The Research Library of Newfound Research

Category: Risk Management Page 6 of 11

Dart-Throwing Monkeys and Process Diversification

This post is available as a PDF download here.

Summary­

  • This week’s commentary is a short addendum to last week’s piece, attempting to serve as a (very) brief and simplified summary of process diversification.
  • Volatility is only one way of measuring risk; dispersion in terminal wealth is another.
  • Using simulations of dart-throwing monkeys, we plot the dispersion in terminal wealth for different levels of portfolio and manager diversification.
  • We find that increased diversification within a portfolio as well as increased diversification across managers can lead to more consistent portfolio outcomes.

Introduction

In last week’s commentary (What do portfolios and teacups have in common?), we explored at great length the potential benefits of diversification in the domains of what, how, and when.

The crux of our argument is that for investors, return dispersions across time (i.e. “volatility”) can be a potentially misleading risk characteristic and that it is important to consider the potential dispersion in terminal wealth as well.

These are by no means original or unique thoughts.  Often the advisors and institutions we work with intuitively understand them: they just have not been presented with the math to justify them.

Therefore, in contrast to last week’s rather expansive note, we aim to keep this week’s note short, simple, and punchy in an effort to drive how manager / process diversification can help deliver more consistent outcomes.

Dart-Throwing Monkeys

Consider the following experiment.

We begin with thousands and thousands of dart-throwing monkeys.  Every month, the monkeys throw their darts at a board that determines how they will be invested for the next month.  In this hypothetical scenario, we will assume that the monkeys are investing in different industry groups.1

Some monkeys are “concentrated managers,” throwing just a single dart and holding that pick for the next month.  Other monkeys are more diversified, throwing up to 30 darts each month and equally allocating their portfolio across their investments.  Portfolio sizes can be either 1, 5, 10, 15, 20, 25, or 30 equally-allocated investments.

It is our job, as an allocator, to choose different monkeys to invest with.  Do we invest with just 1 concentrated monkey manager? Five different diversified managers? How much difference does it really make at the end of the day?

We learn in Finance 101 that once we diversify our portfolio sufficiently, we have eliminated nonsystematic risk.  But does that mean we expect the portfolios to necessarily end up in the same place?

As an example, if we pick 10 dart-throwing monkeys who each pick 10 investments per month, how different would we expect our final wealth level to be from another allocator who picks 10 different dart-throwing monkeys who each pick 10 investments per month?

Process Diversification and Terminal Wealth Dispersion

Below we plot the dispersion in terminal wealth2 as a function of (1) the number of securities picked by each monkey manager and (2) the number of monkey managers we allocate to.

As an example of how to read this graph, the orange line tells us about portfolios comprised of monkey managers who pick five investments each.  As we move from left to right, we learn about the dispersion in terminal wealth based upon the number of managers we allocate to.

We can think of this two ways.  First, we can think of it as potential dispersion in results among our peers who make the same type of decision (e.g. picking 5 managers who pick 5 investments each) but different specific choices (e.g. might pick different managers). Second, we can think of this as the dispersion in possible results if we were able to live across infinite universes simultaneously.

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

 

Unfortunately, we cannot live across infinite universes and this graph tells us that choosing a single, highly concentrated manager can lead to wildly different outcomes depending upon the manager we select.

As the managers further diversify and we further diversify among managers, this dispersion in potential outcomes decreases.3

Conclusion

The intuition behind these results is simple:

  • More diversified managers are more likely to overlap in portfolio holdings with one another, and therefore are likely to have more similar returns.
  • Similarly, as the number of managers we choose goes up, so does the likelihood of overlap in holdings with a peer who also selects the same number of managers.

It is equally valid to interpret this analysis as saying there is greater opportunity for out-performance in taking concentrated bets in highly concentrated managers.  We would argue this is more right thinking: the win condition requires both that we pick the right managers and the managers pick the right stocks.  While a little bit of diversification can go a long way here in clipping outlier events, the dispersion can still far exceed a more diversified approach.

At Newfound, we prefer the less wrong approach.  Allocations to a few diversified managers each taking a different approach can lead to significantly less dispersion in outcomes and, therefore, allow for better financial planning.

 


 

What do portfolios and teacups have in common?

This post is available as a PDF download here.

Summary­

  • Portfolio risk is often measured as the variance of returns over time. Another form of risk is the variance of terminal wealth that can arise from small variations in strategy inputs or asset returns.
  • Strategies or portfolios that are more sensitive to small changes in inputs are inherently “fragile.”
  • Fragile strategy design makes it difficult to rely upon backtests or historical results in setting forward expectations.
  • We explore how diversification across the “what,” “how,” and “when,” axes of portfolio construction can help reduce strategy fragility.

Introduction

At Newfound, we spend a lot less time trying to figure out how to be more right than we spend trying to figure out how to be less wrong.  One area of particular interest for us is the idea of unintended bets: the exposures in a portfolio we may not even be aware of.  And if we knew we had the exposure, we might not even want it.

For example, consider a portfolio that invests in either broad U.S., broad international, or broad emerging market equities based upon valuations.  A significant tilt towards non-U.S. assets may be a valuation-driven decision, but for U.S. investors it creates significant exposure to fluctuations in the U.S. dollar versus foreign currencies.

Of course, exposures are not limited only to assets.  Exposures may be broader macro-economic, stylistic, thematic, geographic, or even political factors.

These unintended bets can go far beyond explicit and implicit exposures.  In our example, the choice of how to measure value may lead to meaningfully different portfolios, despite the same overarching thesis.  For example, a naïve CAPE ratio versus adjusting for differences in relative sector composition dramatically alters the view of whether international equities are significantly cheaper than U.S. equities.  These potential differences capture what we like to call “model specification risk.”

Finally, we can be subject to unintended bets based upon when the portfolio is re-evaluated and reconstituted.  Evaluating valuations in January, for example, may lead to a different decision versus evaluating them in July.

How can we avoid these unintended bets?  At Newfound, we believe that the answer falls back to diversification: not only in the traditional sense of what we invest in, but also across how we make decisions and when we make them.

When left uncontrolled, unintended bets can make a strategy incredibly fragile.

What, precisely, does it mean for a strategy to be fragile?  A strategy is fragile when small variations of strategy inputs – be it asset returns or other measures – lead to meaningful dispersion in realized results.

Now we want to distinguish between volatility and fragility.  Volatility is the dispersion of strategy returns across time, while fragility is the dispersion in end-of-period wealth across variations of the strategy.

As an example, a portfolio that invests only in the S&P 500 is very volatile but not particularly fragile.  Given the last ten years of returns for the S&P 500, slight variations in annual returns would not lead to significant dispersion in end-of-period wealth.  On the other hand, a strategy that flips a coin every December and invests for the next year in the S&P 500 when it lands on heads or short-term U.S. Treasuries when it lands on tails would have lower expected volatility than the S&P 500 but would be much more fragile.  We need simply consider a few scenarios (e.g. all heads or all tails) to understand the potential dispersion such a strategy is subject to.

In the remainder of this commentary, we will demonstrate how diversification across the whathow, and when axes can reduce strategy fragility.

The Experiment Setup

Since a large degree of our focus at Newfound is on managing trend equity mandates, we will explore fragility through the lens of the style of measuring trends.  For those unfamiliar with the approach, trend equity strategies aim to capture a significant portion of equity market growth while avoiding substantial and prolonged drawdowns through the application of trend following.  A naïve implementation of such an idea would be to invest in the S&P 500 when its prior 12-month return has been positive and invest in short-term U.S. Treasuries otherwise.

To learn something about the fragility of a strategy, we are going to have to inject some randomness.  After all, no amount of history will tell us about the fragility of a teacup that has spent its entire life sitting on a shelf; we will need to see it fall on the floor to actually learn something.

As with our recent commentary When Simplicity Met Fragility, we will inject randomness by adding white noise to asset returns. Specifically, we will add to daily returns a draw from a random normal distribution with mean 0% and standard deviation 0.025%. Using this slightly altered history, we will then run our investment strategy.

By performing this process a large number of times (10,000 in this commentary), we can explore how the outcome of the strategy is impacted by these slight variations in return history.  The greater the dispersion in results, the more fragile the strategy is.

To demonstrate how diversification across the three different axes can affect fragility, we will start with a naïve trend equity strategy – investing in broad U.S. equities using a single trend model that is rebalanced on a monthly basis – and vary the three components in isolation.

The What

The “what” axis simply asks, “what are we invested in?”

How can our choice of “what” affect fragility?  Consider a slight variation to our coin-flip strategy from before.  Instead of flipping a single coin, we will now flip two coins.  The first coin determines whether we invest 50% of the portfolio in either the S&P 500 or short-term U.S. Treasuries, while the second coin determines whether we invest the other 50% of the portfolio in either the Russell 1000 or short-term U.S. Treasuries.

In our single coin example, each year we expected to invest in the S&P 500 50% of the time and in short-term U.S. Treasuries 50% of the time.  With two coins, we now expect to be fully invested 25% of the time, partially invested 50% of the time, and divested 25% of the time.

Let’s take this notion to further limits.  Consider now flipping 100 coins where each determines the allocation decision for 1% of our portfolio, where heads leads to an investment in a large-cap U.S. equity portfolio and tails means invest in short-term U.S. Treasuries. Now being fully invested or divested is an infinitesimally small probability event; in fact, for a given year there is a 95% chance that your allocation to equities falls between 40-60%.1

Even though we’ve applied the exact same process to each investment, diversifying across more investments has dramatically reduced the fragility of our coin-flipping strategy.

Now let’s translate this from the theoretical to the practical.  We will begin with a simple trend following strategy that invests in the underlying asset when prior 12-1 month returns have been positive or invests in the risk-free rate, re-evaluating the trend at the end of each month.

To explore the impact of diversifying our what, we will implement this strategy five different ways:

  • A single in-or-out decision on broad U.S. equities.
  • Applied across 5 equally-weighted U.S. equity industry groups.
  • Applied across 12 equally-weighted U.S. equity industry groups.
  • Applied across 30 equally-weighted U.S. equity industry groups.
  • Applied across 48 equally-weighted U.S. equity industry groups.

The graph below plots the distribution of log difference in terminal wealth against the median outcome for each of these five approaches.  Lines within each “violin” show the 25th, 50th, and 75thpercentiles.

The graph clearly demonstrates that by increasing our exposure across the “what” axis, the dispersion in terminal wealth is dramatically reduced.

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

But why is reduced dispersion in terminal wealth necessarily better?

It implies a greater consistency in outcome, which is not only important for setting forward expectations, but is also important for evaluating past performance (whether backtested or live).  This evidence tells us that if we are evaluating a trend equity strategy that employs a single model to make in-or-out decisions on broad U.S. equities on a monthly basis, it will be nearly impossible to tell whether the realized results are in line with reasonable expectations or overly optimistic (we can probably guess that they aren’t overly pessimistic, as those sorts of returns typically aren’t marketed).

To justify a concentration in the “what” axis, we would have to demonstrate that the worst-case scenarios would still represent a meaningful improvement in expected terminal wealth versus a more diversified approach.

It should be noted that our experiment design prohibits dispersion from every being fully reduced, as we are injecting randomness into past returns.  Even if no strategy is applied, there will be some inherent dispersion in final wealth. For example, below we plot the dispersion that occurs simply from adding randomness to past returns with a buy-and-hold approach.

Increasing the number of assets in the portfolio inherently reduces dispersion for buy-and-hold because diversification helps drive the expected impact of the injected randomness towards its mean: zero.  With only one asset, on the other hand, outlier events are free to wreak havoc on results.

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

Note that adding a strategy on top of buy-and-hold can exacerbate the fragility issue, making diversification that much more important.

The How

The “how” axis asks, “how are we making investment decisions.”

Many investors are already somewhat familiar with diversification along the “how” axis, often diversifying their active exposures across multiple managers who might have similar investment mandates but slightly different processes.

We like to call this “process diversification” and think of it as akin to the parable of the blind men and the elephant.  Each blind man touches a different part of the elephant and pronounces his belief in what he is touching based upon his isolated view.  The blind man touching the leg, for example, might think he is touching a sturdy tree while the blind man touching the tail might believe he is grabbing a rope.

None is correct in isolation but taken together we may gain a more well-rounded picture.

Similarly, two managers may claim to invest based upon valuations, but the manner in which they do so gives them a very different picture of where value can be found.

The idea of process diversification was explored in the 1999 paper “Do You Need More than One Manager for a Given Equity Style?” by Franklin Fant and Edward O’Neal.  Fant and O’Neal found that while a multi-manager approach does very little for return variability across time (i.e. portfolio volatility), it does a lot for end-of-period wealth variability. They find this to be true across almost all equity style box categories.  In other words: taking a multi-manager approach can reduce fragility.

Let us return to our prior coin flip example.  Instead of making a choice to invest in the S&P 500 based upon a coin-flip, however, we will combine a number of different signals.  For example, we might flip a coin, roll a die, measure the weather, and look at the second hand of a clock.  Each signal gives us some sort of in-or-out decision, and we average these decisions together to get our allocation.  As with before, as we incorporate more signals, we decrease the probability that we end up with extreme allocations, leading to a more consistent terminal wealth distribution.

Again, we should stress here that the objective is not just outright elimination of dispersion in terminal wealth.  After all, if that were our sole pursuit, we could simply stuff our money under our mattress.  Rather, assuming we will be implementing some active investment strategy that we hope has a positive long-term expected return, our aim should be to reduce the dispersion in terminal wealth for that strategy.

Of course, in investing we would not expect the processes to be entirely independent. With trend following, for example, most popular models are actually mathematically linked to one another, and therefore generate signals that are highly correlated.  Nevertheless, even modest diversification can have meaningful benefits with respect to strategy fragility.

To explore the impact of diversification along the how axis, we implement our trend following strategy six different ways.  Each invests in broad U.S. equities and rebalances monthly but differs in the number of trend-following models employed.2

The results are plotted below.

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

Again, we can see that increased diversification across the how axis dramatically reduces dispersion in terminal wealth.  Our takeaway is largely the same: without an ex-ante view as to which particular model (or group of models) is best (i.e. a view of how to be more right), diversification can lead to greater consistency in results. We will be less wrong.

A subtler conclusion of this analysis is that it should be very, very difficult to necessarily conclude that one model is better than another.  We can see that if we risk selecting just one model to govern our process, seemingly minor variations in historical returns leads can lead to dramatically different terminal wealth results, as evidenced by the bulging distribution.  Inverting this line of thinking, we should also be suspect of any backtest that seeks to demonstrate the superiority of a given model using a single backtest.  For example, just because a 12-1 month total return model performs better than a 10-month moving average model on historical S&P 500 returns, we should be highly skeptical as to the robustness of the conclusion that the 12-1 model is best.

The When

Then “when” axis asks, “when are we making our investment decision?”

This is an oft overlooked question in public markets, but it is commonly addressed in the world of private equity and venture capital.  Due to the illiquid nature of those markets, investors will often attempt to diversify their business cycle risk by establishing positions in multiple funds over time, giving them exposure to different “vintages.” The idea here is simple: the opportunity set available at different points in time can vary and if we allocate all of our earmarked capital to a particular year, we may miss out on later opportunities.

Consider our original coin-flipping example where we flipped a single coin every December to determine whether we would buy the S&P 500 or hold our capital in short-term Treasuries.  But why was it necessary that we make the decision in December?  Why not July?  Or January? Or September?

While we would not expect there to be point-in-time risk for coin flipping, we can still consider the net effect of a vintage-based allocation methodology. Here we will assume that we flip a coin each month and rebalance 1/12thof our capital based upon the result.

Again, the probability of allocating to the extremes (100% invested or 100% divested) is dramatically reduced (each has approximately a 0.02% chance of occurring) and we reduce strategy fragility to any specific coin flip.

But just how impactful is this notion?  Below we plot the rolling 1-year total return difference between two 60% S&P 500 / 40% 5-year U.S. Treasury fixed-mix portfolios, with one being rebalanced in February and one in August.  Even for this highly simplified example, we can see that the total return spread between the two portfolios blows out to over 700 basis points in March 2010 due to the fact that the February portfolio rebalanced back into equities at nearly the exact bottom of the crisis.

Source: Global Financial Data. Past performance is not an indicator of future results.  Performance is backtested and hypothetical. Performance figures are gross of all fees, including, but not limited to, manager fees, transaction costs, and taxes. Performance assumes the reinvestment of all distributions.

To increase diversification across the “when” axis, we want to increase the number of vintages we deploy. For our trend following example, we will assume that the portfolio allocates between broad U.S. equities and the risk-free rate based upon a single model, but with an increasing number of evenly-spaced vintages.  Again, we will run 10,000 simulations that each slightly perturb historical U.S. equity market returns and compare the terminal wealth variation for approaches that employ a different number of vintages.

We can see in the graph below that, as with the other axes of diversification, as we increase the number of vintages employed, the variance decreases.  While the 25thand 75thpercentiles do not decrease as dramatically as for the other axes, we can see that the extreme variations are reined in substantially when we move from 1 monthly tranche to 4 weekly tranches.

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

Conclusion

We see two critical conclusions from this analysis:

  • To develop confidence in achieving our objective we have to consider our sensitivity to unintended bets that may be included within the portfolio.
  • Fragility makes it incredibly difficult to distinguish between luck and skill, particularly as strategy fragility increases. This is true for both backtested and live performance.

To conclude our analysis, below we present a graph that combines diversification across all three axes.  We again run 10,000 samples, randomly perturbing returns. For each sample, we then run four variations:

  • A single, randomly selected model run in broad U.S. equities that is rebalanced monthly.
  • A random selection of 3 models run on 5 industry groups in 2 bi-weekly tranches.
  • A random selection of 6 models run on 12 industry groups in 4 weekly tranches.
  • A random selection of 9 models run on 30 industry groups in 20 daily tranches.

It should come as no surprise that as we increase the amount of diversification across all three axes, the dispersion in terminal wealth is dramatically reduced.3

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

It is also important to note that while our analysis focused on trend following strategies, this same line of thinking applies across all investment approaches.  As an example, consider a quantitative value manager who buys the top five cheapest stocks, as measured by price-to-book, in the S&P 500 each December and then holds them for the next year.  Questions worth pondering are:

  • What does it say about our conviction when the 6thstock in the list is incredibly close to the 5thstock?
  • What happens if some of our measures of book value are incorrect (or even just outdated)?
  • How different would the portfolio look if we ranked on another value measure (e.g. price-to-earnings)?
  • How different would the opportunity set be if we ranked every June versus every December?

While low levels of diversification across the what, how, and when axes are not necessarily an indicator that a model is inherently fragile, it should be a red flag that more effort is required to disprove that it is not fragile.

Measuring the Benefit of Diversification

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:

  1. Equity hedge – designed to offset significant equity losses.
  2. Absolute return – designed to create a stable and consistent return stream in all environments.
  3. 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 70th 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 70th percentile result over a short, 15-month horizon is a result to be pleased with.

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.

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 99.8th 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.

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.

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.

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.

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 42nd percentile while the up capture of 0.60 was in the 93rd 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.

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.

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 99th 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 87th percentile over the set of sample allocations, indicating a very high realized risk-adjusted return.

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.

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

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:

  1. Begin with daily market returns
  2. Add a small amount of white noise (mean 0%; standard deviation 0.025%) to daily market returns
  3. Calculate a long/flat trend equity strategy using 12-1 month momentum signals4
  4. Calculate the rolling 12-month return of the strategy minus the alternate market history return.
  5. 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.


 

Decomposing Trend Equity

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

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.

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.

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