change over time (which we would expect them to), the optimal lookback will be a dynamic function. When trend is much weaker than noise, we our lookback period will be extended; when trend is much stronger than noise, the lookback period shrinks.

But what if we transform the sampling domain? Rather than sampling price every time step, what if we sample price as a function of cumulative noise? For example, using our simple model, we could sample when cumulative noise sums back to zero (which, in this example, will be the equivalent of sampling every 2π time-steps).2

Sampling at that frequency, how many of data points would we need to estimate our trend? We need not even work out the math as before; a bit of analytical logic will suffice. In this case, because we know the cumulative noise equals zero, we know that a point-to-point comparison will be affected only by the trend component. Thus, we only need n=1 in this new domain.

And this is true regardless of the parameterization of trend or noise. Goodbye! dynamic lookback function.

Of course, this is a purely hypothetical – and dramatically over-simplified – model. Nevertheless, it may illuminate why time-based sampling may not be the most efficient practice if we do not believe that information flow is constant.

Below, we again plot the –S&P 500– as well as a standard –200-day simple moving average–.

We also sample prices of the S&P 500 based upon cumulative magnitude of log differences, approximating a cumulative 2.5% volatility move. When the market exhibits low volatility levels, the process samples price less frequently. When the market exhibits high volatility, it samples more frequently. Finally, we plot a –200 period moving average– based upon these samples.

We can see that sampling in a different domain – in this case, the log difference space – we can generate a process that reacts dynamically in the time domain. During the calm markets of 2006 and early 2007, the –200 period moving average– behaves like the –200-day simple moving average–, whereas during the 2008 crisis it adapts to the changing price level far more quickly.

By changing the domain in which we sample, we may be able to create a model that is dynamic in the time domain, avoiding the time-dilation effects of information flow.

Conclusion

Each morning the sun rises and each evening it sets. Every year the Earth travels in orbit around the sun. What occurs during those time spans, however, varies dramatically day-by-day and year-by-year. Yet in finance – and especially quantitative finance – we often find ourselves using time as a measuring stick.

We find the notion of time almost everywhere in portfolio construction. Factors, for example, are often defined by measurements over a certain lookback horizon and reformed based upon the decay speed of the signal.

Even strategic portfolios are often rebalanced based upon the calendar. As we demonstrated in our paper Rebalance Timing Luck: The Difference Between Hired and Fired, fixed-schedule rebalancing can invite tremendous random impact in our portfolios.

Information does not flow into the market at a constant rate. While time may be a convenient measure, it may actually cause us to sample too frequently in some market environments and not frequently enough in others.

One answer may be to transform our measurements into a different domain. Rather than sampling price based upon the market close of each day, we might sample price based upon a fixed amount of cumulative volume, trades, or even variance. In doing so, we might find that our measures now represent a more consistent amount of information flow, despite representing a dynamic amount of data in the time domain.

The Monsters of Investing: Fast and Slow Failure

By

On March 11, 2019

In Risk Management, Trend

This post is available as a PDF download here.

Summary

  • Successful investing requires that investors navigate around a large number of risks throughout their lifecycle. We believe that the two most daunting risks investors face are the risk of failing fast and the risk of failing slow.
  • Slow failure occurs when an investor does not grow their investment capital sufficiently over time to meet future real liabilities. This often occurs because they fail to save enough or because they invest too conservatively.
  • Fast failure occurs when an investor – often those who are living off of portfolio withdrawals and for whom time is no longer an ally – suffers a significant drawdown that permanently impairs their portfolio.
  • We believe that sensitivity to these risks should dictate an investor’s allocation profile. Investors sensitive to slow failure should invest more aggressively and bear more risk in certain bad states of the world for the potential to earn excess returns in good states.  On the other hand, investors sensitive to fast failure should invest more conservatively, sacrificing returns in order to avoid catastrophe.
  • We believe this framework can also be used to inform how investors can fund an allocation from their strategic policy to trend equity strategies.

Homer’s Odyssey follows the epic ten-year journey of Odysseus and his men as they try to make their way home after the fall of Troy.  Along the way, the soldiers faced a seemingly endless string of challenges, including a cyclops who ate them alive, a sorceress who turned them into pigs, and sirens that would have lured them to their deaths with a song had they not plugged their ears with beeswax.

In one trial, the men had to navigate the Strait of Messina between the sea monsters Scylla and Charybdis.  With her six serpentine heads, each with a triple row of sharp teeth, Scylla haunted the cliffs that lined one edge of the strait.  Ships that came too close would immediately lose six sailors to the ravenous monster.  Living under a rock on the other side of the strait was Charybdis.  A few times a day, this monster would swallow up large amounts of water and belch it out, creating whirlpools that could sink an entire ship.

The strait was so narrow that the monsters lived within an arrow’s range of one another. To safely avoid one creature meant almost necessarily venturing too close to the other.  On the one hand was almost certain, but limited, loss; on the other, the low probability of complete catastrophe.

Investors, similarly, must navigate between two risks: what we have called in the past the risks of failing slow and failing fast.

Slow failure results from taking too little risk, often from investors allocating too conservatively or holding excessive cash.  In doing so, they fail to grow their capital at a sufficient rate to meet future real liabilities.  Failure in this arena does not show up as a large portfolio drawdown: it creeps into the portfolio over time through opportunity cost or the slow erosion of purchasing power.

Fast failure results from the opposite scenario: taking too much risk.  By allocating too aggressively (either to highly skewed or highly volatile investments), investors might incur material losses in their portfolios at a time when they cannot afford to do so.

We would argue that much of portfolio design is centered around figuring out which risk an investor is most sensitive to at a given point in their lifecycle and adjusting the portfolio accordingly.

Younger investors, for example, often have significant human capital (i.e. future earning potential) but very little investment capital.  Sudden and large losses in their portfolios, therefore, are often immaterial in the long run, as both time and savings are on their side. Investing too conservatively at this stage in life can rely too heavily on savings and fail to exploit the compounding potential of time.

Therefore, younger, growth-oriented investors should be willing to bear the risk of failing fast to avoid the risk of failing slow.  In fact, we would argue that it is the willingness to bear the risk of failing fast that allows these investors to potentially earn a premium in the first place.  No pain, no premium.

Over time, investors turn their human capital into investment capital through savings and investment.  At retirement, investors believe that their future liabilities are sufficiently funded, and so give-up gainful employment to live off of their savings and investments. In other words, the sensitivity to slow failure has significantly declined.

However, with less time for the potential benefits of compounding and no plan on replenishing investments through further savings, the sensitivity to the risk of fast failure is dramatically heightened, especially in the years just prior to and just after retirement.  This is further complicated by the fact that withdrawals from the portfolio can heighten the impact of sustained and large drawdowns.

Thus, older investors tend shift from riskier stocks to safer bonds, offloading their fast failure risk to those willing to bear it.  Yet we should be hesitant to de-risk entirely; we must also acknowledge longevity risk.  Too conservative a profile may also lead to disaster if an investor outlives their nest-egg.

As we balance the scales of failing fast and slow, we can see why trying to invest a perpetual endowment is so difficult.  Consistent withdrawals invite the risk of failing fast while the perpetual nature invites the risk of failing slow.  A narrow strait to navigate between Scylla and Charybdis, indeed!

We would be remiss if we did not acknowledge that short-term, high quality bonds are not a panacea for fail fast risk.  Inflation complicates the calculus and unexpected bouts of inflation (e.g. the U.S. in the 1970s) or hyper-inflation (e.g. Brazil in the 1980s, Peru from 1988-1991, or present-day Venezuela) can cause significant, if not catastrophic, declines in real purchasing power if enough investment risk is not borne.

Purchasing seemingly more volatile assets may actually be a hedge here.  For example, real estate, when marked-to-market, may exhibit significant relative swings in value over time.  However, as housing frequently represents one the largest real liabilities an investor faces, purchase of a primary residence can lock in the real cost of the asset and provide significant physical utility. Investors can further reduce inflation risk by financing the purchase with a modest amount of debt, a liability which will decline in real value with unexpected positive inflation shocks.

The aforementioned nuances notwithstanding, this broad line of thinking invites some interesting guidance regarding portfolio construction.

Investors sensitive to fast failure should seek to immunize their real future liabilities (e.g. via insurance, real asset purchases, cash-flow matching, structured products, et cetera).  As they survey the infinite potential of future market states, they should be willing to give up returns in all states to avoid significant failure in any given one of them.

Investors sensitive to slow failure should seek to bear a diversified set of risk premia (e.g. equity risk premium, bond risk premium, credit premium, value, momentum, carry, et cetera) that allows their portfolios to grow sufficiently to meet future real liabilities.  These investors, then, are willing to pursue higher returns in the vast majority of future market states, even if it means increased losses in a few states.

I personally imagine this as if the investor sensitive to failing slow has piled up all their risk – like a big mound of dough – in the bad outcome states of the world. For their willingness to bear this risk, they earn more return in the good outcome states.  The investor sensitive to failing fast, on the other hand, smears that mound of risk across all the potential outcomes.  In their unwillingness to bear risk in a particular state, they reduce return potential across all states, but also avoid the risk of catastrophe.

Source: BuzzFeed

 

Quantitatively, we saw exactly this trade-off play out in our piece The New Glide Path, where we attempted to identify the appropriate asset allocation for investors in retirement based upon their wealth level. We found that:

  • Investors who were dramatically under-funded – i.e. those at risk of failing slow – relative to real liabilities were allocated heavily to equities.
  • Investors who were near a safe funding level – i.e. those at risk of failing fast – were tilted dramatically towards assets like Treasury bonds in order to immunize their portfolio against fast failure.
  • The fortunate few investors who were dramatically over-funded could, pretty much, allocate however they pleased.

We believe this same failing slow and failing fast framework can also inform how trend equity strategies – like those we manage here at Newfound Research – can be implemented by allocators.

In our recent commentary Three Applications of Trend Equity we explored three implementation ideas for trend equity strategies: (1) as a defensive equity sleeve; (2) as a tactical pivot; or (3) as an alternative.  While these are the most common approaches we see to implementing trend equity, we would argue that a more philosophically consistent route might be one that incorporates the notions of failing fast and failing slow.

In Risk Ignition with Trend Following we examined the realized efficient frontier of U.S. stocks and bonds from 1962-2017 and found that an investor who wanted to hold a portfolio targeting an annualized volatility of 10% would need to hold between 40-50% of their portfolio in bonds.  If we were able to magically eliminate the three worst years of equity returns, at the cost of giving up the three best, that number dropped to 20-30%.  And if we were able to eliminate the worst five at the cost of giving up the best five? Just 10%.

One interpretation of this data is that, with the benefit of hindsight, a moderate-risk investor would have had to carry a hefty allocation to bonds for the 55 years just to hedge against the low-probability risk of failing fast.  If we believe the historical evidence supporting trend equity strategies, however, we may have an interesting solution at hand:

  • A strategy that has historically captured a significant proportion of the equity risk premium.
  • A strategy that has historically avoided a significant proportion of prolonged equity market declines.

Used appropriately, this strategy may help investors who are sensitive to failing slowly tactically increase their equity exposure when trends are favorable. Conversely, trend equity may help investors who are sensitive to failing fast de-risk their portfolio during negative trend environments.

To explore this opportunity, we will look at three strategic profiles: an 80% U.S. equity / 20% U.S. bond mix, a 50/50 mix, and a 20/80 mix.  The first portfolio represents the profile of a growth investor who is sensitive to failing slow; the second portfolio represents a balanced investor, sensitive to both risks; the third represents a conservative investor who is sensitive to failing fast.

We will allocate a 10% slice of each portfolio to a naïve trend equity strategy in reverse proportion to the stock/bond mix.  For example, for the 80/20 portfolio, 2% of the equity position and 8% of the bond position will be used to fund the trend equity position, creating a 78/12/10 portfolio.  Similarly, the 20/80 will become an 12/78/10 and the 50/50 will become a 45/45/10.

We will use the S&P 500 index for U.S. equities, Dow Jones Corporate Bond index for U.S. bonds, and a 1-Year U.S. Government Note index for our cash proxy. The trend equity strategy will blend signals generated from trailing 6-through-12-month total returns, investing in the S&P 500 over the subsequent month in proportion to the number of positive signals.  Remaining capital will be invested in the cash proxy.  All portfolios are rebalanced monthly from 12/31/1940 through 12/31/2018.

Below we report the annualized returns, volatility, maximum drawdown, and Ulcer index (which seeks to simultaneously measure the duration and depth of drawdowns and can serve as a measure to a portfolio’s sensitivity to failing fast) for each profile.

Fail Fast

Blend

Fail Slow

20/
80

12/
78/
10		50/
50		45/
45/
10		80/
20

78/
12/
10

Annualized Return

7.9%

8.0%9.4%9.6%10.7%

11.0%

Annualized Volatility

5.8%

5.6%8.4%8.4%11.9%

12.4%

Maximum Drawdown

16.9%

16.6%28.8%26.6%42.9%

42.5%

Ulcer Index

0.025

0.0250.0450.0440.083

0.087

Source: Global Financial Data.  Calculations by Newfound Research.  Returns are backtested and hypothetical. Past performance is not a guarantee of future results.  Returns are gross of all fees.  Returns assume the reinvestment of all distributions.  None of the strategies shown reflect any portfolio managed by Newfound Research and were constructed solely for demonstration purposes within this commentary.  You cannot invest in an index. 

 

For conservative investors sensitive to the risk of failing fast, we can see that the introduction of trend equity not only slightly increased returns, but it reduced the maximum drawdown and Ulcer index profile of the portfolio.  Below we plot the actual difference in portfolio drawdowns between a 12/78/10 mix and a 20/80 mix over the backtested period.

While we can see that there are periods where the 12/78/10 mix exhibited higher drawdowns (i.e. values below the 0% line), during major drawdown periods, the 12/78/10 mix historically provided relative relief.  This is in line with our philosophy that risk cannot be destroyed, only transformed: the historical benefits that trend following has exhibited to avoiding significant and prolonged drawdowns have often come at the cost of increased realized drawdowns due to a slightly increased average allocation to equities as well as self-incurred drawdowns due to trading whipsaws.

On the opposite end of the spectrum, we can see that those investors sensitive to failing slowly were able to increase annualized returns without a significant increase to maximum drawdown.  We should note, however, an increase in the Ulcer index, indicating more frequent and deeper drawdowns.

This makes sense, as we would expect the 78/12/10 mix to be on average over-allocated to equities, making it more sensitive to quick and sudden declines (e.g. 1987).  Furthermore, the most defensive the mix can tilt is towards a 78/22 blend, leaving little wiggle-room in its ability to mitigate downside exposure. Nevertheless, we can see below that during periods of more prolonged drawdowns (e.g. 1975, 1980, and 2008), the 78/12/10 mix was able to reduce the drawdown profile slightly.

In these backtests we see that investors sensitive to failing fast can fund a larger proportion of trend equity exposure from their traditional equity allocation in an effort to reduce risk while maintaining their return profile. Conversely, investors sensitive to failing slow can fund a larger proportion of their trend equity exposure from bonds, hoping to increase their annualized return while maintaining the same risk exposure.

Of course, long-term annualized return statistics can belie short-term experience. Examining rolling return periods, we can gain a better sense as to our confidence as to the time horizon over which we might expect, with confidence, that a strategy should contribute to our portfolio.

Below we plot rolling 1-to-10-year annualized return differences between the 78/12/10 and the 80/20 mixes.

We can see that in the short-term (e.g. 1-year), there are periods of both significant out- and under-performance.  Over longer periods (5- and 10-years), which tend to capture “full market cycles,” we see more consistent out-performance.

Of course, this is not always the case: the 78/12/10 mix underperformed the 80/20 portfolio for the 10 years following the October 1987 market crash.  Being over-allocated to equities at that time had a rippling effect and serves to remind us that our default assumption should be that “risk cannot be destroyed, only transformed.”  But when we have the option to adjust our exposure to these risks, the benefit of avoiding slow failure may outweigh the potential to underperform slightly.

This evidence suggests that funding an allocation to trend equity in a manner that is in line with an investor’s risk sensitivities may be beneficial. Nevertheless, we should also acknowledge that the potential benefits are rarely realized in a smooth, continuous manner and that the implementation should be considered a long-term allocation, not a trade.

Conclusion

Investors must navigate a significant number of risks throughout their lifecycle.  At Newfound, we like to think of the two driving risks that investors face as the risk of failing fast and the risk of failing slow.  Much like Odysseus navigating between Scylla and Charybdis, these risks are at direct odds with one another and trying to avoid one increases the risk of the other.

Fortunately, which of these risks an investor cares about evolves throughout their lifecycle.  Young investors typically can afford to fail fast, as they have both future earning potential and time on their side.  By not saving adequately, or investing too conservatively, however, a young investor can invite the risk of slow failure and find themselves woefully underfunded for future real liabilities.  Hence investors at this stage or typically aggressively allocated towards growth assets.

As investors age, time and earning potential dwindle and the risk of fast failure increases. At this point, large and prolonged drawdowns can permanently impair an investor’s lifestyle.  So long as real liabilities are sufficiently funded, the risk of slow failure dwindles.  Thus, investors often de-risk their portfolios towards stable return sources such as high-quality fixed income.

We believe this dual-risk framework is a useful model for determining how any asset or strategy should fit within a particular investor’s plan.  We demonstrate this concept with a simple trend equity strategy.  For an investor sensitive to slow failure, we fund the allocation predominately from bond exposure; for an investor sensitive to fast failure, we fund the allocation predominately form equities.

Ultimately – and consistent with findings in our other commentaries – a risk-based mindset makes it obvious that allocation choices are really all about trade-offs in opportunity (“no pain, no premium”) and risk (“risk cannot be destroyed, only transformed.”)

Three Applications of Trend Equity

By

On February 25, 2019

In Portfolio Construction, Risk & Style Premia, Trend, Weekly Commentary

This post is available as a PDF download here.

What is Trend Equity?

Trend equity strategies seek to meaningfully participate with equity market growth while side-stepping significant and prolonged drawdowns.  These strategies aim to achieve this goal by dynamically adjusting market exposure based upon trend-following signals.

A naïve example of such a strategy would be a portfolio that invests in U.S. equities when the prior 1-year return for U.S. equities is positive and divests entirely into short-term U.S. Treasuries when it is negative.

The Theory

This category of strategies relies upon the empirical evidence that performance tends to persist in the short-run: positive performance tends to beget further positive performance and negative performance tends to beget further negative performance. The theory behind the evidence is that behavioral biases exhibited by investors lead to the emergence of trends.

In an efficient market, changes in the underlying value of an investment should be met by an immediate, commensurate change in the price of that investment.  The empirical evidence of trends suggests that investors may not be entirely efficient at processing new information.  Behavioral theory (Figure I) suggests that investors anchor their views on prior beliefs, causing price to underreact to new information.  As price continues to drift towards fair value, herding behavior occurs, causing price to overreact and extend beyond fair value.  Combined, these effects cause a trend.

Trend equity strategies seek to capture this potential inefficiency by systematically investing in equities when they are exhibiting positively trending characteristics and divesting when they exhibit negative trends.  The potential benefit of this approach is that it can try to exploit two sources of return: (1) the expected long-term risk premium associated with equities, and (2) the convex payoff structure typically associated with trend-following strategies.

The Positive Convexity of Trend Following

As shown in Figure II, we can see that a hypothetical implementation of this strategy on large-cap U.S. equities has historically exhibited a convex return profile with respect to the underlying U.S. equity index, meaningfully participating in positive return years while reducing exposure to significant loss years.

“Risk Cannot Be Destroyed, Only Transformed.”

While the flexibility of trend equity strategies gives them the opportunity to both protect and participate, it also creates the potential for losses due to “whipsaw.”  Whipsaws occur when the strategy changes positioning due to what appears to be a change in trend, only to have the market rapidly reverse course.  Such a scenario can lead to ”buy high, sell low” and “sell low, buy high” scenarios.  These scenarios can be exacerbated by the fact that trend equity strategies may go several years without experiencing whipsaw to only then suddenly experience multiple back-to-back whipsaw events at once.

As Defensive Equity

The most obvious implementation of trend equity strategies is within a defensive equity sleeve.  In this approach, an allocation for the strategy is funded by selling strategic equity exposure (see Figure III).  Typically combined with other defensive styles (e.g. minimum volatility, quality, et cetera), the goal of a defensive equity sleeve is to provide meaningful upside exposure to equity market growth while reducing downside risk.

This implementation approach has the greatest potential to reduce a policy portfolio’s exposure to downside equity risk and therefore may be most appropriate for investors for whom ”failing fast” is a critical threat.  For example, pre-retirees, early retirees, and institutions making consistent withdrawals are highly subject to sequence risk and large drawdowns within their portfolios can create significant impacts on portfolio sustainability.

The drawback of a defensive equity implementation is that vanilla trend equity strategies can, at best, keep up with their underlying index during strong bull markets (see Figure IV).  Given the historical evidence that markets tend to be up more frequently than they are down, this can make this approach a frustrating one to stick with for investors.  Furthermore, up-capture during bull markets can be volatile on a year-to-year basis, with low up-capture during whipsaw periods and strong up-capture during years with strong trends.  Therefore, investors should only allocate in this manner if they plan to do so over a full market cycle.

Implementation within a Defensive Equity sleeve may also be a prudent approach with investors for whom their risk appetite is far below their risk capacity (or even need); i.e. investors who are chronically under-allocated to equity exposure.  Implementation of a strategy that has the ability to pro-actively de-risk may allow investors to feel more comfortable with a larger exposure.

Finally, this approach may also be useful for investors seeking to put a significant amount of capital to work at once.  While evidence suggests that lump-sum investing (“LSI”) almost always out-performs dollar cost averaging (”DCA”), investors may feel uncomfortable with the significant timing luck from LSI.  One potential solution is to utilize trend equity as a middle ground; for example, investors could DCA but hold trend equity rather than cash.

Pros

  • Maintains overall strategic allocation policy.
  • May help risk-averse investors more confidently maintain an appropriate risk profile.
  • May provide meaningful reduction in exposure to significant and prolonged equity losses.

Cons

  • High year-to-year tracking error relative to traditional equity benchmarks.
  • Typically under-performs equities during prolonged bull markets (see Figure IV).

As a Tactical Pivot

One creative way of implementing a trend equity strategy is as a tactical pivot within a portfolio.  In this implementation, an allocation to trend equity is funded by selling both stocks and bonds, typically in equal amounts (see Figure V).  By implementing in this manner, the investor’s portfolio will pivot around the policy benchmark, being more aggressively allocated when trend equity is fully invested, and more defensively allocated when trend equity de-risks.

This approach is often appealing because it offers a highly intuitive allocation sizing policy.  The size of the tactical pivot sleeve as well as the mixture of stocks and bonds used to fund the sleeve defines the tactical range around the strategic policy portfolio (see Figure VI).

One benefit of this implementation is that trend equity no longer needs to out-perform an equity benchmark to add value.  Rather, so long as the strategy outperforms the mixture of stocks and bonds used to fund the allocation (e.g. a 50/50 mix), the strategy can add value to the holistic portfolio design.  For example, assume a trend equity strategy only achieves an 80% upside capture to an equity benchmark during a given year.  Implemented as a defensive equity allocation, this up-capture would create a drag on portfolio returns relative to the policy benchmark.  If, however, trend equity is implemented as a tactical pivot – funded, for example, from a 50/50 mixture of stocks and bonds – then so long as it outperformed the funding mixture, the portfolio return is improved due to its tilt towards equities.

Implementation as a tactical pivot can also add potential value during environments where stocks and bonds exhibit positive correlations and negative returns (e.g. the 1970s).

One potential drawback of this approach is that the portfolio can be more aggressively allocated than the policy benchmark during periods of sudden and large declines.  How great a risk this represents will be dictated both by the size of the tactical pivot as well as the ratio of stocks and bonds in the funding mixture.  For example, the potential overweight towards equities is significantly lower using a 70/30 stock/bond funding mix than a 30/70 mixture.  A larger allocation to bonds in the funding mixture creates a higher downside hurdle rate for trend equity to add value during a negative equity market environment.

Pros

  • Lower hurdle rate for strategy to add value to portfolio during positive equity environments.
  • Intuitive allocation policy based on desired level of tactical tilts within the portfolio.
  • May provide cushion in environments where stocks and bonds are positively correlated.

Cons

  • Portfolio may be allocated above benchmark policy to risky assets during a sudden market decline.
  • Higher hurdle rate for strategy to add value to portfolio during negative equity environments.

As a Liquid Alternative

Due to its historically convex return profile and potentially high level of tracking error exhibited over short measurement horizons, trend equity may also be a natural fit within a portfolio’s alternative sleeve.  Indeed, when analyzed more thoroughly, trend equity shares many common traits with other traditionally alternative strategies.

For example, a vanilla trend equity implementation can be decomposed into two component sources of returns: a strategic portfolio and a long/short trend-following overlay.  Trend following can also be directly linked to the dynamic trading strategy required to replicate a long option position.

There are even strong correlations to traditional alternative categories.  For example, a significant driver of returns in equity hedge and long/short equity categories is dynamic market beta exposure, particularly during significant market declines (see Figure VII).  Trend equity strategies that are implemented with factor-based equity exposures or with the flexibility to make sector and geographic tilts may even more closely approximate these categories.

One potential benefit of this approach is that trend equity can be implemented in a highly liquid, highly transparent, and cost-effective manner when compared against many traditional alternatives.  Furthermore, by implementing trend equity within an alternatives sleeve, investors may give it a wider berth in their mental accounting of tracking error, allowing for a more sustainable allocation versus implementation as a defensive equity solution.

A drawback of this implementation, however, is that trend equity will increase a portfolio’s exposure to equity beta.  Therefore, more traditional alternatives may offer better correlation- and pay-off-based diversification, especially during sudden and large negative equity shocks.  Furthermore, trend equity may lead to overlapping exposures with existing alternative exposures such as equity long/short or managed futures.  Investors must therefore carefully consider how trend equity may fit into an already existing alternative sleeve.

Pros

  • Highly transparent, easy-to-understand investment process.
  • Implemented with highly liquid underlying exposures.
  • Investors often given alternatives a wider berth of allowable tracking error than more traditional allocations.

Cons

  • May be more highly correlated with existing portfolio exposures than other alternatives.
  • Potentially overlapping exposure with existing alternatives such as equity long/short or managed futures.

G̷̖̱̓́̀litch

By

On February 19, 2019

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

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 24th.  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 overlay2).  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.”

 

 

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