This post is available as a PDF download here.

Summary

The benefits of diversification are often touted, but many investors feel disappointed in diversified portfolios because of the dispersion in performance of the individual holdings.
In the context of three different unconstrained sleeves, we look at a way to measure and visualize the benefit (or detriment) of diversification based on achieving different objectives.
Through this lens, we get a picture of how good or bad the results might have been, which can lead to confidence either in the robustness of the allocation or in the need to take a different approach.
Since we only experience one path of history, it is difficult to assess the benefit of diversification unless we consider what could have happened.
We believe that taking a systematic approach does not fully remove the art of the analysis but can remove some of the behavioral biases that make sticking with a portfolio difficult in the first place.

Introduction

Diversification is a standard risk management tool in any portfolio. Reducing the impact of idiosyncratic risks in individual investments by holding a suite of stocks, asset classes, strategies, etc. produces a smoother investment ride most of the time and reduces the risk of negative surprises.

But in a world where we only experience one outcome out of the multitude of possibilities, gauging the benefit of diversification is difficult. It is even hard to do in hindsight, not so much because we can’t but more often that we won’t. The results already happened.

Over a single time period with no rebalancing, a diversified portfolio will underperform the best asset that it holds. This is a mathematical fact when there is any dispersion in the returns of the assets and it is why we have said that diversification will always disappoint. Our natural behavioral tendencies can often get the better of us, despite the fact that diversification might be doing a great job, especially when examined through the appropriate lens and measured in the context of what could have happened.

Last summer, we published a presentation entitled Building an Unconstrained Sleeve. In it, we looked at ways to combine traditional and non-traditional assets and strategies to target specific objectives: equity hedging, absolute return, and equity-like with downside management.

Now that we have 15 months of subsequent data for all the underlying strategies, we want to revisit that piece and explore the benefit of diversification in the context of hindsight.

A Recap of the Process

As a quick refresher, we included seven strategies and asset classes in the construction of our unconstrained sleeves:

Long/flat trend-following equities
Minimum volatility equities
Macro trend-following (managed futures)
Macro risk parity
Macro value
Macro income
Intermediate U.S. Treasuries

While these strategies are surely not exhaustive, they cover a range of factors (value, momentum, low volatility, etc.) and a global set of asset classes (equities, bonds, commodities, and currencies) commonly included in unconstrained sleeves. They were also selected because many of these strategies are conveniently packaged as ETFs or mutual funds, making the resulting sleeves more easily implementable.

Source: St. Louis Federal Reserve, MSCI, Salient, HFRI, 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.

Over the 15 months, world equity was by far the best performer and the spread between best-performing and worst-performing positions exceeded 20 percentage points. If you wanted high returns – and going back to our statement about how diversification will always disappoint – you could have just held world equities and been quite content.

But putting ourselves back in June 2017, we did not know a priori that simply holding equities would have generated the highest returns. Looking at this type of chart in November 2008 would have led to a very different emotional conclusion.

The aim of our original study was to develop unconstrained sleeves that would meet their objectives regardless of how the future played out. Therefore, we employed a simulation-based method that aimed to preserve some of the unique correlation structure between the strategies across different market environments and reduce the risk of overfitting to a single realization of history. With this approach, we constructed portfolios that targeted three different objectives that investors might be interested in:

Equity hedge – designed to offset significant equity losses.
Absolute return – designed to create a stable and consistent return stream in all environments.
Equity-like – designed to capture significant equity upside with reduced downside.

(Note: Greater detail about portfolio construction process, strategy descriptions, and performance attributes of each strategy can be found in our original presentation.)

But were our constructed portfolios successful in achieving their objectives out-of-sample? To analyze this question, as well as explore the benefits/detractors of diversification for each objective, we will calculate the distribution of what could have happened. The hope is that, each strategy would perform well relative to all other possible portfolios that could have been chosen for the sleeve.

Saying exactly what portfolios we could have chosen is where a little art comes into play. For example, in the equity-like strategies, it is difficult to say that a 100% bond portfolio would have ever been a viable option and therefore may not be an apt out-of-sample comparison.

However, since our original process did not have any specific override for these intuitive constraints, and since we do not wish to assert after-the-fact which portfolios would have been rejected, we will allow the entire potential allocation space to be fair game in our comparison.

There are a number of ways to sample the set of allocations over the 7 asset classes that could have formed the portfolios for each sleeve. Perhaps the most obvious choice would be to sample uniformly over the possible allocations. The issue to balance in this case is coverage of the space (a 6-dimensional simplex) with the number of samples. To be 95% confident that we sampled an allocation above 95% for only a single asset class would require nearly 200 million samples. We have used modified Sobol sequences in the past to ensure coverage of more of the space with fewer points. However, in the current case, to mimic the rounding that is often found in portfolio allocations, we will use a lattice of points spaced 2.5% apart covering the entire space. This requires just under 10 million points in the simulations.

Equity Hedge

This sleeve was designed to offset significant equity losses by limiting downside capture. The resulting optimized portfolio was relatively concentrated in two main positions that historically have exhibited low-to-negative correlations to equities and exhibited potential crisis alpha during significant and prolonged drawdowns.Source: St. Louis Federal Reserve, MSCI, Salient, HFRI, CSI Analytics. Calculations by Newfound Research.

The down capture this portfolio during the out-of-sample period was 0.44. This result falls in the 70^th percentile (that is, better than 70% of the other sample portfolios and where lower down-capture is better) when compared to the 10 million possible other portfolios we could have originally selected. Not surprisingly, the 100% intermediate-term Treasury portfolio had the best down capture (-0.05) over the out-of-sample. Of the portfolios with better down capture, Intermediate Treasuries and Macro – Income were generally the highest allocations.

This does not come as much of a surprise to anyone who has followed the managed futures space for the last 15 months. The category largely remains in a multi-year drawdown (peaking in early 2014), but it has also done little to offset the rapid sell-offs seen in equities in 2018. Therefore, with the full benefit of hindsight, any allocation to Macro – Trend in the original portfolio would be a detriment realizing our out-of-sample objective.

Yet even with this lackluster performance, an out-of-sample realized 70^th percentile result over a short, 15-month horizon is a result to be pleased with.

Absolute Return

This sleeve was designed to seek a stable and consistent return stream in all market environments. We aimed to accomplish this by utilizing a risk parity approach. As expected, this sleeve holds all asset classes and is very well diversified across them.

Source: St. Louis Federal Reserve, MSCI, Salient, HFRI, CSI Analytics. Calculations by Newfound Research.

To measure the success of the risk parity over the live period, we will look at the Gini coefficient for each of the ten million potential portfolios we could have initially selected. The Gini coefficient quantifies the equality of the distribution, with a value of 1 representing 100% concentration and 0 representing perfect equality.

The Gini coefficient of the actual portfolio was 0.25 which was in the 99.8^th percentile of possible outcomes (i.e. highly diversified on a relative basis). Here, the percentile estimate is padded by the fact that many of the simulated portfolios (e.g. the 100% ones) would clearly not be close to equal risk contribution.

Did our original portfolio achieve its out-of-sample goal? Here, we can evaluate success as to whether the realized contribution to risk of each exposure was close to equivalent; i.e. did we actually achieve risk parity as desired? We can see below that indeed we did, with the main exception of Macro – Trend, which was the most volatile asset class over the period.

Source: St. Louis Federal Reserve, MSCI, Salient, HFRI, CSI Analytics. Calculations by Newfound Research.

Over the sample space of potential portfolios, the portfolio with the minimum out-of-sample Gini coefficient (0.08) was tilted toward the less volatile and more diversifying asset classes (Intermediate Treasuries and Macro – Income). Even so, due to the limited granularity of the sampled portfolios, the risk contribution of Macro – Income was still half of that for each of the other strategies.

It is also worth noting how similar this solution is – generated with the complete benefit of hindsight – to our originally constructed portfolio.

Source: St. Louis Federal Reserve, MSCI, Salient, HFRI, CSI Analytics. Calculations by Newfound Research.

Equity-like with Downside Management

This sleeve was designed in an effort to capture equity market growth while managing the risk of severe and prolonged drawdowns. It was tilted toward the equity-like exposures with a split among risk management styles (trend, minimum volatility, macro strategies, etc.). The allocation to U.S. Treasuries is very small.

Source: St. Louis Federal Reserve, MSCI, Salient, HFRI, CSI Analytics. Calculations by Newfound Research.

For this portfolio, we have two variables to analyze: the up capture relative to global equities and the Ulcer index, a measure of the severity and duration of drawdowns. In the construction of the sleeve, the target was to keep the Ulcer index less than 25% of the value for global equities. The joint distribution of these quantities over the live period is shown below with the actual values over the live period for the sleeve indicated.

The realized Ulcer level was 68% of that of world equity – a far cry from the 25% that the portfolio was optimized for – and was in the 42^nd percentile while the up capture of 0.60 was in the 93^rd percentile.

With the explicit goal of achieving a relative Ulcer level, a comparison against the entire potential allocation space of 10 million portfolios is not appropriate. Therefore, we reduce the set of 10 million comparative portfolios to only those that would have given a relative Ulcer index less than 25% compared to world equities, eliminating approximately 40% of possible portfolios.

The distributions of allocations to each of the strategies in the acceptable subset are shown below. We can see that the more diversifying strategies take on a larger range of allocations.

Interestingly, looking only over this subset of the original 10 million portfolios improves the out-of-sample up capture of our originally constructed portfolio to the 99^th percentile but does not change the percentile of the Ulcer index over the live period. Why is this?

The correlation of the relative Ulcer index over the live period with that over the historical period is only 0.1, indicating that the out of sample data did not line up with our expectations at first glance. However, this makes sense when we recall that the optimization was carried out using data from much more extreme market environments (think 2001 and 2008). It is a good reminder that, just because you optimize for a certain parameter value does not mean you will get it over the live data.

Higher up-capture typically goes hand-in-hand with a higher Ulcer index, as higher return often requires bearing more risk. Therefore, one way to standardize our measures across the potential set of portfolios is to calculate the ratio of up-capture to the Ulcer index. With this transformation, the risk-adjusted up capture falls in the 87^th percentile over the set of sample allocations, indicating a very high realized risk-adjusted return.

Conclusion

We only experience one path of the world and do not know the infinite alternate course history could have taken. But it is exactly this infinitude of alternate states that diversification is meant to address.

Diversification generally has no apparent benefit unless we envision what could have happened. Unfortunately our innate natures make this difficult. We do not often value our realized path in this context. After all, none of these alternate states actually happened, so it is difficult to picture what we did not experience.

A quantitative approach can yield a systematic way to evaluate the benefit (or detriment) of diversification. This way, we are not relying as much on intuition – how did our performance feel? – and are looking through a more objective lens at our initial decisions.

In the examples using the Unconstrained Sleeves, diversification focused on more than just returns. The objectives that initially went in to the portfolio construction were the parameters of interest.

Taking a systematic approach does not fully remove the art of the analysis, as was evident in the construction of the potential sample of portfolios used in the comparisons, but having a process can remove some of the behavioral biases that make sticking with a portfolio difficult in the first place.

When Simplicity Met Fragility

By Corey Hoffstein

On October 29, 2018

In Craftsmanship, Portfolio Construction, Risk Management, Weekly Commentary

This post is available as a PDF download here.

Summary

Research suggests that simple heuristics are often far more robust than more complicated, theoretically optimal solutions.
Taken too far, we believe simplicity can actually introduce significant fragility into an investment process.
Using trend equity as an example, we demonstrate how using only a single signal to drive portfolio allocations can make a portfolio highly sensitive to the impact of randomness, clouding our ability to determine the difference between skill and luck.
We demonstrate that a slightly more complicated process that combines signals significantly reduces the portfolio’s sensitivity to randomness.
We believe that the optimal level of simplicity is found at the balance of diversification benefit and introduced estimation risk. When a more complicated process can introduce meaningful diversification gain into a strategy or portfolio with little estimation risk, it should be considered.

Introduction

In the world of finance, simple can be surprisingly robust. DeMiguel, Garlappi, and Uppal (2005)¹, for example, demonstrate that a naïve, equal-weight portfolio frequently delivers higher Sharpe ratios, higher certainty-equivalent returns, and lower turnover out-of-sample than competitive “optimal” allocation policies. In one of our favorite papers, Haldane (2012)²demonstrates that simplified heuristics often outperform more complicated algorithms in a variety of fields.

Yet taken to an extreme, we believe that simplicity can have the opposite effect, introducing extreme fragility into an investment strategy.

As an absurd example, consider a highly simplified portfolio that is 100% allocated to U.S. equities. Introducing bonds into the portfolio may not seem like a large mental leap but consider that this small change introduces an axis of decision making that brings with it a number of considerations. The proportion we allocate between stocks and bonds requires, at the very least, estimates of an investor’s objectives, risk tolerances, market outlook, and confidence levels in these considerations.³

Despite this added complexity, few investors would consider an all-equity portfolio to be more “robust” by almost any reasonable definition of robustness.

Yet this is precisely the type of behavior we see all too often in tactical portfolios – and particularly in trend equity strategies – where investors follow a single signal to make dramatic allocation decisions.

So Close and Yet So Far

To demonstrate the potential fragility of simplicity, we will examine several trend-following signals applied to broad U.S. equities:

Price minus the 10-month moving average
12-1 month total return
13-minus-34-week exponential moving average cross-over

Below we plot over time the distance each of these signals is from turning off. Whenever the line crosses over the 0% threshold, it means the signal has flipped direction, with negative values indicating a sell and positive values indicating a buy.

In orange we highlight those periods where the signal is within 1% of changing direction. We can see that for each signal there are numerous occasions where the signal was within this threshold but avoided flipping direction. Similarly, we can see a number of scenarios where the signal just breaks the 0% threshold only to revert back shortly thereafter. In the former case, the signal has often just managed to avoid whipsaw, while in the latter it has usually become unfortunately subject to it.

Source: Kenneth French Data Library. Calculations by Newfound Research.

Is the avoidance of whipsaw representative of the “skill” of the signals while the realization of whipsaw is just bad luck? Or might it be that the avoidance of whipsaw is often just as much luck as the realization of whipsaw is poor skill? How can we determine what is skill and what is luck when there are so many “close calls” and “just hits”?

What is potentially confusing for investors new to this space is that academic literature and practitioner evidence finds that these highly simplified approaches are surprisingly robust across a variety of investment vehicles, geographies, and time periods. What we must stress, however, is that evidence of general robustness is not evidence of specific robustness; i.e. there is little evidence suggesting that a single approach applied to a single instrument over a specific time horizon will be particularly robust.

What Randomness Tells Us About Fragility

To emphasize the potential fragility on utilizing a single in-or-out signal to drive our allocation decisions, we run a simple test:

Begin with daily market returns
Add a small amount of white noise (mean 0%; standard deviation 0.025%) to daily market returns
Calculate a long/flat trend equity strategy using 12-1 month momentum signals⁴
Calculate the rolling 12-month return of the strategy minus the alternate market history return.
Repeat 1,000 times to generate 1,000 slightly alternate histories.

The design of this test aims to deduce how fragile a strategy is via the introduction of randomness. By measuring 12-month rolling relative returns versus the modified benchmarks, we can compare the 1,000 slightly alternate histories to one another in an effort to determine the overall stability of the strategy itself.

Now bear with us, because while the next graph is a bit difficult to read, it succinctly captures the thrust of our entire thesis. At each point in time, we first calculate the average 12-month relative return of all 1,000 strategies. This average provides a baseline of expected relative strategy performance.

Next, we calculate the maximum and minimum relative 12-month relative performance and subtract the average. This spread – which is plotted in the graph below – aims to capture the potential return differential around the expected strategy performance due to randomness. Or, put another way, the spread captures the potential impact of luck in strategy results due only to slight changes in market returns.

Source: Kenneth French Data Library. Calculations by Newfound Research.

We can see that the spread frequently exceeds 5% and sometimes even exceeds 10. Thus, a tiny bit of injected randomness has a massive effect upon our realized results. Using a single signal to drive our allocation appears particularly fragile and success or failure over the short run can largely be dictated by the direction the random winds blow.

A backtest based upon a single signal may look particularly good, but this evidence suggests we should dampen our confidence as the strategy may actually have just been the accidental beneficiary of good fortune. In this situation, it is nearly impossible to identify skill from luck when in a slightly alternate universe we may have had substantially different results. After all, good luck in the past can easily turn into misfortune in the future.

Now let us perform the same exercise again using the same random sequences we generated. But rather than using a single signal to drive our allocation we will blend the three trend-following approaches above to determine the proportional amount of equities the portfolio should hold.⁵ We plot the results below using the same scale in the y-axis as the prior plot.

Source: Kenneth French Data Library. Calculations by Newfound Research.

We can see that our more complicated approach actually exhibits a significant reduction in the effects of randomness, with outlier events significantly decreased and far more symmetry in both positive and negative impacts.

Below we plot the actual spreads themselves. We can see that the spread from the combined signal approach is lower than the single signal approach on a fairly consistent basis. In the cases where the spread is larger, it is usually because the sensitivity is arising from either the 10-month SMA or 13-minus-34-week EWMA signals. Were spreads for single signal strategies based upon those approaches plotted, they would likely be larger during those time periods.

Source: Kenneth French Data Library. Calculations by Newfound Research.

Conclusion

So, where is the balance? How can we tell when simplicity creates robustness and simplicity introduces fragility? As we discussed in our article A Case Against Overweighting International Equity, we believe the answer is diversificationversus estimation risk.

In our case above, each trend signal is just a model: an estimate of what the underlying trend is. As with all models, it is imprecise and our confidence level in any individual signal at any point in time being correct may actually be fairly low. We can wrap this all together by simply saying that each signal is actually shrouded in a distribution of estimation risk. But by combining multiple trend signals, we exploit the benefits of diversification in an effort to reduce our overall estimation risk.

Thus, while we may consider a multi-model approach less transparent and more complicated, that added layer of complication serves to increase internal diversification and reduce estimation risk.

It should not go overlooked that the manner in which the signals were blended represents a model with its own estimation risk. Our choice to simply equally-weight the signals indicates a zero-confidence position in views about relative model accuracy and relative marginal diversification benefits among the models. Had we chosen a more complicated method of combining signals, it is entirely possible that the realized estimation risk could overwhelm the diversification gain we aimed to benefit from in the first place. Or, conversely, that very same added estimation risk could be entirely justified if we could continue to meaningfully improve diversification benefits.

If we return back to our original example of a 100% equity portfolio versus a blended stock-bond mix, the diversification versus estimation risk trade-off becomes obvious. Introducing bonds into our portfolio creates such a significant diversification gain that the estimation risk is often an insignificant consideration. The same might not be true, however, in a tactical equity portfolio.

Research and empirical evidence suggest that simplicity is surprisingly robust. But we should be skeptical of simplicity for the sake of simplicity when it foregoes low-hanging diversification opportunities, lest we make our portfolios and strategies unintentionally fragile.

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.

Flirting with Models

The Research Library of Newfound Research

Measuring the Benefit of Diversification

Summary

Introduction

A Recap of the Process

Equity Hedge

Absolute Return

Equity-like with Downside Management

Conclusion

When Simplicity Met Fragility

Summary

Introduction

So Close and Yet So Far

What Randomness Tells Us About Fragility

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

Measuring the Benefit of Diversification

Summary­

Introduction

A Recap of the Process

Equity Hedge

Absolute Return

Equity-like with Downside Management

Conclusion

When Simplicity Met Fragility

Summary­

Introduction

So Close and Yet So Far

What Randomness Tells Us About Fragility

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

Summary

Summary

Summary

Summary

Summary