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Macro Timing with Trend Following

By

On October 7, 2019

In Portfolio Construction, Trend, Weekly Commentary

This post is available for download here.

Summary

  • While it may be tempting to time allocations to active strategies, it is generally best to hold them as long-term allocations.
  • Despite this, some research has shown that there may be certain economic environments where trend following equity strategies are better suited.
  • In this commentary, we replicate this data and find that a broad filter of recessionary periods does indeed show this for certain trend equity strategies but not for the style of trend equity in general.
  • However, further decomposing the business cycle into contractions, recoveries, expansions, and slowdowns using leading economic indicators such as PMI and unemployment does show some promising relationships between the forecasted stage of the business cycle and trend following’s performance relative to buy-and-hold equities.
  • Even if this data is not used to time trend equity strategies, it can be beneficial to investors for setting expectations and providing insight into performance differences.


Systematic active investing strategies are a way to achieve alternative return profiles that are not necessarily present when pursuing standard asset allocation and may therefore play an important role in developing well-diversified portfolios.

But these strategies are best viewed as allocations rather than trades.1 This is a topic we’ve written about a number of times with respect to factor investing over the past several years, citing the importance of weathering short-term pain for long-term gains. For active strategies to outperform, some underperformance is necessary. Or, as we like to say, “no pain, no premium.”

That being said, being tactical in our allocations to active strategies may have some value in certain cases. In one sense, we can view the multi-layered active decisions simply as another active strategy, distinct from the initial one.

An interesting post on Philosophical Economics looked at using a variety of recession indicators (unemployment, earnings growth, industrial production, etc.) as ways to systematically invest in either U.S. equities or a trend following strategy on U.S. equities. If the economic indicator was in a favorable trend, the strategy was 100% invested in equities. If the economic indicator was in an unfavorable trend, the strategy was invested in a trend following strategy applied to equities, holding cash when the market was in a downtrend.

The reasoning behind this strategy is intuitively appealing. Even if a recession indicator flags a likely recession, the market may still have room to run before turning south and warranting capital protection. On the other hand, when the recession indicator was favorable, purely investing in equities avoids some of the whipsaw costs that are inherent in trend following strategies.

In this commentary, we will first look at the general style of trend equity in the context of recessionary and non-recessionary periods and then get a bit more granular to see when trend following has worked historically through the economic cycle of Expansion, Slowdown, Contraction, and Recovery.

Replicating the Data

To get our bearings, we will first attempt to replicate some of the data from the Philosophical Economics post using only the classifications of “recession” and “not-recession”.

Keeping in line with the Philosophical Economics method, we will use whether the economic metric is above or below its 12-month moving average as the recession signal for the next month. We will use market data from the Kenneth French Data Library for the total U.S. stock market returns and the risk-free rate as the cash rate in the equity trend following model.

The following table shows the results of the trend following timing models using the United States ISM Purchasing Managers Index (PMI) and the Unemployment Rate as indicators.

U.S. Equities12mo MA Trend Equity12m MA Trend Timing Model (PMI)12mo MA Trend Timing Model (Unemployment)
Annualized Return11.3%11.1%11.3%12.2%
Annualized Volatility14.7%11.2%11.9%12.4%
Maximum Drawdown50.8%24.4%32.7%30.0%
Sharpe Ratio0.490.620.610.66

Source: Quandl and U.S. Bureau of Labor Statistics. Calculations by Newfound Research. Results are hypothetical. Results assume the reinvestment of all distributions. Results are gross of all fees, including, but not limited to, manager fees, transaction costs, and taxes. Past performance is not an indicator of future results. You cannot invest in an index. Data is from Jan 1948 – Sep 2019.

With the trend timing model, we see an improvement in the absolute returns compared to the trend equity strategy alone. However, this comes at the expense of increasing the volatility and maximum drawdown.

In the case of unemployment, which was the strongest indicator that Philosophical Economics found, there is an improvement in risk-adjusted returns in the timing model.

Still, while there is a benefit, it may not be robust.

If we remove the dependence of the trend following model on a single metric or lookback parameter, the benefit of the macro-timing decreases. Specifically, if we replace our simple 12-month moving average trend equity rule with the ensemble approach utilized in the Newfound Trend Equity Index, we see very different results. This may indicate that one specific variant of trend following did well in this overall model, but the style of trend following might not lend itself well to this application.

U.S. EquitiesNewfound Trend Equity IndexTrend Equity Index Blend (PMI)Trend Equity Index Blend (Unemployment)
Annualized Return11.3%10.7%10.9%10.9%
Annualized Volatility14.7%11.1%11.8%13.5%
Maximum Drawdown50.8%25.8%36.1%36.0%
Sharpe Ratio0.490.590.580.50

Source: Quandl and U.S. Bureau of Labor Statistics. Calculations by Newfound Research. Results are hypothetical. Results assume the reinvestment of all distributions. Results are gross of all fees, including, but not limited to, manager fees, transaction costs, and taxes. Past performance is not an indicator of future results. You cannot invest in an index. Data is from Jan 1948 – Sep 2019.

A more robust trend following model may already provide more upside capture during non-recessionary periods but at the expense of more downside capture during recessions. However, we cannot confidently assert that the lower level of down-capture in the single specification of the trend model is not partially due to luck.

If we desire to more thoroughly evaluate the style of trend following, we must get more granular with the economic cycles.

Breaking Down the Economic Cycle

Moving beyond the simple classification of “recession” and “not-recession”, we can follow MSCI’s methodology, which we used here previously, to classify the economic cycle into four primary states: Expansion, Slowdown, Contraction and Recovery.

We will focus on the 3-month moving average (“MA”) minus the 12-month MA for each indicator we examine according to the decision tree below. In the tree, we use the terms better or worse since lower unemployment rate and higher PMI values signal a stronger economy.

Economic cycle

There is a decent amount of difference in the classifications using these two indicators, with the unemployment indicator signaling more frequent expansions and slowdowns. This should be taken as evidence that economic regimes are difficult to predict.

Source: Quandl and U.S. Bureau of Labor Statistics. Calculations by Newfound Research. Results are hypothetical. Results assume the reinvestment of all distributions. Results are gross of all fees, including, but not limited to, manager fees, transaction costs, and taxes. Past performance is not an indicator of future results. You cannot invest in an index. Data is from Jan 1948 – Sep 2019.

Once each indicator is in each state the transition probabilities are relatively close.

Source: Quandl and U.S. Bureau of Labor Statistics. Calculations by Newfound Research. Results are hypothetical. Past performance is not an indicator of future results.

This agrees with intuition when we consider the cyclical nature of these economic metrics. While not a perfect mathematical relationship, these states generally unfold sequentially without jumps from contractions to expansions or vice versa.

Trend Following in the Economic Cycle

Applying the four-part classification to the economic cycle shows where trend equity outperformed.

PMI IndicatorUnemployment Indicator
U.S. EquitiesTrend EquityU.S. EquitiesTrend Equity
Contraction7.6%10.3%1.0%7.3%
Recovery12.2%9.3%15.4%15.0%
Expansion14.3%14.4%13.9%11.3%
Slowdown7.2%5.4%10.5%8.0%

Source: Quandl and U.S. Bureau of Labor Statistics. Calculations by Newfound Research. Results are hypothetical. Results assume the reinvestment of all distributions. Results are gross of all fees, including, but not limited to, manager fees, transaction costs, and taxes. Past performance is not an indicator of future results. You cannot invest in an index. Data is from Jan 1948 – Sep 2019.

During contraction phases, regardless of indicators, trend equity outperformed buy-and-hold.

For the PMI indicator, trend equity was able to keep up during expansions, but this was not the case with the unemployment indicator. The reverse of this was true for recoveries: trend following was close to keeping up in the periods denoted by the unemployment indicator but not by the PMI indicator.

For both indicators, trend following underperformed during slowdowns.

This may seem contradictory at first, but these may be periods of more whipsaw as markets try to forecast future states. And since slowdowns typically occur after expansions and before contractions (at least in the idealized model), we may have to bear more of this whipsaw risk for the strategy to be adaptable enough to add value during the contraction.

The following two charts show the longest historical slowdowns for each indicator: the PMI indicator was for 11 months in late 2009 through much of 2010 and the unemployment rate indicator was for 16 months in 1984-85.

Source: Quandl and U.S. Bureau of Labor Statistics. Calculations by Newfound Research. Results are hypothetical. Results assume the reinvestment of all distributions. Results are gross of all fees, including, but not limited to, manager fees, transaction costs, and taxes. Past performance is not an indicator of future results. You cannot invest in an index.

In the first slowdown period, the trend equity strategy rode in tandem with equities as they continued to climb and then de-risked when equities declined. Equities quickly rebounded leaving the trend equity strategy underexposed to the rally.

In the second slowdown period, the trend equity strategy was heavily defensive going into the slowdown. This protected capital initially but then caused the strategy to lag once the market began to increase steadily.

The first period illustrates a time when the trend equity strategy was ready to adapt to changing market conditions and was unfortunately whipsawed. The second period illustrates a time when the trend equity strategy was already adapted to a supposedly oncoming contraction that did not materialize.

Using these historical patterns of performance, we can now explore how a strategy that systematically allocates to trend equity strategies might be constructed.

Timing Trend Following with the Economic Cycle

One simple way to apply a systematic timing strategy for shifting between equities and trend following is to only invest in equities when a slowdown is signaled.

The charts below show the returns and risk metrics for models using the PMI and unemployment rate individually and a model that blends the two allocations.

Growth trend timing

Source: Quandl and U.S. Bureau of Labor Statistics. Calculations by Newfound Research. Results are hypothetical. Results assume the reinvestment of all distributions. Results are gross of all fees, including, but not limited to, manager fees, transaction costs, and taxes. Past performance is not an indicator of future results. You cannot invest in an index. Data is from Jan 1948 – Sep 2019.

Source: Quandl and U.S. Bureau of Labor Statistics. Calculations by Newfound Research. Results are hypothetical. Results assume the reinvestment of all distributions. Results are gross of all fees, including, but not limited to, manager fees, transaction costs, and taxes. Past performance is not an indicator of future results. You cannot invest in an index. Data is from Jan 1948 – Sep 2019.

The returns increased slightly in every model relative to buy-and-hold, and the blended model performed consistently high across all metrics.

Blending multiple models generally produces benefits like these shown here, and in an actual implementation, utilizing additional economic indicators may make the strategy even more robust. There may be other ways to boost performance across the economic cycle, and we will explore these ideas in future research.

Conclusion

Should investors rotate in and out of active strategies?

Not in most cases, since the typical drivers are short-term underperformance that is a necessary component of active strategies.

However, there may be opportunities to make allocation tweaks based on the economic cycle.

The historical data suggests that a specification-neutral trend-equity strategy has outperformed buy-and-hold equities during economic contractions for both economic indicators. The performance during recoveries and expansions was mixed across indicators. It kept up with the buy-and-hold strategy during expansions denoted by PMI but not unemployment. This relationship was reversed for recoveries denoted by unemployment. In both models, trend equity has also lagged during economic slowdowns as whipsaw becomes more prevalent.

Based on the most recent PMI data, the current cycle is a contraction, indicating a favorable environment for trend equity under both cycle indicators. However, we should note that December 2018 through March 2019 was also labeled as a contraction according to PMI. Not all models are perfect.

Nevertheless, there may be some evidence that trend following can provide differentiated benefits based on the prevailing economic environment.

While an investor may not use this knowledge to shift around allocations to active trend following strategies, it can still provide insight into performance difference relative to buy-and-hold and set expectations going forward.

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.

 

Trend Following in Cash Balance Plans

By

On March 18, 2019

In Popular, Risk Management, Weekly Commentary

This post is available as a PDF download here.

Summary

  • Cash balance plans are retirement plans that allow participants to save higher amounts than in traditional 401(k)s and IRAs and are quickly becoming more prevalent as an attractive alternative to defined benefit retirement plans.
  • The unique goals of these plans (specified contributions and growth credits) often dictate modest returns with a very low volatility, which often results in conservative allocations.
  • However, at closely held companies, there is a balance between the tax-deferred amount that can be contributed by partners and the returns that the plan earns.  If returns are too low, the company must make up the shortfall, but if the returns are too high the partners cannot maximize their tax-deferred contributions.
  • By allocating to risk-managed strategies like trend equity, a cash balance plan can balance the frequency and size of shortfalls based on how the trend following strategy is incorporated within the portfolio.
  • Trend following strategies have historically reduced the exposure to large shortfalls in exchange for more conservative performance during periods where the plan is comfortably hitting its return target.

Retirement assets have grown each year since the Financial Crisis, exhibiting the largest gains in the years that were good for the market such as 2009, 2013, and 2017.

Source: Investment Company Institute (ICI).

With low interest rates, an aging workforce, and continuing pressure to reduce expected rates of return going forward, many employers have shifted from the defined benefit (DB) plans used historically to defined contribution (DC) models, such as 401(k)s and 403(b)s. While assets within DB plans have still grown over the past decade, the share of retirement assets in IRAs and DC plans has grown from around 50% to 60%.

But even with this shift toward more employee directed savings and investment, there is a segment of the private DB plan space that has seen strong growth since the early 2000s: cash balance plans.

Source: Kravitz. 2018 National Cash Balance Research Report.

What is a cash balance plan?

It’s sort of a hybrid retirement plan type. Employers contribute to it on behalf of their employees or themselves, and each participant is entitled to those assets plus a rate of return according to a prespecified rule (more on that in a bit).

Like a defined contribution plan, participants have an account value rather than a set monthly payment.

Like a defined benefit plan, the assets are managed professionally, and the actual asset values do not affect the value of the participant benefits. Thus, as with any liability-driven outcome, the plan can be over- or under-funded at a given time.

What’s the appeal?

According to Kravitz, (2018)1 over 90% of cash balance plans are in place at companies with fewer than 100 participants. These companies tend to be white-collar professionals, where a significant proportion of the employees are highly compensated (e.g. groups of doctors, dentists, lawyers, etc.).

Many of these professionals likely had to spend a significant amount of time in professional school and building up practices. Despite higher potential salaries, they may have high debt loads to pay down. Similarly, entrepreneurs may have deferred compensating themselves for the sake of building a successful business.

Thus, by the time these professionals begin earning higher salaries, the amount of time that savings can compound for retirement has been reduced.

Source: Kravitz. 2018 National Cash Balance Research Report.

One option for these types of investors is to simply save more income in a traditional brokerage account, but this foregoes any benefit of deferring taxes until retirement. 

Furthermore, even if these investors begin saving for retirement at the limit for 401(k) contributions, it is possible that they could end up with a lower account balance than a counterpart saving half as much per year but starting 10 years earlier. Time lost is hard to make up.

This, of course, depends on the sequence and level of investment returns, but an investor who is closer to retirement has less ability to bear the risk of failing fast. Not being able to take as much investment risk necessitates having a higher savings rate.

Cash balance plans can help solve this dilemma through significantly higher contribution limits.

Source: Kravitz.

An extra $6,000 in catch-up contributions starting for a 401(k) at age 50 seems miniscule compared to what a cash balance plan allows.

Now that we understand why cash balance plans are becoming more prevalent in the workplace, let’s turn to the investment side of the picture to see how a plan can make good on its return guarantees.

The Return Guarantee

Aside from the contribution schedule for each plan participant, the only other piece of information needed to determine the size of the cash balance plan liability in a given year is the annual rate at which the participant accounts grow.2 There are a few common ways to set this rate:

  1. A fixed rate of return per year, between 2% and 6%.
  2. The 30-year U.S. Treasury rate.
  3. The 30-year U.S. Treasury rate with a floor of between 3% and 5%.
  4. The actual rate of return of the invested assets, often with a ceiling between 3% and 6%.

The table below shows that of the plans surveyed by Kravitz (2018), the fixed rate of return was by far the most common and the actual rate of return credit was the least common.

The Actual Rate of Return option is actually becoming more popular, especially with large cash balance plans, now that federal regulations allow plan sponsors to offer multiple investments in a single plan to better serve the participants who may have different retirement goals. This return option removes much of the investment burden from the plan sponsor since what the portfolio earns is what the participants get, up to the ceiling. Anything earned above the ceiling increases the plan’s asset value above its liabilities. Actual rate of return guarantees make it so that there is less risk of a liability shortfall when large stakeholders in the cash balance plan leave the company unexpectedly.

In this commentary, we will focus on the cases where the plan may become underfunded if it does not hit the target rate of return.

We often say, “No Pain, No Premium.” Well, in the case of cash balance plans, plan sponsors typically only want to bear the minimal amount of pain that is necessary to hit the premium.

With large firms that can rely more heavily on actuarial assumptions for participant turnover, much of this risk can be borne over multiyear periods. A shortfall in one year can be replenished by a combination of extra contributions from the company according to IRS regulations and (hopefully) more favorable portfolio gains in subsequent years. Any excess returns can be used to offset how much the company must contribute annually for participants.

In the case of closely held firms, things change slightly.

At first glance, it should be a good thing for a plan sponsor to earn a higher rate of return than the committed rate. But when we consider that many cash balance plans are in place at firms where the participants desire to contribute as much as the IRS allows to defer taxation, then earning more than the guaranteed rate of return actually represents a risk. At closely held firms, “the company” and “the participants” are essentially one in the same. The more the plan earns, the less you can contribute.

And with higher return potential comes a higher risk of earning below the guaranteed rate. When a company is small, making up shortfalls out of company coffers or stretching for higher returns in subsequent years may not be in the company’s best interest.

Investing a Cash Balance Plan

Because of the aversion to both high returns and high risk, many cash balance plans are generally invested relatively conservatively, typically in the range of a 20% stock / 80% bond portfolio (20/80) to a 40/60.

To put some numbers down on paper, we will examine the return profile of three different portfolios: a 20/80, 30/70, and 40/60 fixed mix of the S&P 500 and a constant maturity 10-year U.S. Treasury index.

We will also calculate the rate of return guarantees described above each year from 1871 to 2018.

Starting each January, if the return of one of the portfolio profiles meets hits the target return for the year, then we will assume it is cashed out. Otherwise, the portfolio is held the entire year.

As the 30-year U.S. Treasury bond came into inception in 1977 and had a period in the 2000s where it was not issued, we will use the 10-year Treasury rate as a proxy for those periods.

The failure rate for the portfolios are shown below.3

Source: Robert Shiller Data Library, St. Louis Fed. 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.

We can see that as the rate of return guarantee increases, either through the fixed rate or the floor on the 30-year rate, the rate of shortfall increases for all allocations, most notably for the conservative 20/80 portfolio.

In these failure scenarios, the average shortfall and the average shortfall in the 90% of the worst cases (similar to a CVaR) are relatively consistent.

Source: Robert Shiller Data Library, St. Louis Fed. 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.

Source: Robert Shiller Data Library, St. Louis Fed. 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.

These shortfall numbers may not be a big deal for new plans when the contributions represent a significant percentage of the asset base. For example, for a $1M plan with $500k in contributions per year, a 15% shortfall is only $150k, which can be amortized over a number of years. Higher returns in the subsequent years can offset this, or partners could agree to reduce their personal contributions so that the company can have free cash to make up for the shortfall.

The problem is more pressing for plans where the asset base is significantly larger than the yearly contributions. For a $20M plan with $500k in yearly contributions, a 15% shortfall is $3M. Making up this shortfall from company assets may be more difficult, even with amortization.

Waiting for returns from the market can also be difficult in this case when there have been historical drawdowns in the market lasting 2-3 years from peak to trough (e.g. 1929-32, 2000-02, and 1940-42).

Risk-managed strategies can be a natural way to mitigate these shortfalls, both in their magnitude and frequency.

Using Trend Following in a Cash Balance Plan

Along the lines of our Three Uses of Trend Equity, we will look at adding a 20% allocation to a simple trend-following equity (“trend equity”) strategy in a cash balance plan. By taking the allocation either from all equities, all bonds, or an equal share of each.

For ease of illustration, we will only look at the 20/80 and 40/60 portfolios. The following charts show the benefit (i.e. reduction in shortfall) or detriment (i.e. increase in shortfall) of adding the 20% trend equity sleeve to the cash balance plan based on the metrics from the previous section.

Source: Robert Shiller Data Library, St. Louis Fed. 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.

For most of these return guarantees, substituting a greater proportion of bonds for trend equity reduced the frequency of shortfalls. This makes sense over a period where equities generally did well and a trend equity strategy increased participation during the up-markets.

Substituting in trend equity solely from the equity allocation was detrimental for a few of the return guarantees, especially the higher ones.

But the frequency of shortfalls is only one part of the picture.

Source: Robert Shiller Data Library, St. Louis Fed. 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.

Many of the cases that showed a benefit from a frequency of shortfall perspective sacrifice the average shortfall or average shortfall in the most extreme scenarios. Conversely, case that sacrifice on the frequency of shortfalls generally saw a meaningful reduction in the average shortfalls.

This is in line with our philosophy that risks are not destroyed, only transformed.

Source: Robert Shiller Data Library, St. Louis Fed. 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.

So which risks should a cash balance plan bear?

This can be answered by determining the balance of the plan to be exposure to failing fast and failing slow.

If a cash balance plan is large, even a moderate shortfall can be very large in dollar terms. These plans are at risk of failing fast. Mitigating the size of the shortfalls is definitely a primary concern.

If a cash balance plan is new or relatively small, it is somewhat like an investor early in their working career. Larger losses from a percentage perspective are smaller in dollar terms compared to a larger plan. These plans can stand to have larger shortfalls. If the shortfalls occur less frequently, there is the ability to generate higher returns in years after a loss to recoup some of the losses.

However, these small plans should still be concerned mostly about fast failure. The yearly reckoning of the liability to the participants skews the risks more heavily in the direction of fast failure. This is especially true when we factor in the demographic of the workforce. When employees leave, they are entitled to their account value based on the guaranteed return, not the underlying asset value. If a participant cashes out at a time when the assets are down, then the remaining participant are less funded based on the assets that are left.

Therefore, allocating to the trend strategy out of the equity sleeve or an equal split between equities and bonds is likely more in line with the goals of a cash balance plan.

Conclusion

Cash balance plans are quickly becoming more prevalent as an attractive alternative to defined benefit retirement plans. They are desirable both from an employer and employee perspective and can be a way to accelerate retirement savings, especially for highly compensated workers at small companies.

The unique goals of these plans (e.g. guaranteed returns, maximizing tax-deferred contributions, etc.) often dictate modest returns with a very low volatility. Since some risk must be borne in order to generate returns, these portfolios are typically allocated very conservatively.

Even so, there is a risk they will not hit their return targets.

By allocating to risk-managed strategies like trend equity, a cash balance plan can balance the frequency and size of shortfalls based on how the trend following strategy is incorporated within the portfolio.

Allocating to a trend equity strategy solely from bonds can reduce the frequency of shortfalls in exchange for larger average shortfalls. Allocating to a trend following equity strategy solely from equities can increase the frequency of shortfalls but reduce the average size of shortfalls and the largest shortfalls.

The balance for a specific plan depends on its size, the demographic of the participants, the company’s willingness and ability to cover shortfalls, and the guaranteed rate of return.

As with most portfolio allocation problems the solution exists on a sliding scale based on what risks the portfolio is more equipped to bear. For cash balance plans, managing the size of shortfalls is likely a key issue, and trend following strategies can be a way to adjust the exposure to large shortfalls in exchange for more conservative performance during periods where the plan is comfortably hitting its return target.

How Much Accuracy Is Enough?

By

On March 4, 2019

In Craftsmanship, Portfolio Construction, Trend, Weekly Commentary

Available as a PDF download here.

Summary­

  • It can be difficult to disentangle the difference between luck and skill by examining performance on its own.
  • We simulate the returns of investors with different prediction accuracy levels and find that an investor with the skill of a fair coin (i.e. 50%) would likely under-perform a simple buy-and-hold investor, even before costs are considered.
  • It is not until an investor exhibits accuracy in excess of 60% that a buy-and-hold investor is meaningfully “beaten” over rolling 5-year evaluation periods.
  • In the short-term, however, a strategy with a known accuracy rate can still masquerade as one far more accurate or far less accurate due to luck.
  • Further confounding the analysis is the role of skewness of the return distribution. Positively skewed strategies, like trend following, can actually exhibit accuracy rates lower than 50% and still be successful over the long run.
  • Relying on perceptions of accuracy alone may lead to highly misguided conclusions.

The only thing sure about luck is that it will change. — Bret Harte1

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 next 5 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 Investor

To 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 1/30th 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:

  1. The Plain Investor – This investor simply holds all 30 sectors, equally weighted, all the time.
  2. 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.
  3. 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.

Annualized ReturnAnnualized VolatilityMaximum Drawdown
Plain Investor10.5%19.3%83.9%
Perfect Investor42.6%11.0%0.0%
Anti-Perfect Investor-20.0%12.1%100.0%

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 Accuracy

Now 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.

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.

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.

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.

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.

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.

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 Schmaccuracy

Our 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? 

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.

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.

Conclusion

While 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 below 50% 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).

Tightening the Uncertain Payout of Trend-Following

By

On January 28, 2019

In Craftsmanship, Portfolio Construction, Risk Management, Trend, Weekly Commentary

This post is available as a PDF download here.

Summary­

  • Long/flat trend-following strategies have historically delivered payout profiles similar to those of call options, with positive payouts for larger positive underlying asset returns and slightly negative payouts for near-zero or negative underlying returns.
  • However, this functional relationship contains a fair amount of uncertainty for any given trend-following model and lookback period.
  • In portfolio construction, we tend to favor assets that have a combination of high expected returns or diversifying return profiles.
  • Since broad investor behavior provides a basis for systematic trend-following models to have positive expected returns, taking a multi-model approach to trend-following can be used to reduce the variance around the expected payout profile.

Introduction

Over the past few months, we have written much about model diversification as a tactic for managing specification risk, even with specific case studies. When we consider the three axes of diversification, model diversification pertains to the “how” axis, which focuses on strategies that have the same overarching objective but go about achieving it in different ways.

Long/flat trend-following, especially with equity investments, aims to protect capital on the downside while maintaining participation in positive markets. This leads to a payout profile that looks similar to that of a call option.1

However, while a call option offers a defined payout based on the price of an underlying asset and a specific maturity date, a trend-following strategy does not provide such a guarantee. There is a degree of uncertainty.

The good news is that uncertainty can potentially be diversified given the right combinations of assets or strategies.

In this commentary, we will dive into a number of trend-following strategies to see what has historically led to this benefit and the extent that diversification would reduce the uncertainty around the expected payoff.

Diversification in Trend-Following

The justification for a multi-model approach boils down to a simple diversification argument.

Say you would like to include trend-following in a portfolio as a way to manage risk (e.g. sequence risk for a retiree). There is academic and empirical evidence that trend-following works over a variety of time horizons, generally ranging from 3 to 12 months. And there are many ways to measure trends, such as moving average crossovers, trailing returns, deviations from moving averages, risk adjusted returns, etc.

The basis for deciding ex-ante which variant will be the best over our own investment horizon is tenuous at best. Backtests can show one iteration outperforming over a given time horizon, but most of the differences between strategies are either noise from a statistical point of view or realized over a longer time period than any investor has the lifespan (or mettle) to endure.

However, we expect each one to generate positive returns over a sufficiently long time horizon. Whether this is one year, three years, five years, 10 years, 50 years… we don’t know. What we do know is that out of the multitude the variations of trend-following, we are very likely to pick one that is not the best or even in the top segment of the pack in the short-term.

From a volatility standpoint, when the strategies are fully invested, they will have volatility equal to the underlying asset. Determining exactly when the diversification benefits will come in to play – that is, when some strategies are invested and others are not – is a fool’s errand.

Modern portfolio theory has done a disservice in making correlation seem like an inherent trait of an investment. It is not.

Looking at multiple trend-following strategies that can coincide precisely for stretches of time before behaving completely differently from each other, makes many portfolio construction techniques useless.  We do not expect correlation benefits to always be present.  These are nonlinear strategies, and fitting them into a linear world does not make sense.

If you have pinned up ReSolve Asset Management’s flow chart of portfolio choice above your desk (from Portfolio Optimization: A General Framework for Portfolio Choice), then the decision on this is easy.

Source: ReSolve Asset Management.  Reprinted with permission

From this simple framework, we can break the different performance regimes down as follows:

The Math Behind the Diversification

The expected value of a trend-following strategy can be thought of as a function of the underlying security return:

Where the subscript i is used to indicate that the function is dependent on the specific trend-following strategy.

If we combine multiple trend-following strategies into a portfolio, then the expectation is the average of these functions (assuming an equal weight portfolio per the ReSolve chart above):

What’s left to determine is the functional form of f.

Continuing in the vein of the call option payoff profile, we can use the Black-Scholes equation as the functional form (with the risk-free rate set to 0). This leaves three parameters with which to fit the formula to the data: the volatility (with the time to expiration term lumped in, i.e. sigma * sqrt(T-t)), the strike, and the initial cost of the option.

where d1 and d2 are defined in the standard fashion and N is the cumulative normal distribution function.

rK is the strike price in the option formula expressed as a percent relative to the current value of the underlying security.

In the following example, we will attempt to provide some meaning to the fitted parameters. However, keep in mind that any mapping is not necessarily one-to-one with the option parameters. The functional form may apply, but the parameters are not ones that were set in stone ex-ante.2

An Example: Trend-Following on the S&P 500

As an example, we will consider a trend-following model on the S&P 500 using monthly time-series momentum with lookback windows ranging from 4 to 16 months. The risk-free rate was used when the trends were negative.

The graph below shows an example of the option price fit to the data using a least-squares regression for the 15-month time series momentum strategy using rolling 3-year returns from 1927 to 2018.

Source: Global Financial Data and Kenneth French Data Library. Calculation by Newfound. Returns are backtested and hypothetical. Returns assume the reinvestment of all distributions. Returns are gross of all fees. 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.

The volatility parameter was 9.5%, the strike was 2.3%, and the cost was 1.7%.

What do these parameters mean?

As we said before this can be a bit tricky. Painting in broad strokes:

  • The volatility parameter describes how “elbowed” payoff profile is. Small values are akin to an option close to expiry where the payoff profile changes abruptly around the strike price. Larger values yield a more gentle change in slope.
  • The strike represents the point at which the payoff profile changes from participation to protection using trend-following lingo. In the example where the strike is 2.3%, this means that the strategy would be expected to start protecting capital when the S&P 500 return is less than 2.3%. There is some cost associated with this value being high.
  • The cost is the vertical shift of the payoff profile, but it is not good to think of it as the insurance premium of the trend-following strategy. It is only one piece. To see why this is the case, consider that the fitted volatility may be large and that the option price curve may be significantly above the final payout curve (i.e. if the time-scaled volatility went to zero).

So what is the actual “cost” of the strategy?

With trend-following, since whipsaw is generally the largest potential detractor, we will look at the expected return on the strategy when the S&P 500 is flat, that is, an absence of an average trend. It is possible for the cost to be negative, indicating a positive expected trend-following return when the market was flat.

Looking at the actual fit of the data from a statistical perspective, the largest deviations from the expected value (the residuals from the regression) are seen during large positive returns for the S&P 500, mainly coming out of the Great Depression. This characteristic of individual trend-following models is generally attributable to the delay in getting back into the market after a prolonged, severe drawdown due to the time it takes for a new positive trend to be established.

Source: Global Financial Data and Kenneth French Data Library. Calculation by Newfound. Returns are backtested and hypothetical. Returns assume the reinvestment of all distributions. Returns are gross of all fees. 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.

Part of the seemingly large number of outliers is simply due to the fact that these returns exhibit autocorrelation since the periods are rolling, which means that the data points have some overlap. If we filtered the data down into non-overlapping periods, some of these outliers would be removed.

The outliers that remain are a fact of trend-following strategies. While this fact of trend-following cannot be totally removed, some of the outliers may be managed using multiple lookback periods.

The following chart illustrates the expected values for the trend-following strategies over all the lookback periods.

Source: Global Financial Data and Kenneth French Data Library. Calculation by Newfound. Returns are backtested and hypothetical. Returns assume the reinvestment of all distributions. Returns are gross of all fees. 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.

The shorter-term lookback windows have the expected value curves that are less horizontal on the left side of the chart (higher volatility parameter).

As we said before the cost of the trend-following strategy can be represented by the strategy’s expected return when the S&P 500 is flat. This can be thought of as the premium for the insurance policy of the trend-following strategies.

Source: Global Financial Data and Kenneth French Data Library. Calculation by Newfound. Returns are backtested and hypothetical. Returns assume the reinvestment of all distributions.  Returns are gross of all fees. 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.

The blend does not have the lowest cost, but this cost is only one part of the picture. The parameters for the expected value functions do nothing to capture the distribution of the data around – either above or below – these curves.

The diversification benefits are best seen in the distribution of the rolling returns around the expected value functions.

Source: Global Financial Data and Kenneth French Data Library. Calculation by Newfound. Returns are backtested and hypothetical. Returns assume the reinvestment of all distributions. Returns are gross of all fees. 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.

Now with a more comprehensive picture of the potential outcomes, a cost difference of even 3% is less than one standard deviation, making the blended strategy much more robust to whipsaw for the potential range of S&P 500 returns.

As a side note, the cost of the short window (4 and 5 month) strategies is relatively high. However, since there are many rolling periods when these models are the best performing of the group, there can still be a benefit to including them. With them in the blend, we still see a reduction in the dispersion around the expected value function.

Expanding the Multitude of Models

To take the example even further down the multi-model path, we can look at the same analysis for varying lookback windows for a price-minus-moving-average model and an exponentially weighted moving average model.

Source: Global Financial Data and Kenneth French Data Library. Calculation by Newfound. Returns are backtested and hypothetical. Returns assume the reinvestment of all distributions. Returns are gross of all fees. 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.

Source: Global Financial Data and Kenneth French Data Library. Calculation by Newfound. Returns are backtested and hypothetical. Returns assume the reinvestment of all distributions. Returns are gross of all fees. 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.

And finally, we can combine all three trend-following measurement style blends into a final composite blend.

Source: Global Financial Data and Kenneth French Data Library. Calculation by Newfound. Returns are backtested and hypothetical. Returns assume the reinvestment of all distributions. Returns are gross of all fees. 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.

As with nearly every study on diversification, the overall blend is not the best by all metrics. In this case, its cost is higher than the EWMA blended model and its dispersion is higher than the TS blended model. But it exhibits the type of middle-of-the-road characteristics that lead to results that are robust to an uncertain future.

Conclusion

Long/flat trend-following strategies have payoff profiles similar to call options, with larger upsides and limited downsides. Unlike call options (and all derivative securities) that pay a deterministic amount based on the underlying securities prices, the payoff of a trend-following strategy is uncertain,

Using historical data, we can calculate the expected payoff profile and the dispersion around it. We find that by blending a variety of trend-following models, both in how they measure trend and the length of the lookback window, we can often reduce the implied cost of the call option and the dispersion of outcomes.

A backtest of an individual trend-following model can look the best over a given time period, but there are many factors that play into whether that performance will be valid going forward. The assets have to behave similarly, potentially both on an absolute and relative basis, and an investor has to hold the investment for a long enough time to weather short-term underperformance.

A multi-model approach can address both of these.

It will reduce the model specification risk that is present ex-ante. It will not pick the best model, but then again, it will not pick the worst.

From an investor perspective, this diversification reduces the spread of outcomes which can lead to an easier product to hold as a long-term investment. Diversification among the models may not always be present (i.e. when style risk dominates and all trend-following strategies do poorly), but when it is, it reduces the chance of taking on uncompensated risks.

Taking on compensated risks is a necessary part of investing, and in the case of trend-following, the style risk is something we desire. Removing as many uncompensated risks as possible leads to more pure forms of this style risk and strategies that are robust to unfavorable specifications.

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