Category: Risk & Style Premia Page 10 of 16

Fragility Case Study: Dual Momentum GEM

By Corey Hoffstein

On January 14, 2019

In Craftsmanship, Momentum, Popular, Portfolio Construction, Risk Management, Trend

This post is available as a PDF download here.

Summary

Recent market volatility has caused many tactical models to make sudden and significant changes in their allocation profiles.
Periods such as Q4 2018 highlight model specification risk: the sensitivity of a strategy’s performance to specific implementation decisions.
We explore this idea with a case study, using the popular Dual Momentum GEM strategy and a variety of lookback horizons for portfolio formation.
We demonstrate that the year-to-year performance difference can span hundreds, if not thousands, of basis points between the implementations.
By simply diversifying across multiple implementations, we can dramatically reduce model specification risk and even potentially see improvements in realized metrics such as Sharpe ratio and maximum drawdown.

Introduction

Among do-it-yourself tactical investors, Gary Antonacci’s Dual Momentum is the strategy we tend to see implemented the most. The Dual Momentum approach is simple: by combining both relative momentum and absolute momentum (i.e. trend following), Dual Momentum seeks to rotate into areas of relative strength while preserving the flexibility to shift entirely to safety assets (e.g. short-term U.S. Treasury bills) during periods of pervasive, negative trends.

In our experience, the precise implementation of Dual Momentum tends to vary (with various bells-and-whistles applied) from practitioner to practitioner. The most popular benchmark model, however, is the Global Equities Momentum (“GEM”), with some variation of Dual Momentum Sector Rotation (“DMSR”) a close second.

Recently, we’ve spoken to several members in our extended community who have bemoaned the fact that Dual Momentum kept them mostly aggressively positioned in Q4 2018 and signaled a defensive shift at the beginning of January 2019, at which point the S&P 500 was already in a -14% drawdown (having peaked at over -19% on December 24^th). Several DIYers even decided to override their signal in some capacity, either ignoring it entirely, waiting a few days for “confirmation,” or implementing some sort of “half-and-half” rule where they are taking a partially defensive stance.

Ignoring the fact that a decision to override a systematic model somewhat defeats the whole point of being systematic in the first place, this sort of behavior highlights another very important truth: there is a significant gap of risk that exists between the long-term supporting evidence of an investment style (e.g. momentum and trend) and the precise strategy we attempt to implement with (e.g. Dual Momentum GEM).

At Newfound, we call that gap model specification risk. There is significant evidence supporting both momentum and trend as quantitative styles, but the precise means by which we measure these concepts can lead to dramatically different portfolios and outcomes. When a portfolio’s returns are highly sensitive to its specification – i.e. slight variation in returns or model parameters lead to dramatically different return profiles – we label the strategy as fragile.

In this brief commentary, we will use the Global Equities Momentum (“GEM”) strategy as a case study in fragility.

Global Equities Momentum (“GEM”)

To implement the GEM strategy, an investor merely needs to follow the decision tree below at the end of each month.

From a practitioner stand-point, there are several attractive features about this model. First, it is based upon the long-run evidence of both trend-following and momentum. Second, it is very easy to model and generate signals for. Finally, it is fairly light-weight from an implementation perspective: only twelve potential rebalances a year (and often much less), with the portfolio only holding one ETF at a time.

Despite the evidence that “simple beats complex,” the simplicity of GEM belies its inherent fragility. Below we plot the equity curves for GEM implementations that employ different lookback horizons for measuring trend and momentum, ranging from 6- to 12-months.

Source: CSI Analytics. Calculations by Newfound Research. Returns are backtested and hypothetical. Returns assume the reinvestment of all distributions. Returns are gross of all fees except for underlying ETF expense ratios. 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.

We can see a significant dispersion in potential terminal wealth. That dispersion, however, is not necessarily consistent with the notion that one formation period is inherently better than another. While we would argue, ex-ante, that there should be little performance difference between a 9-month and 10-month lookback – they both, after all, capture the notion of “intermediate-term trends” – the former returned just 43.1% over the period while the latter returned 146.1%.

These total return figures further hide the year-to-year disparity that exists. The 9-month model, for example, was not a consistent loser. Below we plot these results, highlighting both the best (blue) and worst (orange) performing specifications. We see that the yearly spread between these strategies can be hundreds-to-thousands of basis points; consider that in 2010, the strategy formed using a 10-month lookback returned 12.2% while the strategy formed using a 9-month lookback returned -9.31%.

Same thesis. Same strategy. Slightly different specification. Dramatically different outcomes. That single year is likely the difference between hired and fired for most advisors and asset managers.

☞ Explore a diversified approach with the Newfound/ReSolve Robust Equity Momentum Index.

For those bemoaning their 2018 return, note that the 10-month specification would have netted a positive result! That specification turned defensive at the end of October.

Now, some may cry “foul” here. The evidence for trend and momentum is, after all, centuries in length and the efficacy of all these horizons is supported. Surely the noise we see over this ten-year period would average out over the long run, right?

The unfortunate reality is that these performance differences are not expected to mean-revert. The gambler’s fallacy would have us believe that bad luck in one year should be offset by good luck in another and vice versa. Unfortunately, this is not the case. While we would expect, at any given point in time, that each strategy has equal likelihood of experiencing good or bad luck going forward, that luck is expected to occur completely independently from what has happened in the past.

The implication is that performance differences due to model specification are not expected to mean-revert and are therefore expected to be random, but very permanent, return artifacts.¹

The larger problem at hand is that none of us have a hundred years to invest. In reality, most investors have a few decades. And we act with the temperament of having just a few years. Therefore, bad luck can have very permanent and very scarring effects not only upon our psyche, but upon our realized wealth.

But consider what happens if we try to neutralize the role of model specification risk and luck by diversifying across the seven different models equally (rebalanced annually). We see that returns closer in line with the median result, a boost to realized Sharpe ratio, and a reduction in the maximum realized drawdown.

These are impressive results given that all we employed was naïve diversification.

Conclusion

The odd thing about strategy diversification is that it guarantees we will be wrong. Each and every year, we will, by definition, allocate at least part of our capital to the worst performing strategy. The potential edge, however, is in being vaguely wrong rather than precisely wrong. The former is annoying. The latter can be catastrophic.

In this commentary we use the popular Dual Momentum GEM strategy as a case study to demonstrate how model specification choices can lead to performance differences that span hundreds, if not thousands, of basis points a year. Unfortunately, we should not expect these performance differences to mean revert. The realizations of good and bad luck are permanent, and potentially very significant, artifacts within our track records.

By simply diversifying across the different models, however, we can dramatically reduce specification risk and thereby reduce strategy fragility.

To be clear, no amount of diversification will protect you from the risk of the style. As we like to say, “risk cannot be destroyed, only transformed.” In that vein, trend following strategies will always incur some sort of whipsaw risk. The question is whether it is whipsaw related to the style as a whole or to the specific implementation.

For example, in the graphs above we can see that Dual Momentum GEM implemented with a 10-month formation period experienced whipsaw in 2011 when few of the other implementations did. This is more specification whipsaw than style whipsaw. On the other hand, we can see that almost all the specifications exhibited whipsaw in late 2015 and early 2016, an indication of style whipsaw, not specification whipsaw.

Specification risk we can attempt to control for; style risk is just something we have to bear.

At Newfound, evidence such as this informs our own trend-following mandates. We seek to diversify ourselves across the axes of what (“what are we investing in?”), how (“how are we making the decisions?”), and when (“when are we making those decisions?”) in an effort to reduce specification risk and provide the greatest style consistency possible.

Attack of the Clone: Lessons from Replicating Long/Short Equity

By Corey Hoffstein

On October 22, 2018

In Risk & Style Premia, Weekly Commentary

This post is available as a PDF download here.

Summary

In this commentary we attempt to identify the sources of performance in long/short equity strategies.
Using Kalman Filtering, we attempt to replicate the Credit Suisse Long/Short Liquid Index with a set of common factors designed to capture equity beta, regional, and style tilts.
We find that as a category, long/short equity managers make significant changes to their equity beta and regional tilts over time.
Year-to-date, we find that tilts towards foreign developed equities, emerging market equities, and the value premium have been the most significant detractors from index performance.
We believe that the consistent relative out-performance of U.S. equities against international peers has removed an important alpha source for long/short equity managers when they are benchmarked against U.S. equities.

Please note that analysis performed in this commentary is only through 8/31/2018 despite a publishing date of 10/22/2018 due to data availability.

Introduction

Since 4/30/1994, the Credit Suisse Long/Short Equity Hedge Fund (“CS L/S EQHF”) Index has returned 9.0% annualized with an 8.8% annualized volatility and a maximum drawdown of just 22%. While the S&P 500 has bested it on an absolute return basis – returning 10.0% annualized – it has done so with considerably more risk, exhibiting 14.4% annualized volatility and a maximum drawdown of 51%. Capturing 90% of the long-term annualized return of the S&P 500 with only 60% of the volatility and less than half the maximum drawdown is an astounding feat. Particularly because this is not the performance of a single star manager, but the blended returns of dozens of managers.

Yet absolute performance in this category has languished as of late. While the S&P 500 has returned an astounding 13.5% annualized over the last five years, the CS L/S EQHF Index has only returned 5.6% annualized. Of course, returns are only part of the story, but this performance is in stark contrast to the relative performance experienced during the 2003-2007 bull market. From 12/31/2003 to 12/31/2007, the average rolling 1-year performance difference between the S&P 500 and the CS L/S EQHF Index was less than 1 basis point whereas the average rolling 1-year performance differential from 12/31/2010 to 12/31/2017 was 877 basis points. Year-to-date performance in 2018 has been no exception to this trend. The CS L/S EQHF Index is up just 2.1% compared to a positive 9.7% for the S&P 500, with several popular strategies faring far worse.

Now, before we dive any deeper, we want to address the obvious: comparing long/short equity returns against the S&P 500 is foolish. The long-term beta of the category is less than 0.5, so it should not come as a surprise that absolute returns have languished during a period where vanilla U.S. equity beta has been one of the best performing asset classes. Nevertheless, while the CS L/S EQHF typically exhibited higher risk-adjusted returns than equity beta from 1994 through 2011, the reverse has been true since 2012.

Identifying precisely why both absolute and relative risk-adjusted performance has declined over the last several years can be difficult, as the category as a whole is incredibly varied in nature. Consider this index definition from Credit Suisse:

The Credit Suisse Long/Short Equity Hedge Fund Index is a subset of the Credit Suisse Hedge Fund Index that measures the aggregate performance of long/short equity funds. Long/short equity funds typically invest in both long and short sides of equity markets, generally focusing on diversifying or hedging across particular sectors, regions or market capitalizations. Managers typically have the flexibility to shift from value to growth; small to medium to large capitalization stocks; and net long to net short. Managers can also trade equity futures and options as well as equity-related securities and debt or build portfolios that are more concentrated than traditional long-only equity funds.

The wide degree of flexibility means that we would expect significant dispersion in individual strategy performance. Examining a broad index may still be useful, however, as we may be able to decipher the large muscle movements that have driven common performance. In order to do so, we have to get under the hood and try to replicate the index using common factor exposures.

Figure 1: Credit Suisse Long/Short Equity Indices

Data from 12/1993-8/2018

	Annualized Return	Annualized Volatility	Sharpe Ratio
Credit Suisse Long/Short Hedge Fund Index	8.6%	8.9%	0.68
Credit Suisse Long/Short Liquid Index	7.7%	9.4%	0.60
Credit Suisse AllHedge Long/Short Equity Index	3.6%	8.0%	0.29

Source: Kenneth French Data Library and Credit Suisse. Calculations by Newfound Research. It is not possible to invest in an index. Past performance does not guarantee future results.

Replicating Long/Short Equity Returns

To gain a better understanding of what is driving long/short equity returns, we attempt to construct a strategy that replicates the returns of the Credit Suisse Long/Short Liquid Index (“CS L/S LAB”). We have selected this index because return data is available on a daily basis, unlike many other long/short equity indexes which only provide monthly returns.

It is worth noting that this index is itself a replicating index, attempting to track the CS L/S EQHF Index using liquid instruments. In other words, we’re attempting a rather meta experiment: replicating a replicator. This may introduce unintended noise into our effort, but we feel that the benefit of daily index level data more than offsets this risk.

Based upon the category description above, we pre-construct several long/short indices that aim to isolate equity beta, regional tilts, and style tilt effects. To capture beta, we construct the following long/short index:

Long S&P 500 / Short Cash: The excess returns offered by U.S. large-cap equities

To capture regional, size, and industry effects, we construct the following long/short indexes:

Long Russell 2000 / Short S&P 500: Relative performance of small-cap equities versus large-cap equities
Long MSCI EAFE / Short S&P 500: Relative performance of international developed equities versus U.S. equities
Long MSCI EM / Short S&P 500: Relative performance of emerging market equities versus U.S. equities
Long Nasdaq 100 / Short S&P 500: Relative performance of “concentrated” large-cap equities versus broad large-cap equities¹

To capture certain style premia, we construct the following long/short indexes:

Long Russell 1000 Value / Short Russell 1000 Growth: Relative performance of large-cap value versus large-cap growth.²
Long High Momentum / Short Low Momentum: Relative performance of recent winners versus recent losers.

All long/short indexes are assumed to be dollar-neutral in construction and are rebalanced on a monthly basis.

A simple way of implementing index tracking is through a rolling-window regression. In such an approach, the returns of the CS L/S LAB Index are regressed against the returns of the long/short portfolios. The factor loadings would then reflect the weights of the replicating portfolio.

In practice, the problem with such an approach is that achieving statistical significance requires a number of observations far in excess to the number of factors. Were we to use monthly returns, for example, we might need to employ upwards of three years of data. Yet, as we know from the introductory description of the long/short equity category, these strategies are likely to change their exposures rapidly, even on an aggregate scale. One potential solution is to employ weekly or daily returns. Yet even when this data is available, we must still determine the appropriate rolling window length as well as consider how to handle statistically insignificant explanatory variables and perform model selection.

With this in mind, we elected to utilize an approach called Kalman Filtering. This algorithm is designed to produce estimates for a series of unknown variables based upon a series of inputs that may contain statistical noise or other inaccuracies. The benefit of this model is that we need not specify a lookback window: the model dynamically updates for each new observation based upon how well the model fits the data and how noisy the algorithm believes the data to be.

As it pertains to the problem at hand, we set up our unknown variables to be the weights of the replicating factors in our portfolio. We feed the algorithm the daily returns of these factors and set it to solve for the weights that will minimize the tracking distance to the daily returns of the CS L/S LAB Index. In Figure 2 we plot the cumulative returns of the CS L/S LAB Index and our Kalman Tracker portfolio. We can see that while the Kalman Tracker does not perfectly capture the magnitude of the moves exhibited by the CS L/S LAB Index, it does generally capture the shape and significant transitions within the index. While not a perfect replica, this may be a “good enough” approximation for us to glean some information from the underlying exposures.

Figure 2: Credit Suisse Long/Short Liquid Index and Hypothetical Kalman Tracker

Source: Kenneth French Data Library, Credit Suisse, and CSI Analytics. Calculations by Newfound Research. It is not possible to invest in an index. Past performance does not guarantee future results. Index returns are total returns and are gross of all fees except for underlying ETF expense ratios of ETFs utilized by the Kalman Tracker. The Kalman Tracker does not reflect any strategy offered or managed by Newfound Research and was constructed exclusively for the purpose of this commentary.

The Time-Varying Exposures of Long/Short Equity

In Figure 3 we plot the underlying factor weights of our replicating strategy over time, specifically magnifying year-to-date exposures.

Figure 3: Underlying Exposure Weights for Kalman Tracker

We can see several effects:

Factor exposures do indeed exhibit significant time-varying behavior. For example, prior to 2008 there was a large tilt towards foreign-developed equities, whereas post-2008 exposure remained largely U.S. focused.
Beta exposure is time-varying. While there is latent beta exposure in the long/short factors, we can approximate overall beta exposure by simply isolating S&P 500 exposure. In March 2008, exposure peaked at 72% and then was cut quickly throughout the year. By January 2009, the index was net short. Post-crisis, exposure was rebuilt back to nearly 70% by September 2011, but has been declining since. Exposure currently sits at 28%. Has all this equity timing been valuable? In Figure 4 we plot the cumulative return of the index’s long-term average beta exposure and the cumulative return from beta timing. We can see that beta timing has, over the long run, been neither a significant contributor nor detractor from performance. Yet crisis-period returns suggest that long/short equity strategies may employ convex trading strategies (e.g. trend-following or constant proportion portfolio insurance).
Size, value, and momentum tilts are not particularly significant in magnitude, with the exception of value during the 2008 crisis. Interestingly, exposure to value was negative during that time period, implying that the index was long growth and short value. Concentrated large-cap exposure has been a rather consistent bet in the post-2008 era, reflecting a tilt towards growth.
Regional bets have been largely absent post-2008, at least with respect to their pre-2008 magnitude. We think it is important to pause and acknowledge the impact that benchmarking can have on perceived value add. Consider Figure 5 where we plot the cumulative returns of regional tilts towards international developed and emerging markets. We can see that prior to 2008, a tilt away from U.S. equities was successful in both cases, and after 2011 both were a losing bet. In the post-2011 environment, if a manager successfully makes the call to tilt towards U.S. equities, an entirely U.S. equity benchmark will effectively nullify the impact since the bet is already fully encapsulated in the benchmark! In other words, by choice of benchmark we have eliminated a source of value-add for the manager. Had we elected a global equity benchmark instead, the manager’s flexibility could potentially create value in both environments.

Figure 4: Cumulative Returns of Kalman Tracker’s Long-Term Average S&P 500 Exposure and Time-Varying Exposure

Source: Kenneth French Data Library, Credit Suisse, and CSI Analytics. Calculations by Newfound Research. It is not possible to invest in an index. Past performance does not guarantee future results.

Figure 5: Cumulative Returns of Regional Tilts

Source: CSI Analytics. Calculations by Newfound Research. It is not possible to invest in an index. Past performance does not guarantee future results.

What has driven performance in 2018? We see three primary components.

Entering the year, the index carried a nearly 40% allocation to equity beta. While exposure declined to about 33% by the end of the month, it was rapidly cut down to just 20% after the first week February. By mid-March this position was rebuilt to approximately 30%.We estimate that average beta exposure has been a 3.4% contributor to year-to-date returns, while market timing has been a -0.3% detractor.
After Q1, there was an increase in exposure to MSCI EAFE, MSCI EM, and value tilts. We estimate that these tilts have been -1.9%, -2.3%, and -1.1% detractors from performance, respectively.It is possible that these tilts all reflect the same underlying bet towards global value. Or it may be the case that the global tilts reflect a bet on a weakening dollar. We should not hesitate to remember that these figures are all statistically derived, so an equally valid possibility is that they are entirely wrong in the first place. It is worth noting that the value tilt – which is expressed as long Russell 1000 Value and short Russell 1000 Growth – does neutralize some of the sectors tilts expressed in the concentrated large-cap position discussed in the next bullet. The true net effect may not actually be a tilt towards value within the index, but rather just a reduction in the tilt towards growth.
The largest positive contributor to returns year-to-date has been the concentrated large-cap tilt. Implemented as long Nasdaq 100 / short S&P 500, this tilt largely expresses a bet on information technology, telecommunication services, and consumer discretionary sectors. Specifically, year-to-date is represents a significant overweight towards individual names like Apple, Amazon, Microsoft, Google, and Facebook.

Conclusion

Has long/short equity lost its mojo?

By replicating index performance using liquid factors, we can extract the common drivers of performance. What we found was that pre-2008 performance was largely driven by equity beta and a significant tilt towards foreign developed equities.

After 2011, regional tilts were losing bets. Fortunately, we can see that such tilts were significantly reduced – if not outright removed – from the index composition. Nevertheless, if we benchmark to a U.S. equity index (even if properly risk-adjusted), the accuracy of this trade will be entirely discounted because it is fully embedded in the index itself. In other words, by benchmarking against U.S. equities, the best a manager can do during a period when U.S. equities outperform is keep up with the index. Consider that year-to-date the MSCI ACWI has returned just 3.5%: much closer to the 2.1% of the CS L/S EQHF Index quoted in the introduction.

We can also see a significant tilt towards concentrated U.S. equities in the post-crisis era. This trade captured the relative performance of sectors like technology, telecommunication services, and consumer discretionary and from 12/31/2009 to 8/31/2018 returned 4.5% annualized.

Taken together, it is hard to argue that aggregate timing skill is not being displayed in the long/short equity category. We simply have to use the right measuring stick and not expect the timing to work over every shorter-term period.

Of course, this analysis should all be taken with a grain of salt. Our replicating index is by no means a perfect fit (though it is a very good fit from 2012 onward) and it is entirely possible that we selected the wrong set of explanatory features. Furthermore, we have only analyzed one index. The performance of the Credit Suisse Liquid Long/Short Index is not identical to that of the HFRI Equity Hedge Index, the Wilshire BRI Long/Short Equity Index, or the Morningstar Global Long/Short Index. Analysis using those indices may very well lead to different conclusions. Finally, the mathematics of this exercise does not make the factor tea-leaves any easier to decipher: we are ultimately attempting to create a narrative where one need not apply.

It is worth acknowledging that our analysis is categorical about an asset class where investors have little ability to make an indexed investment. Rather, allocation to long/short equity is still dominated by individual manager selection. This means that that investor mileage will vary considerably and that our analysis herein may not apply to any specific manager. After all, we are attempting to analyze aggregate results and it is impossible to unscramble eggs.

Yet it does raise the question: if the aggregate category has such attractive features and can be tracked well with liquid factors, why have trackers not taken off as a popular – and much lower cost – solution for investors looking to index their long/short equity exposure? Another potential solution may be for investors to unbundle and rebuild. For example, we find that the beta exposure of $1 invested in the long/short category can be captured efficiently by $0.5 of trend equity exposure, freeing up $0.5 for other high-conviction alpha strategies.

Diversifying core equity exposure is a goal of many investors. Long/short equity provides one way to do this. In addition to potentially highlighting some of the performance drivers for long/short equity, this replication exercise shows that there may be other, more transparent, ways to achieve this goal.

A Carry-Trend-Hedge Approach to Duration Timing

By Corey Hoffstein

On October 15, 2018

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

This post is available as a PDF download here.

Summary

In this paper we discuss simple rules for timing exposure to 10-year U.S. Treasuries.
We explore signals based upon the slope of the yield curve (“carry”), prior returns (“trend”), and prior equity returns (“hedge”).
We implement long/short implementations of each strategy covering the time period of 1962-2018.
We find that all three methods improve both total and risk-adjusted returns when compared to long-only exposure to excess bond returns.
Naïve combination of both strategies and signals appears to improve realized risk-adjusted returns, promoting the benefits of process diversification.

Introduction

In this strategy brief, we discuss three trading rules for timing exposure to duration. Specifically, we seek to time the excess returns generated from owning 10-year U.S. Treasury bonds over short rates. This piece is meant as a companion to our prior, longer-form explorations Duration Timing with Style Premiaand Timing Bonds with Value, Momentum, and Carry. In contrast, the trading rules herein are simplistic by design in an effort to highlight the efficacy of the signals.

We explore three different signals in this piece:

The slope of the yield curve (“term spread”);
Prior realized excess bond returns; and
Prior realized equity market returns.

In contrast to prior studies, we do not consider traditional value measures, such as real yields, or explicit estimates of the bond risk premium, as they are less easily calculated. Nevertheless, the signals studied herein capture a variety of potential influences upon bond markets, including inflation shocks, economic shocks, policy shocks, marginal utility shocks, and behavioral anomalies.

The strategies based upon our signals are implemented as dollar-neutral long/short portfolios that go long a constant maturity 10-year U.S. Treasury bond index and short a short-term U.S. Treasury index (assumed to be a 1-year index prior to 1982 and a 3-month index thereafter). We compare these strategies to a “long-only” implementation that is long the 10-year U.S. Treasury bond index and short the short-term U.S. Treasury index in order to capture the excess realized return associated with duration.

Implementing our strategies as dollar-neutral long/short portfolios allows them to be interpreted in a variety of useful manners. For example, one obvious interpretation is an overlay implemented on an existing bond portfolio using Treasury futures. However, another interpretation may simply be to guide investors as to whether to extend or contract their duration exposure around a more intermediate-term bond portfolio (e.g. a 5-year duration).

At the end of the piece, we explore the potential diversification benefits achieved by combining these strategies in both an integrated (i.e. signal combination) and composite (i.e. strategy combination) fashion.

Slope of the Yield Curve

In past research on timing duration, we considered explicit measures of the bond risk premium as well as valuation. In Duration Timing with Style Premiawe used a simple signal based upon real yield, which had the problem of being predominately long over the last several decades. In Timing Bonds with Value, Momentum, and Carry we compared a de-trended real yield against recent levels in an attempt to capture more short-term valuation fluctuations.

In both of these prior research pieces, we also explicitly considered the slope of the yield curve as a predictor of future excess bond returns. One complicating factor to carry signals is that rate steepness simultaneously captures both the expectation of rising short rates as well as an embedded risk premium. In particular, evidence suggests that mean-reverting rate expectations dominate steepness when short rates are exceptionally low or high. Anecdotally, this may be due to the fact that the front end of the curve is determined by central bank policy while the back end is determined by inflation expectations.

Thus, despite being a rather blunt measure, steepness may simultaneously be related to business cycles, credit cycles and monetary policy cycles. To quote Ilmanen (2011):

A steep [yield curve] coincides with high unemployment rate (correlation +0.45) and predictsfast economic growth. [Yield curve] countercyclicality may explain its ability to predict near-term bond and stock returns: high required premia near business cycle troughs result in a steep [yield curve], while low required premia near business cycle peaks result in an inverted [yield curve].

Therefore, while estimates of real yield may seek to be explicit measures of value, we may consider carry to be an ancillary measure as well, as a high carry tends to be associated with a high term premium. In Figure 1 we plot the annualized next month excess bond return based upon the quartile (using the prior 10 years of information) that the term spread falls into. We can see a significant monotonic improvement from the 1^stto the 4^thquartiles, indicating that higher levels of carry, relative to the past, are positive indicators of future returns.

Therefore, we construct our carry strategy as follows:

At the end of each month, calculate the term spread between 10- and 1-year U.S. Treasuries.
Calculate the realized percentile of this spread by comparing it against the prior 10-years of daily term spread measures.
If the carry score is in the top two thirds, go long excess bond returns. If the carry score is in the bottom third, go short excess bond returns.
Trade at the close of the 1^sttrading day of the month.

Returns for this strategy are plotted in Figure 2. Our research suggests that the backtested results of this model can be significantly improved through the use of longer holding periods and portfolio tranching. Another potential improvement is to scale exposure linearly to the current percentile. We will leave these implementations as exercises to readers.

Figure 1

Source: Kenneth French Data Library, Federal Reserve of St. Louis. Calculations by Newfound Research. Returns are backtested and hypothetical. Return data relies on hypothetical indices and is exclusive of all fees and expenses. Returns assume the reinvestment of all distributions. The Carry Long/Short strategy does not reflect any 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. Past performance does not guarantee future results.

Figure 2

Data from 1972-2018

	Annualized Return	Annualized Volatility	Sharpe Ratio
Long Only	2.1%	7.6%	0.27
CARRY L/S	2.6%	7.7%	0.33

Trend in Bond Returns

Momentum, in both its relative and absolute (i.e. “trend”) forms, has a long history among both practitioners and academics (see our summary piece Two Centuries of Momentum).

The literature covering momentum in bond returns, however, varies in precisely whatprior returns matter. There are three primary categories: (1) change in bond yields (e.g. Ilmanen (1997)), (2) total return of individual bonds (e.g. Kolanovic and Wei (2015) and Brooks and Moskowitz (2017)), and (3) total return of bond indices (or futures) (e.g. Asness, Moskowitz, and Pedersen (2013), Durham (2013), and Hurst, Ooi, Pedersen (2014))

In our view, the approaches have varying trade-offs:

While empirical evidence suggests that nominal interest rates can exhibit secular trends, rate evolution is most frequently modeled as mean-reversionary. Our research suggests that very short-term momentum can be effective, but leads to a significant amount of turnover.
The total return of individual bonds makes sense if we plan on running a cross-sectional bond model (i.e. identifying individual bonds), but is less applicable if we want to implement with a constant maturity index.
The total return of a bond index may capture past returns that are attributable to securities that have been recently removed.

We think it is worth noting that the latter two methods can capture yield curve effects beyond shift, including roll return, steepening and curvature changes. In fact, momentum in general may even be able to capture other effects such as flight-to-safety and liquidity (supply-demand) factors.

In this piece, we elect to measure momentum as an exponentially-weighting average of prior log returns of the total return excess between long and short bond indices. We measure this average at the end of each month and go long duration when it is positive and short duration when it is negative. In Figure 4 we plot the results of this method based upon a variety of lookback periods that approximate 1-, 3-, 6-, and 12-month formation periods.

Figure 3

	MOM 21	MOM 63	MOM 126	MOM 252
MOM 21	1.00	0.87	0.65	0.42
MOM 63	0.87	1.00	0.77	0.53
MOM 126	0.65	0.77	1.00	0.76
MOM 252	0.42	0.53	0.76	1.00

We see varying success in the methods, with only MOM 63 and MOM 256 exhibiting better risk-adjusted return profiles. Despite this long-term success, we can see that MOM 63 remains in a drawdown that began in the early 2000s, highlighting the potential risk of relying too heavily on a specific measure or formation period. In Figure 3 we calculate the correlation between the different momentum strategies. As we found in Measuring Process Diversification in Trend Following, diversification opportunities appear to be available by mixing both short- and long-term formation periods.

With this in mind, we elect for the following momentum implementation:

At the end of each month, calculate both a 21- and 252-day exponentially-weighted moving average of realized daily excess log returns.
When both signals are positive, go long duration; when both signals are negative, go short duration; when signals are mixed, stay flat.
Rebalance at the close of the next trading day.

The backtested results of this strategy are displayed in Figure 5.

As with carry, we find that there are potential craftsmanship improvements that can be made with this strategy. For example, implementing with four tranches, weekly rebalances appears to significantly improve backtested risk-adjusted returns. Furthermore, there may be benefits that can be achieved by incorporating other means of measuring trends as well as other lookback periods (see Diversifying the What, When, and How of Trend Following and Measuring Process Diversification in Trend Following).

Figure 4

Data from 1963-2018

	Annualized Return	Annualized Volatility	Sharpe Ratio
Long Only	1.5%	7.3%	0.21
MOM 21	1.4%	7.5%	0.19
MOM 63	1.8%	7.4%	0.25
MOM 128	1.3%	7.4%	0.18
MOM 252	1.9%	7.4%	0.26

Source: Kenneth French Data Library, Federal Reserve of St. Louis. Calculations by Newfound Research. Returns are backtested and hypothetical. Return data relies on hypothetical indices and is exclusive of all fees and expenses. Returns assume the reinvestment of all distributions. The Momentum strategies do not reflect any strategies offered or managed by Newfound Research and were constructed exclusively for the purposes of this commentary. It is not possible to invest in an index. Past performance does not guarantee future results.

Figure 5

Data from 1963-2018

	Annualized Return	Annualized Volatility	Sharpe Ratio
Long Only	1.5%	7.2%	0.21
MOM L/S	1.7%	6.3%	0.28

Source: Kenneth French Data Library, Federal Reserve of St. Louis. Calculations by Newfound Research. Returns are backtested and hypothetical. Return data relies on hypothetical indices and is exclusive of all fees and expenses. Returns assume the reinvestment of all distributions. The Momentum Long/Short strategy does not reflect any 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. Past performance does not guarantee future results.

Safe-Haven Premium

Stocks and bonds generally exhibit a positive correlation over time. One thesis for this long-term relationship is the present value model, which argues that declining yields, and hence increasing bond prices, increase the value of future discounted cash flows and therefore the fair value of equities. Despite this long-term relationship, shocks in economic growth, inflation, and even monetary policy can overwhelm the discount rate thesis and create a regime-varying correlation structure.

For example, empirical evidence suggests that high quality bonds can exhibit a safe haven premium during periods of economic stress. Using real equity prices as a proxy for wealth, Ilmanen (1995) finds that “wealth-dependent relative risk aversion appears to be an important source of bond return predictability.” Specifically, inverse wealth is a significant positive predictor of future excess bond returns at both world and local (U.S., Canada, Japan, Germany, France, and United Kingdom) levels. Ilmanen (2003) finds that, “stock-bond correlations are more likely to be negative when inflation is low, growth is slow, equities are weak, and volatility is high.”

To capitalize on this safe-haven premium, we derive a signal based upon prior equity returns. Specifically, we utilize an exponentially weighted average of prior log returns to estimate the underlying trend of equities. We then compare this estimate to a 10-year rolling window of prior estimates, calculating the current percentile.

In Figure 6 we plot the annualized excess bond return for the month following, assuming signals are generated at the close of each month and trades are placed at the close of the following trading day. We can see several effects. First, next month returns for 1^stquartile equity momentum – i.e. very poor equity returns – tends to be significantly higher than other quartiles. Second, excess bond returns in the month following very strong equity returns tend to be poor. We would posit that these two effects are two sides of the same coin: the safe-haven premium during 1^stquartile periods and an unwind of the premium in 4^thquartile periods. Finally, we can see that 2^ndand 3^rdquartile returns tend to be positive, in line with the generally positive excess bond return over the measured period.

In an effort to isolate the safe-haven premium, we construct the following strategy:

At the end of each month, calculate an equity momentum measure by taking a 63-day exponentially weighted average of prior daily log-returns.
Calculate the realized percentile of this momentum measure by comparing it against the prior 10-years of daily momentum measures.
If the momentum score is in the bottom quartile, go long excess bond returns. If the momentum score is in the top quartile, go short excess bond returns. Otherwise, remain flat.
Trade at the close of the 1^sttrading day of the month.

Returns for this strategy are plotted in Figure 7. As expected based upon the quartile design, the strategy only spends 24% of its time long, 23% of its time short, and the remainder of its time flat. Despite this even split in time, approximately 2/3^rdsof the strategy’s return comes from the periods when the strategy is long.

Figure 6

Source: Kenneth French Data Library, Federal Reserve of St. Louis. Calculations by Newfound Research. Returns are backtested and hypothetical. Return data relies on hypothetical indices and is exclusive of all fees and expenses. Returns assume the reinvestment of all distributions. The Equity Momentum Long/Short strategy does not reflect any 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. Past performance does not guarantee future results.

Figure 7

Data from 1962-2018

	Annualized Return	Annualized Volatility	Sharpe Ratio
Long Only	1.5%	7.2%	0.21
Equity Mom L/S	1.9%	5.7%	0.34

Source: Kenneth French Data Library, Federal Reserve of St. Louis. Calculations by Newfound Research. Returns are backtested and hypothetical. Return data relies on hypothetical indices and is exclusive of all fees and expenses. Returns assume the reinvestment of all distributions. The Equity Momentum Long/Short strategy does not reflect any 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. Past performance does not guarantee future results.

Combining Signals

Despite trading the same underlying instrument, variation in strategy construction means that we can likely benefit from process diversification in constructing a combined strategy. Figure 8 quantifies the available diversification by measuring full-period correlations among the strategies from joint inception (1972). We can also see that the strategies exhibit low correlation to the Long Only implementation, suggesting that they may introduce diversification benefits to a strategic duration allocation as well.

Figure 8

	LONG ONLY	CARRY L/S	MOM L/S	EQ MOM L/S
LONG ONLY	1.00	0.42	0.33	-0.09
CARRY L/S	0.42	1.00	0.40	-0.09
MOM L/S	0.33	0.40	1.00	-0.13
EQ MOM L/S	-0.10	-0.10	-0.19	1.00

We explore two different implementations of a diversified strategy. In the first, we simply combine the three strategies in equal-weight, rebalancing on a monthly basis. This implementation can be interpreted as three sleeves of a larger portfolio construction. In the second implementation, we combine underlying long/short signals. When the net signal is positive, the strategy goes 100% long duration and when the signal is negative, it goes 100% short. This can be thought of as an integrated approach that takes a majority-rules voting approach. Results for these strategies are plotted in Figure 9. We note the substantial increase in the backtested Sharpe Ratio of these diversified approaches in comparison to their underlying components outlined in prior sections.

It is important to note that despite strong total and risk-adjusted returns, the strategies spend only approximately 54% of their time net-long duration, with 19% of their time spent flat and 27% of their time spent short. While slightly biased long, this breakdown provides evidence that strategies are not simply the beneficiaries of a bull market in duration over the prior several decades.

Figure 9

Data from 1972-2018

	Annualized Return	Annualized Volatility	Sharpe Ratio
Long Only	2.1%	7.6%	0.27
Combined L/S	2.5%	4.3%	0.58
Integrated L/S	3.5%	7.1%	0.49

Source: Kenneth French Data Library, Federal Reserve of St. Louis. Calculations by Newfound Research. Returns are backtested and hypothetical. Return data relies on hypothetical indices and is exclusive of all fees and expenses. Returns assume the reinvestment of all distributions. Neither the Combined Long/Short or Integrated Long/Short strategies reflect any strategy offered or managed by Newfound Research and were constructed exclusively for the purposes of this commentary. It is not possible to invest in an index. Past performance does not guarantee future results.

Conclusion

In this research brief, we continued our exploration of duration timing strategies. We aimed to implement several signals that were simple by construction. Specifically, we evaluated the impact of term spread, prior excess bond returns, and prior equity returns on next month’s excess bond returns. Despite their simplicity, we find that all three signals can potentially offer investors insight for tactical timing decisions.

While we believe that significant craftsmanship improvements can be made in all three strategies, low hanging improvement may simply come from combining the approaches. We find a meaningful improvement in Sharpe Ratio by naively combining these strategies in both a sleeve-based and integrated signal fashion.

Bibliography

Asness, Clifford S. and Moskowitz, Tobias J. and Pedersen, Lasse Heje, Value and Momentum Everywhere (June 1, 2012). Chicago Booth Research Paper No. 12-53; Fama-Miller Working Paper. Available at SSRN: https://ssrn.com/abstract=2174501 or http://dx.doi.org/10.2139/ssrn.2174501

Brooks, Jordan and Moskowitz, Tobias J., Yield Curve Premia (July 1, 2017). Available at SSRN: https://ssrn.com/abstract=2956411 or http://dx.doi.org/10.2139/ssrn.2956411

Durham, J. Benson, Momentum and the Term Structure of Interest Rates (December 1, 2013). FRB of New York Staff Report No. 657. Available at SSRN: https://ssrn.com/abstract=2377379 or http://dx.doi.org/10.2139/ssrn.2377379

Hurst, Brian and Ooi, Yao Hua and Pedersen, Lasse Heje, A Century of Evidence on Trend-Following Investing (June 27, 2017). Available at SSRN: https://ssrn.com/abstract=2993026 or http://dx.doi.org/10.2139/ssrn.2993026

Ilmanen, Antti, Time-Varying Expected Returns in International Bond Markets, Journal of Finance, Vol. 50, No. 2, 1995, pp. 481-506.

Ilmanen, Antti, Forecasting U.S. Bond Returns, Journal of Fixed Income, Vol. 7, No. 1, 1997, pp. 22-37.

Ilmanen, Antti, Stock-Bond Correlations, Journal of Fixed Income, Vol. 13, No. 2, 2003, pp. 55-66.

Ilmanen, Antti. Expected Returns an Investor’s Guide to Harvesting Market Rewards. John Wiley, 2011.

Kolanovic, Marko, and Wei, Zhen, Momentum Strategies Across Asset Classes (April 2015). Available at https://www.cmegroup.com/education/files/jpm-momentum-strategies-2015-04-15-1681565.pdf

Decomposing Trend Equity

By Corey Hoffstein

On September 24, 2018

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

This post is available as a PDF download here.

Summary

We introduce the simple arithmetic of portfolio construction where a strategy can be broken into a strategic allocation and a self-financing trading strategy.
For long/flat trend equity strategies, we introduce two potential decompositions.
The first implementation is similar to equity exposure with a put option overlay. The second is similar to a 50% equity / 50% cash allocation with a 50% overlay to a straddle.
By evaluating the return profile of the active trading strategy in both decompositions, we can gain a better understanding for how we expect the strategy to perform in different environments.
In both cases, we can see that trend equity can be thought of as a strategic allocation to equities – seeking to benefit from the equity risk premium – plus an alternative strategy that seeks to harvest benefits from the trend premium.

The Simple Arithmetic of Portfolio Construction

In our commentary A Trend Equity Primer, we introduced the concept of trend equity, a category of strategies that aim to harvest the long-term benefits of the equity risk premium while managing downside risk through the application of trend following. In this brief follow-up piece, we aim to provide further transparency into the behavior of trend equity strategies by decomposing this category of strategies into component pieces.

First, what do we mean by “decompose”?

As it turns out, the arithmetic of portfolios is fairly straight forward. Consider this simple scenario: we currently hold a portfolio consisting entirely of asset A and want to hold a portfolio that is 50% A and 50% of some asset B. What do we do?

Figure 1

No, this is not a trick question. The straightforward answer is that we sell 50% of our exposure in A and buy 50% of our exposure in B. As it turns out, however, this is entirely equivalent to holding our portfolio constant and simply going short 50% exposure in A and using the proceeds to purchase 50% notional portfolio exposure in B (see Figure 2). Operationally, of course, these are very different things. Thinking about the portfolio in this way, however, can be constructive to truly understanding the implications of the trade.

The difference in performance between our new portfolio and our old portfolio will be entirely captured by the performance of this long/short overlay. This tells us, for example, that the new portfolio will outperform the old portfolio when asset B outperforms asset A, since the long/short portfolio effectively captures the spread in performance between asset B and asset A.

Figure 2: Portfolio Arithmetic – Long/Short Overlay

Relative to our original portfolio, the long/short represents our active bets. A slightly more nuanced view of this arithmetic requires scaling our active bets such that each leg is equal to 100%, and then only implementing a portion of that overlay. It is important to note that the overlay is “dollar-neutral”: in other words, the dollars allocated to the short leg and the long leg add up to zero. This is also called “self-funding” because it is presumed that we would enter the short position and then use the cash generated to purchase our long exposure, allowing us to enter the trade without utilizing any capital.

Figure 3: Portfolio Arithmetic – Scaled Long/Short Overlay

In our prior example, a portfolio that is 50% long B and 50% short A is equivalent to 50% exposure to a portfolio that is 100% long B and 100% short A. The benefit of taking this extra step is that it allows us to decompose our trade into two pieces: the active bets we are making and the sizing of these bets.

Decomposing Trend Equity

Trend equity strategies are those strategies that seek to combine structural exposure to equities with the potential benefits of an active trend-following trading strategy. A simple example of such a strategy is a “long/flat” strategy that invests in large-cap U.S. equities when the measured trend in large-cap U.S. equities is positive and otherwise invests in short-term U.S. Treasuries (or any other defensive asset class).

An obvious question with a potentially non-obvious answer is, “how do we benchmark such a strategy?” This is where we believe decomposition can be informative. Our goal should be to decompose the portfolio into two pieces: the strategic benchmark allocation and a dollar-neutral long/short trading strategy that captures the manager’s active bets.

For long/flat trend equity strategies, we believe there are two obvious decompositions, which we outline in Figure 4.

Figure 4

	Strategic Position	Trend Strategy
Decomposition		Positive Trend	Negative Trend
Strategic + Flat/Short Trend Strategy	100% Equity	No Position	-100% Equity 100% ST US Treasuries
Strategic + 50% Long/Short Trend Strategy	50% Equity 50% ST US Treasuries	100% Equity -100% ST US Treasuries	-100% Equity +100% ST US Treasuries

Equity + Flat/Short

The first decomposition achieves the long/flat strategy profile by assuming a strategic allocation that is allocated to U.S. equities. This is complemented by a trading strategy that goes short large-cap U.S. equities when the trend is negative, investing the available cash in short-term U.S. Treasuries, and does nothing otherwise.

The net effect is that when trends are positive, the strategy remains fully invested in large-cap U.S. equities. When trends are negative, the overlay nets out exposure to large-cap U.S. equities and leaves the portfolio exposed only to short-term U.S. Treasuries.

In Figures 5, we plot the return profile of a hypothetical flat/short large-cap U.S. equity strategy.

Figure 5: A Flat/Short U.S. Equity Strategy

Source: Newfound Research. Return data relies on hypothetical indices and is exclusive of all fees and expenses. Returns assume the reinvestment of all dividends. Flat/Short Equity shorts U.S. Large-Cap Equity when the prior month has a positive 12-1 month total return, investing available capital in 3-month U.S. Treasury Bills. The strategy assumes zero cost of shorting. The Flat/Short Equity strategy does not reflect any 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. Past performance does not guarantee future results.

The flat/short strategy has historically achieved a payoff structure that looks very much like a put option: positive returns during significantly negative return regimes, and (on average) slight losses otherwise. Of course, unlike a put option where the premium paid is known upfront, the flat/short trading strategy pays its premium in the form of “whipsaw” resulting from trend reversals. These head-fakes cause the strategy to “short low” and “cover high,” creating realized losses.

Our expectation for future returns, then, is a combination of the two underlying strategies:

100% Strategic Equity: We should expect to earn, over the long run, the equity risk premium at the risk of large losses due to economic shocks.
100% Flat/Short Equity: Empirical evidence suggests that we should expect a return profile similar to a put option, with negative returns in most environments and the potential for large, positive returns during periods where large-cap U.S. equities exhibit large losses. Historically, the premium for the trend-following “put option” has been significantly less than the premium for buying actual put options. As a result, hedging with trend-following has delivered higher risk-adjusted returns. Note, however, that trend-following is rarely helpful in protecting against sudden losses (e.g. October 1987) like an actual put option would be.

Taken together, our long-term return expectation should be the equity risk premium minus the whipsaw costs of the flat/short strategy. The drag in return, however, is payment for the expectation that significant left-tail events will be meaningfully offset. In many ways, this decomposition lends itself nicely to thinking of trend equity as a “defensive equity” allocation.

Figure 6: Combination of U.S. Large-Cap Equities and a Flat/Short Trend-Following Strategy

Source: Newfound Research. Return data relies on hypothetical indices and is exclusive of all fees and expenses. Returns assume the reinvestment of all dividends. Flat/Short Equity shorts U.S. Large-Cap Equity when the prior month has a negative 12-1 month total return, investing available capital in 3-month U.S. Treasury Bills. The strategy assumes zero cost of shorting. The Flat/Short Equity strategy does not reflect any 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. Past performance does not guarantee future results.

50% Equity/50% Cash + 50% Long/Short

The second decomposition achieves the long/flat strategy profile by assuming a strategic allocation that is 50% large-cap U.S. equities and 50% short-term U.S. Treasuries. The overlaid trend strategy now goes both long and short U.S. equities depending upon the underlying trend signal, going short and long large-cap U.S. Treasuries to keep the dollar-neutral profile of the overlay.

One difference in this approach is that to achieve the desired long/flat return profile, only 50% exposure to the long/short strategy is required. As before, the net effect is such that when trends are positive, the portfolio is invested entirely in large-cap U.S. equities (as the short-term U.S. Treasury positions cancel out), and when trends are negative, the portfolio is entirely invested in short-term U.S. Treasuries.

In Figures 7, we plot the return profile of a hypothetical long/short large-cap U.S. equity strategy.

Figure 7: A Long/Short Equity Trend-Following Strategy

Source: Newfound Research. Return data relies on hypothetical indices and is exclusive of all fees and expenses. Returns assume the reinvestment of all dividends. Long/Short Equity goes long U.S. Large-Cap Equity when the prior month has a positive 12-1 month total return, shorting an equivalent amount in 3-month U.S. Treasury Bills. When the prior month has a negative 12-1 month total return, the strategy goes short U.S. Large-Cap Equity, investing available capital in 3-month U.S. Treasury Bills. The strategy assumes zero cost of shorting. The Long/Short Equity strategy does not reflect any 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. Past performance does not guarantee future results.

We can see the traditional “smile” associated with long/short trend-following strategies. With options, this payoff profile is reminiscent of a straddle, a strategy that combines a position in a put and a call option to profit in both extremely positive and negative environments. The premium paid to buy these options causes the strategy to lose money in more normal environments. We see a similar result with the long/short trend-following approach.

As before, our expectation for future returns is a combination of the two underlying strategies:

50% Equity / 50% Cash: We should expect to earn, over the long run, about half the equity risk premium, but only expect to suffer about half the losses associated with equities.
50% Long/Short Equity: The “smile” payoff associated with trend following should increase exposure to equities in the positive tail and help offset losses in the negative tail, at the cost of whipsaw during periods of trend reversals.

Taken together, we should expect equity up-capture exceeding 50% in strongly trending years, a down-capture less than 50% in strongly negatively trending years, and a slight drag in more normal environments. We believe that this form of decomposition is most useful when investors are planning to fund their trend equity from both stocks and bonds, effectively using it as a risk pivot within their portfolio.

In Figure 8, we plot the return combined return profile of the two component pieces. Note that it is identical to Figure 6.

Figure 8

Conclusion

In this commentary, we continued our exploration of trend equity strategies. To gain a better sense of how we should expect trend equity strategies to perform, we introduce the basic arithmetic of portfolio construction that we later use to decompose trend equity into a strategic allocation plus a self-funded trading strategy.

In the first decomposition, we break trend equity into a strategic, passive allocation in large-cap U.S. equities plus a self-funding flat/short trading strategy. The flat/short strategy sits in cash when trends in large-cap U.S. equities are positive and goes short large-cap U.S. equities when trends are negative. In isolating the flat/short trading strategy, we see a return profile that is reminiscent of the payoff of a put option, exhibiting negative returns in positive market environments and large gains during negative market environments.

For investors planning on utilizing trend equity as a form of defensive equity, this decomposition is appropriate. It clearly demonstrates that we should expect returns that are less than passive equity during almost all market environments, with the exception being extreme negative tail events, where the trading strategy aims to hedge against significant losses. While we would expect to be able to measure manager skill by the amount of drag created to equities during positive markets (i.e. the “cost of the hedge”), we can see from the hypothetical example inn Figure 5 that there is considerable variation year-to-year, making short-term analysis difficult.

In our second decomposition, we break trend equity into a strategic portfolio that is 50% large-cap U.S. equity / 50% short-term U.S. Treasury plus a self-funding long/short trading strategy. If the flat/short trading strategy was similar to a put option, the long/short trading strategy is similar to a straddle, exhibiting profit in the wings of the return distribution and losses near the middle.

This particular decomposition is most relevant to investors who plan on funding their trend equity exposure from both stocks and bonds, allowing the position to serve as a risk pivot within their overall allocation. The strategic contribution provides partial exposure to the equity risk premium, but the trading strategy aims to add value in both tails, demonstrating that trend equity can potentially increase returns in both strongly positive and strongly negative environments.

In both cases, we can see that trend equity can be thought of as a strategic allocation to equities – seeking to benefit from the equity risk premium – plus an alternative strategy that seeks to harvest benefits from the trend premium.

In this sense, trend equity strategies help investors achieve capital efficiency. Allocations to the alternative return premia, in this case trend, does not require allocating away from the strategic, long-only portfolio. Rather, exposure to both the strategic holdings and the trend-following alternative strategy can be gained in the same package.

A Trend Equity Primer

By Corey Hoffstein

On September 17, 2018

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

This post is available as a PDF download here.

Summary

Trend-following strategies exploit the fact that investors exhibit behavioral biases that cause trends to persist.
While many investment strategies have a concave payoff profile that reaps small rewards at the risk of large losses, trend-following strategies exhibit a convex payoff profile, one that pays small premiums with the potential of a large reward.
By implementing a trend-following strategy on equities, investors can tap into both the long-term return premium from holding equities and the convex payoff profile associated with trend following.
There are multiple ways to include a trend-following equity strategy in a portfolio, and the method of incorporation will affect the overall risk and return expectations in different market environments.
As long as careful consideration is given to whipsaw, hedging ability, and implementation costs, trend-following equity can be a potentially useful diversifier in most traditionally allocated portfolios.

A Balance of Risks

Most investors – individual and institutional alike – live in the balance of two risks: failing slow and failing fast. Most investors are familiar with the latter: the risk of large and sudden drawdowns that can permanently impair an investor’s lifestyle or ability to meet future liabilities. Slow failure, on the other hand, occurs when an investor fails to grow their portfolio at a speed sufficient to offset inflation and withdrawals.

Investors have traditionally managed these risks through asset allocation, balancing exposure to growth-oriented asset classes (e.g. equities) with more conservative, risk-mitigating exposures (e.g. cash or bonds). How these assets are balanced is typically governed by where an investor falls in their investment lifecycle and which risk has the greatest impact upon the probability of their future success.

For example, younger investors who have a large proportion of their future wealth tied up in human capital often have very little risk of failing fast, as they are not presently relying upon withdrawals from their investment capital. Evidence suggests that the risk of fast failure peaks for pre- and early-retirees, whose future lifestyle will be largely predicated upon the amount of capital they are able to maintain into early retirement. Later-stage retirees, on the other hand, once again become subject to the risk of failing slow, as longer lifespans put greater pressure upon the initial retirement capital to last.

Trend equity strategies seek to address both risks simultaneously by maintaining equity exposure when trends are positive and de-risking the portfolio when trends are negative. Empirical evidence suggests that such strategies may allow investors to harvest a significant proportion of the long-term equity risk premium while significantly reducing the impact of severe and prolonged drawdowns.

The Potential Hedging Properties of Trend Following

When investors buy stocks and bonds, they are exposing themselves to “systematic risk factors.” These risk factors are the un-diversifiable uncertainties associated with any investment. For bearing these risks, investors expect to earn a reward. For example, common equity is generally considered to be riskier than fixed income because it is subordinate in the capital structure, does not have a defined payout, and does not have a defined maturity date. A rational investor would only elect to hold stocks over bonds, then, if they expected to earn a return premium for doing so.

Similarly, the historical premium associated with many active investment strategies are also assumed to be risk-based in nature. For example, quantitatively cheap stocks have historically outperformed expensive ones, an anomaly called the “value factor.” Cheap stocks may be trading cheaply for a reason, however, and the potential excess return earned from buying them may simply be the premium required by investors to bear the excess risk.

In many ways, an investor bearing risk can be thought of as an insurer, expecting to collect a premium over time for their willingness to carry risk that other investors are looking to offload. The payoff profile for premiums generated from bearing risk, however, is concave in nature: the investor expects to collect a small premium over time but is exposed to potentially large losses (see Figure 1). This approach is often called being “short volatility,” as the manifestation of risk often coincides with large (primarily negative) swings in asset values.

Even the process of rebalancing a strategic asset allocation can create a concave payoff structure. By reallocating back to a fixed mixture of assets, an investor sells assets that have recently outperformed and buys assets that have recently underperformed, benefiting when the relative performance of investments mean-reverts over time.

When taken together, strategically allocated portfolios – even those with exposure to alternative risk premia – tend to combine a series of concave payoff structures. This implies that a correlation-based diversification scheme may not be sufficient for managing left-tail risk during bad times, as a collection of small premiums may not offset large losses.

In contrast, trend-following strategies “cut their losers short and let their winners run” by design, creating a convex payoff structure (see Figure 1).¹ Whereas concave strategies can be thought of as collecting an expected return premium for bearing risk, a convex payoff can be thought of as expecting to pay an insurance premium in order to hedge risk. This implies that while concave payoffs benefit from stability, convex payoffs benefit from instability, potentially helping hedge portfolios against large losses at the cost of smaller negative returns during normal market environments.

Figure 1: Example Concave and Convex Payoff Structures; Profit in Blue and Loss in Orange

Source: Newfound Research. For illustrative purposes only and not representative of any Newfound Research product or investment.

What is Trend Equity?

Trend equity strategies rely upon the empirical evidence² 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 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.

As shown in Figure 2, a hypothetical implementation of this strategy on large-cap U.S. equities has historically matched the long-term annualized return while significantly reducing exposure to both tails of the distribution. This is quantified in Figure 3, which demonstrates a significant reduction in both the skew and kurtosis (“fat-tailedness”) of the return distribution.

Figure 2

Figure 3

	U.S. Large-Cap Equities	Trend Equity
Annualized Return	11.1%	11.6%
Volatility	16.9%	11.3%
Skewness	-1.4	0.0
Excess Kurtosis	2.2	-1.0

Source: Newfound Research. Return data relies on hypothetical indices and is exclusive of all fees and expenses. Returns assume the reinvestment of all dividends. Trend Equity invests in U.S. Large-Cap Equity when the prior month has a positive 12-1 month total return and in 3-month U.S. Treasury Bills otherwise. The Trend Equity strategy does not reflect any 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. Past performance does not guarantee future results.

Implementing Trend Equity

With trend equity seeking to benefit from both the long-term equity risk premium and the convex payoff structure of trend-following, there are two obvious examples of how it can be implemented in the context of an existing strategic portfolio. The preference as to the approach taken will depend upon an investor’s goals.

Investors seeking to reduce risk in their portfolio may prefer to think of trend equity as a form of dynamically hedged equity, replacing a portion of their traditional equity exposure. In this case, when trend equity is fully invested, the portfolio will match the original allocation profile; when the trend equity strategy is divested, the portfolio will be significantly underweight equity exposure. The intent of this approach is to match the long-term return profile of equities with less realized risk.

On the other hand, investors seeking to increase their returns may prefer to treat trend equity as a pivot within their portfolio, funding the allocation by drawing upon both traditional stock and bond exposures. In this case, when fully invested, trend equity will create an overweight to equity exposure within the portfolio; when divested, it will create an underweight. The intent of this approach is to match the long-term realized risk profile of a blended stock/bond mix while enhancing long-term returns.

To explore these two options in the context of an investor’s lifecycle, we echo the work of Freccia, Rauseo, and Villalon (2017). Specifically, we will begin with a naïve “own-your-age” glide path, which allocates a proportion of capital to bonds equivalent to the investor’s age. We assume the split between domestic and international exposures is 60/40 and 70/30 respectively for stocks and bonds, selected to approximate the split between domestic and international exposures found in Vanguard’s Target Retirement Funds.

An investor seeking to reduce exposure to negative equity tail events could fund trend equity exposure entirely from their traditional equity allocation. Applying the own-your-age glide path over the horizon of June 1988 to June 2018, carving out 30% of U.S. equity exposure for trend equity (e.g. an 11.7% allocation for a 35 year old investor and an 8.1% allocation for a 55 year old investor) would have offered the same long-term return profile while reducing annualized volatility and the maximum drawdown experienced.

For an investor seeking to increase return, funding a position in trend equity from both U.S. equities and U.S. bonds may be a more applicable approach. Again, applying the own-your-age glide-path from June 1988 to June 2018, we find that replacing 50% of existing U.S. equity exposure and 30% of existing U.S. bond exposure with trend equity would have offered a nearly identical long-term volatility profile while increasing long-term annualized returns.

Figure 4

Source: Newfound Research. For illustrative purposes only and not representative of any Newfound Research product or investment.

Figure 5: Hypothetical Portfolio Statistics, June 1988 – June 2018

	Original Glidepath	Same Return, Decrease Risk	Increase Return, Same Risk
Annual Return	8.20%	8.25%	8.60%
Volatility	8.58%	8.17%	8.59%
Maximum Drawdown	-28.55%	-24.71%	-23.80%
Sharpe Ratio	0.61	0.64	0.65

Figure 6: Own-Your-Age Glide Paths Including Trend Equity

Source: Newfound Research. For illustrative purposes only and not representative of any Newfound Research product or investment. Allocation methodologies described in the preceding section.

A Discussion of Trade-Offs

At Newfound Research, we champion the philosophy that “risk cannot be destroyed, only transformed.” While we believe that a convex payoff structure – like that empirically found in trend-following strategies – can introduce beneficial diversification into traditionally allocated portfolios, we believe any overview is incomplete without a discussion of the potential trade-offs of such an approach.

The perceived trade-offs will be largely dictated by how trend equity is implemented by an investor. As in the last section, we will consider two cases: first the investor who replaces their traditional equity exposure, and second the investor that funds an allocation from both stocks and bonds.

In the first case, we believe that the convex payoff example displayed Figure 1 is important to keep in mind. Traditionally, convex payoffs tend to pay a premium during stable environments. When this payoff structure is combined with traditional long-only equity exposure to create a trend equity strategy, our expectation should be a return profile that is expected to lag behind traditional equity returns during calm market environments.

This is evident in Figure 7, which plots hypothetical rolling 3-year annualized returns for both large-cap U.S. equities and a hypothetical trend equity strategy. Figure 8 also demonstrates this effect, plotting rolling 1-year returns of a hypothetical trend equity strategy against large-cap U.S. equities, highlighting in orange those years when trend equity underperformed.

For the investor looking to employ trend equity as a means of enhancing return by funding exposure from both stocks and bonds, long-term risk statistics may be misleading. It is important to keep in mind that at any given time, trend equity can be fully invested in equity exposure. While evidence suggests that trend-following strategies may be able to act as an efficient hedge when market downturns are gradual, they are typically inefficient when prices collapse suddenly.

In both cases, it is important to keep in mind that convex payoff premium associated with trend equity strategies is not consistent, nor is the payoff guaranteed. In practice, the premium arises from losses that arrive during periods of trend reversals, an effect popularly referred to as “whipsaw.” A trend equity strategy may go several years without experiencing whipsaw, seemingly avoiding paying any premium, then suddenly experience multiple back-to-back whipsaw events at once. Investors who allocate immediately before a series of whipsaw events may be dismayed, but we believe that these are the costs necessary to access the convex payoff opportunity and should be considered on a multi-year, annualized basis.

Finally, it is important to consider that trend-following is an active strategy. Beyond management fees, it is important to consider the impact of transaction costs and taxes.

Figure 7Source: Newfound Research. Return data relies on hypothetical indices and is exclusive of all fees and expenses. Returns assume the reinvestment of all dividends. Trend Equity invests in U.S. Large-Cap Equity when the prior month has a positive 12-1 month total return and in 3-month U.S. Treasury Bills otherwise. The Trend Equity strategy does not reflect any 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. Past performance does not guarantee future results.

Figure 8

Conclusion

In this primer, we have introduced trend equity, an active strategy that seeks to provide investors with exposure to the equity risk premium while mitigating the impacts of severe and prolonged drawdowns. The strategy aims to achieve this objective by blending exposure to equities with the convex payoff structure traditionally exhibited by trend-following strategies.

We believe that such a strategy can be a particularly useful diversifier for most strategically allocated portfolios, which tend to be exposed to the concave payoff profile of traditional risk factors. While relying upon correlation may be sufficient in normal market environments, we believe that the potential premiums collected can be insufficient to offset large losses generated during bad times. It is during these occasions that we believe a convex payoff structure, like that empirically found in trend equity, can be a particularly useful diversifier.

We explored two ways in which investors can incorporate trend equity into a traditional profile depending upon their objective. Investors looking to reduce realized risk without necessarily sacrificing long-term return can fund their trend equity exposure with their traditional equity allocation. Investors looking to enhance returns while maintaining the same realized risk profile may be better off funding exposure from both traditional stock and bond allocations.

Finally, we discussed the trade-offs associated with incorporating trend equity into an investor’s portfolio, including (1) the lumpy and potentially large nature of whipsaw events, (2) the inability to hedge against sudden losses, and (3) the costs associated with managing an active strategy. Despite these potential drawbacks, we believe that trend-following equity can be a potentially useful diversifier in most traditionally allocated portfolios.

Bibliography

Freccia, Maxwell, and Rauseo, Matthew, and Villalon, Daniel, DC Solutions Series: Defensive Equity, Part 2. Available at https://www.aqr.com/Insights/Research/DC-Solutions/DC-Solutions-Series-Defensive-Equity-Part-2. Accessed September 2018.

Hsieh, David A. and Fung, William, The Risk in Hedge Fund Strategies: Theory and Evidence from Trend Followers. The Review of Financial Studies, Vol. 14, No. 2, Summer 2001. Available at SSRN: https://ssrn.com/abstract=250542

Lempérière, Yves, and Deremble, Cyril and Seager, Philip and Potters, Marc, and Bouchaud, Jean-Phillippe. (April, 2014), Two Centuries of Trend Following, Journal of Investment Strategies, 3(3), pp. 41-61.

Category: Risk & Style Premia Page 10 of 16

Fragility Case Study: Dual Momentum GEM

Summary­

Introduction

Global Equities Momentum (“GEM”)

Conclusion

Attack of the Clone: Lessons from Replicating Long/Short Equity

Summary­

Introduction

Replicating Long/Short Equity Returns

The Time-Varying Exposures of Long/Short Equity

Conclusion

A Carry-Trend-Hedge Approach to Duration Timing

Summary­

Introduction

Slope of the Yield Curve

Trend in Bond Returns

Safe-Haven Premium

Combining Signals

Conclusion

Bibliography

Decomposing Trend Equity

Summary­

The Simple Arithmetic of Portfolio Construction

Decomposing Trend Equity

Equity + Flat/Short

50% Equity/50% Cash + 50% Long/Short

Conclusion

A Trend Equity Primer

Summary­

A Balance of Risks

The Potential Hedging Properties of Trend Following

What is Trend Equity?

Implementing Trend Equity

A Discussion of Trade-Offs

Conclusion

Bibliography

Summary

Summary

Summary

Summary

Summary