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No Pain, No Premium

By

On February 4, 2019

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

Summary

  • In this commentary, we discuss what we mean by the phrase, “no pain, no premium.”
  • We re-frame the discussion of portfolio construction from one about returns to one about risk and argue that without risk, there should be no expectation of return.
  • With a risk-based framework, we argue that investors inherently act as insurance companies, earning a premium for bearing risk.  This risk often manifests as significant negative skew and kurtosis in the distribution of asset returns.
  • We introduce the philosophical limits of diversification, arguing that we should not be able to eliminate risk from the portfolio without eliminating return as well.
  • Therefore, we should seek to eliminate uncompensated risks while diversifying across compensated ones.
  • We explore the three axes of diversification – what, how, and when – and demonstrate how thinking in a correlation-driven, payoff-driven, and opportunity-driven framework may help investors find better diversification.

1. Is it About Risk or Return?

For graduate school, I pursued my Masters of Science in Computational Finance at Carnegie Mellon University.  One of the first degrees of its kind in the late 1990s, this financial engineering program is a cross-disciplinary collaboration between the finance, mathematics, statistics, and computer-science departments.

In practice, it was an intensive year-and-a-half study on the theoretical and practical considerations of pricing financial derivatives.

I do not recall quite when it struck me, but at some point I recognized a broader pattern at play in every assignment.  The instruments we were pricing were always about the transference of risk in some capacity.  Our goal was to identify that risk, figure out how to isolate and extract it, package it into the appropriate product type, and then price it for sale.

Risk was driving the entire equation.  Pricing was all about understanding distribution of the potential payoffs and trying to identify “fair compensation” for the variety of risks and assumptions we were making.

For every buyer, there is a seller and vice versa and, at the end of the day, sellers who did not want risk and would have to compensate buyers to bear it.

1.1 Stocks for the Long Run

The idea that reward is compensation for risk is certainly not a new one.  It is, more or less, the entire foundation of modern finance.

But sometimes, it seems, we forget it.

We are often presented with a return-based lens through which to evaluate the world of finance.  Commonly reprinted are graphs like the one below, demonstrating century-long returns for stocks, bonds, and cash and accompanied by broad, sweeping generalizations like, “stocks for the long run.”

The truth is, if you plot anything on a log-axis over a long enough time horizon and draw it with a thick enough crayon, the line will eventually look pretty straight.

But if we zoom in to a horizon far more relevant to the lifecycle of most individual investors, we see a very different picture.

What we see is the realization of risk.  We have to remember that the excess returns we expect to earn over the long run are compensation for bearing risk.  And that risk needs to manifest, from time-to-time.  Otherwise, if the probability of the risk being realized goes down, then so should the excess premium we expect to earn.

From a quantitative perspective, risk is often measured as volatility.  In our opinion, that’s not quite right.  We believe, given a long enough return history with enough realized risk events, risk can be better measured in a return’s distribution symmetry and fat-tailed-ness (i.e. “skew” and “kurtosis” respectively).

Below we plot the annualized excess real return distribution for U.S. equities over the last 100 years.  We can see that the distribution is “leaning” to the right, indicating that large losses are more frequent than large gains.

We would argue that when we buy equities, what we are really buying is a risk.  In particular, we are buying an uncertain stream of cash flows.

Now, this might seem a little weird.  Why would we ever pay someone to bear their risk?

The answer is because, in many ways, we can think of equities as a swap of cashflows: one up-front bullet payment for the rights to an uncertain stream of future cash flows generated by the underlying business.

In theory, the price we pay today should be less than the net present value of all those future cash flows, with the difference representing the premium we expect to earn over time.

Uncertainty is the wedge between the values.  Without uncertainty, no rational seller would give up their future cash flows for less than they are worth (or, if we do have an irrational seller, we would expect buyers to compete over those cashflows to the point they are fairly valued).

Thus, the premium will be driven both by certainty about the future cash flows (growth rate and duration) as well as the market’s appetite for bearing risk.

The more certain we are of those future cash flows or the higher the market’s appetite to bear risk, the smaller the expected premium should be.

1.2 “Funding Secured”

To get a better sense of the play between certainty and premium in the market, we can explore an example where we effectively collapse price into a binary “yes or no” event.

On August 7th, 2018, Elon Musk sent out the following tweets:

At the time he sent the tweet, Tesla shares were trading around approximately $365.  The stock had opened around $340 that day and had jumped on news reporting that the Saudi sovereign fund had built a $2b stake in Tesla and some speculation about a potential buy-out.

Now let’s assume, for a moment, that Elon’s tweet said, “Deal struck to take Tesla private at $420, effectively immediately”  What should the price of Tesla’s stock jump to?  $420, of course.

Now Elon’s tweet merely said he was considering it.  He also did not specify a timeline.  But let’s consider two cases:

  • The market believes a deal will be struck to take Tesla at $420 in the near future.
  • The market does not believe Tesla will be taken private.

In the former case, the right price is approximately $420.  In the latter case, the appropriate price is whatever the shares were trading at before the announcement.1

Thus, where price trades between the two points can be interpreted as to the market’s confidence in the deal being done.

Hence, I tweeted the following:

(Note that when I sent out the first tweet, I hadn’t realized trading had been halted in Tesla.)

Assuming the entire day’s move was attributed to the buyout news, a price change from $340 to $380 only represents a 50% move towards the buy-out price of $420.  The market was basically saying, “we give this coin-flip odds.”

1.2 Well ‘Skews Me

While modern portfolio theory uses volatility as the measure of risk, the connection between excess realized premia and volatility is tenuous at best.  It certainty falls apart in highly skewed, fat-tailed return distributions.

Rather, skewness appears to be a much better measure of risk for most financial assets.  And when we look at equity markets around the globe, we see the same fact pattern emerge: return distributions with negative skew indicating that losses tend to be (much) bigger than gains.

2. You’re An Insurance Company

What this type of risk-based thinking all boils down to is that you – and your portfolio – are really acting as an insurance company of sorts.

When we purchase insurance, we are really transferring our associated risk to the insurance company.  To incentivize them to bear the risk, we have to pay an annual premium.

Similarly, when we buy stocks, we are really trading a certain cashflow today (the price) for a stream of uncertain cash flows in the future.  The discount between the price we pay and the net present value of future cash flows is the premium we expect to earn.  And when we sell stocks, we are effectively paying that premium.

So in building our portfolios, we should think like an insurance company.

Like an insurance company, we want to diversify the premiums we earn.  Not only do we want to diversify within a given type of insurance, but we probably also want to diversify the type of insurance we offer.  And, in an ideal world, the type of insurance would be uncorrelated!

2.1 Diversifying with Bonds

Enter the most traditional portfolio diversifier: bonds.  Typically considered to be a “safe” asset, if we look at them through the lens of real excess returns, we can see that bond returns also exhibit negative skew and fat tails.

This makes sense, as when we buy a bond we are still bearing all sorts of risks.  Not only do we bear the risk of a default, but we also bear inflation risk and interest rate path-dependency risk.

With U.S. Treasuries, default risk is likely minimized (depending on your perspective), and the other two risks might be less correlated than the traditional risks (e.g. economic growth) we see with equities.  So combining stocks and bonds should help us control skew, right?

Well, not quite.  Below we plot the annualized excess real returns for a 60/40 portfolio.

We see that skew and kurtosis remain.  What gives?

Well, one answer is that while a 60/40 portfolio might be close to balanced in the terms of notional dollar exposure to each asset, it is completely unbalanced from the perspective of residual volatility.

Below we plot the relative contribution to risk of stocks and bonds over time in a 60/40 portfolio.

Because the payout for bonds is far more certain than the payout for stocks, not only is the expected excess premium much lower, but volatility tends to be much lower as well.  This means that the premium earned from holding bonds is not large enough to offset the losses realized in equities.

Savvy readers will recognize this as the driving thesis behind risk parity.  To strike a balance, we need to allocate to stocks and bonds in such a manner that they provide equal contribution to portfolio risk.

Below, we plot the annual excess real return distribution for a stock/bond risk parity portfolio that is levered to a constant volatility target of 8%.

What do we see?  Skew and fat tails remain.  Perhaps the answer is simply that we need more diversification.  While in practice this might mean buying different assets, in theory it means exposing ourselves to different types of risk sources that lead to uncertainty in the value of future cash flows.  We enumerate a few below.

In traditional asset allocation, trying to isolate and add these different exposures is very difficult.

First, it is worth acknowledging that not every type of risk necessarily deserves to earn compensation.  In theory, we should only be compensated for un-diversifiable risks.

Furthermore, many of these risks have time-varying correlations and magnitudes, and often collapse towards a single risk factor during crisis states of the world.

Yet we would argue that there is a deeper, philosophical limit we should consider.

3. The Philosophical Limits of Diversification

What we keep running up against is what we call the “philosophical limit of diversification.”

The simplest way to think about the limit is this: If we can diversify away all of our risk, we should not expect to earn any reward.

After all, if we found some magical combination of assets that eliminated downside risk in all future states of the world, we would have constructed an arbitrage.  We could simply borrow at the risk-free rate, invest in the appropriate blend of assets, and reap our risk-free reward.

That is why years like 2018, when 90% of assets lose money, have to occur from time to time.  Without the eventual realization of risk, there is no reason to expect return.

3.1 The Frustrating Law of Active Management

A corollary of this philosophical limit is what we like to call “The Frustrating Law of Active Management.”

We go further in depth into this idea in another commentary, but the basic idea follows: if an investment strategy is perceived both to have alpha and to be easy, investors will allocate to it and erode the associated premium.

How can a strategy be “hard”?  Well, a manager might have a substantial informational or analytical edge.  Or, the manager might have a structural moat, accessing trades others do not have the opportunity to pursue.

But for most well-known edges (e.g. most major style premia), “hard” is going to be behavioral.  The strategy has to be hard enough to hold on to that it does not get arbitraged away.  Which implies that,

For any disciplined investment approach to outperform over the long run, it must experience periods of underperformance in the short run.

This also implies that,

For any disciplined investment approach to underperform over the long run, it must experience periods of outperformance in the short run.

For active managers, the frustration is that not only does their investment approach have to under-perform from time-to-time, but bad strategies will have to out-perform.  The latter may seem confusing until we consider that a purposefully bad strategy could simply be inverted to create a purposefully good one.2

And, as above, we cannot simply diversify our way out of the problem.  After all, if there were a magic combination of active strategies that earned the same expected alpha but reduced the risk, everybody would pursue that combination.

4. Investment versus Investor Returns

So is the answer here to just, “suck it up?”  Do we simply look at periods like 2000-2010 and say, “it’s the price we pay for the opportunity to earn long-run returns?”

We would argue both “yes” and “no.”

It all depends upon where an investor falls within their lifecycle.  Young investors who are pursuing growth mandates may simply need to accept that skew and fat tails are the cost of earning the long-run premium.  Too much diversification may lead to “failing slow.”

For investors in the later stages of their lifecycle, however, the math changes.  Indeed, this is true for any individual or institution where withdrawals are concerned.  When we have a withdrawal-driven mandate, it is the risk of “failing fast” that we need to concern ourselves with.

The problem is that investment-centric thinking often makes diversification seem foolish.  To quote Brian Portnoy, “diversification means always having to say you’re sorry.”

Not only do we have to contend with the fact that the relative performance of the investments in our portfolio will vary wildly from one another year-to-year, but evidence suggests that so will the investor’s utility function.

Consider the graphic below, where the investor’s utility oscillates between relative (“I didn’t do as well as my peers!”) and absolute returns (“I lost money!”), making the diversified profile a consistent loser.

Source: BlackRock.

(3/14/2019 Update: It was pointed out to me that based upon the numbers in the table above, the total return reported the Diversified Portfolio is actually understated.  Total return should be 202.4%, with $100K turning into $302,420.) 

However, if we actually think about investor returns, rather than investment returns, the picture changes.  Below we plot the growth of $1,000,000 since 2000 with a fixed $40,000 withdrawal.  In this highly simplified example, we can begin to see the benefits of increased diversification.

Despite the philosophical limits of diversification, we clearly should not forgo it entirely.  But what is the right framework to think about diversification and how it can be introduced into a portfolio?

5. The Three Axes of Diversification

At Newfound, we talk about three potential axes of diversification that investors can try to exploit.

We call these axes the what, the how, and the when axes, and they aim to capture what we invest in (“correlation driven”), how we make the decisions (“pay-off driven”), and when we make those decisions (“opportunity driven”).

Below, we explore each axis individually and how to might be able to contribute to a portfolio’s overall diversification profile.

5.1 What Axis (“Correlation Diversification”)

The “what” axis asks the question, “what are we investing in?”  It captures the traditional notions of asset class and geographic diversification.  As we have explored in this commentary, it also implicitly captures risk-based diversification.

We can also think of this axis as being responsible for “correlation-driven” diversification.  As we will see, however, the empirical evidence of the effectiveness of this type of diversification is limited.

5.1.1 It’s Hard to Allocate Our Way Out of a Bear Market

Empirical evidence suggests that correlation-driven diversification is not tremendously effective at limited losses in crisis events.  Consider the returns plotted below for a number of asset classes during 2008.  We can see that by the end of the year, almost all had fallen between -20% to -50%.


As it turns out, most of the risk reduction benefits seen in a traditional asset allocation are not actually due to diversification benefits, but rather simply due to outright de-risking.

In their 2016 paper The Free Lunch Effect: The Value of Decoupling Diversification and Risk, Croce, Guinn and Robinson demonstrate that most of the risk reduction seen in moving from and all-stock portfolio to a balanced portfolio is simply due to the fact that bonds are less volatile than stocks.

That is not to say that de-risking is without its own merits.  Outright de-risking a portfolio is simple way to reduce total loss potential and is one of the driving forces behind the benefits of glide-path investing’s ability to control sequence risk.

Investors looking to maintain a return profile while reducing risk through the benefits of diversification, however, may be disappointed.

In When Diversification Fails, Page and Panariello demonstrate that asset correlations tend to be bi-modal in nature.  Unfortunately, the dynamics exhibited are the exact opposite of what we would like to see: diversification opportunity is ample in positive market states, but correlations tend to crash towards one during equity crises.

This does not make traditional diversification outright worthless, however, for growth-oriented investors.

Consider the table below from a paper titled, The Risk of Premiums, in which the author summarizes his findings about the statistical significance of different realized equity risk premia around the globe over different time horizons.

The five countries with stars on the left-hand side of the table have historically exhibited statistically significant risk premia across rolling 1-, 5-, 10-, and 20-year periods.  Those with stars on the right did not exhibit statistically significant risk premia across any of the rolling periods.

It is important to remember that risk premia are expected, but by no means guaranteed.  It is entirely possible that markets mis-estimate the frequency or magnitude with which risks manifest and fail to demand an adequately compensating premium.

Things have worked out exceptionally well for U.S. investors, but the same cannot be said for investors around the globe.

With the exception of explicit de-risking, what diversification may not necessarily provide much support in managing the left-tails of systematic risk factors.  Nevertheless, what diversification may be critical in helping reduce exposure to idiosyncratic risks associated with a specific geographic region or asset class.

5.2 The How Axis – Payoff Diversification

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

How need not be complex.  Low-cost, tax-efficient passive asset allocation is a legitimate how.

But this axis also captures the variety of other active investment styles that can create their own, and often independent, return streams.

One might go so far as to call them “synthetic assets,” but most popular literature simply refers to them as “styles.”  Popular categories include: value, momentum, carry, defensive (quality / low-volatility), trend, and event-driven.

The how axis is able to take the same what and create what are potentially unique return streams.  The return profile of a currency momentum portfolio may be inherently different than a commodity value portfolio, both of which may offer diversification from traditional, economic risk factors that drive currency and commodity beta.

If the what axis captures correlation driven diversification, we would argue that the how axis captures pay-off driven diversification.

5.2.1 Style Diversification

In When Diversification Fails, Page and Panariello also found that correlations for many styles are bi-modal, but some may offer significant diversification in equity crisis states.

2018, however, once again proved that there are philosophical limits to the benefits of diversification.  For styles to work over the long run, not only do there have to be periods where they fail individually, but there have to be periods where they fail simultaneously.

If we want to keep earning reward, we have to bear some risk in some potential state of the world.

It is no surprise, then, that it appears that most major styles appear to offer compensation for their own negative skew.  In their 2014 paper Risk Premia: Asymmetric Tail Risks and Excess Returns, Lemperiere, Deremble, Nguyen, Seager, Potters and Bouchaud find that not only do most styles exhibit negative skew, but that there appears to be a positive relationship with skew and the style’s Sharpe ratio.

As with asset classes, return appears to be a compensation for bearing asymmetric risk.

The two exceptions in the graph are trend and equity value (Fama-French HML).

The authors of the paper note that the positive skew of equity value is somewhat problematic, as it implies it is an anomaly rather than a risk compensation.  However, using monthly returns to recreate the above graph shifts the skew of equity value back to negative, implying perhaps that there is a somewhat regime-driven nature to value that needs to be further explored.

Trend, on the other hand, has long-been established to exhibit positive skew.  Indeed, it may very well be a mathematical byproduct of the trading strategy itself rather than an anomaly.

5.2.2 Payoff Diversification

While the findings of Lemperiere, Deremble, Nguyen, Seager, Potters and Bouchaud (2016) imply that style premia are not exceptions to the “no pain, no premium” rule, we should not be dissuaded from considering the potential benefits of their incorporation within a portfolio.

After all, not only might we potentially benefit from the fact that their negative states might be somewhat independent of economic risk factors (acknowledging, as always, the philosophical limits of diversification), but the trading strategies themselves create varying payoff profiles that differ from one another.

By combining different asset classes and payoff functions, we may be able to create a higher quality of portfolio return.

For example, when we overlay a naive trend strategy on top of U.S. equities, the result converges towards a distribution where we simply miss the best and worst years.  However, because the worst years tend to be worse than the best years are good, it leads to a less skewed distribution.

In effect, we’ve fought negative skew with positive skew.

At Newfound, we often say that “risk cannot be destroyed, but only transformed.”  We tend to think of risk as a blob that is spread across future states of the world.  When we push down on that blob in one future state, in effect “reducing risk,” it simply displaces to another state.

Trend may have historically helped offset losses during crisis events, but it can create drawdowns during reversal markets.  Similarly, style / alternative premia may be able to harvest returns when traditional economic factors are going sideways, but may suffer during coincidental drawdowns like 2018.

Source: PIMCO

That is why we repeat ad nauseam “diversify your diversifiers.”

5.2.3 Specification Risk

While the above discussion of how pertained to style risks, there is another form of risk worth briefly discussing: specification risk.

Specification risk acknowledges that two investors implementing two identical styles in theory may end up with very different results in practice.  Style risk tells us that equity value managers struggled as a category in 2016; specification risk tells us how each manager did individually.

Whether we are compensated for bearing specification risk is up for debate and largely depends upon your personal view of a manager’s skill.

In the absence of a view of skill, what we find is that combining multiple managers tends to do little for a reduction in traditional portfolio volatility (except in highly heterogenous categories), but can tremendously help reduce portfolio skew as well as the dispersion in terminal wealth.

For example, below we generate a number of random 30-stock portfolios and plot their returns over the last decade.

We can see that while the results are highly correlated, the terminal wealth achieved varies dramatically.

If instead of just picking one manager we pick several – say 3 or 4 – we find that the potential dispersion in terminal wealth drops dramatically and our achieved outcome is far more certain.

You can read more on this topic in our past commentary Is Multi-Manager Diversification Worth It?

5.3 When Axis

We believe that the when axis may be one of the most important, yet overlooked opportunities for diversification in portfolio construction.  So much so, we wrote a paper about it titled Rebalance Timing Luck: The Difference Between Hired and Fired.

The basic intuition behind this axis is that our realized portfolio results will be driven by the opportunities presented to us at the time we rebalance.

In many ways, diversification along the when axis can be thought of as opportunity-diversification.

For example, Blitz, van der Grient, and van Vliet demonstrated in their 2010 paper Fundamental Indexation: Rebalancing Assumptions and Performance that the quarter in which an annually-rebalanced fundamental index is reconstituted can lead to significant performance disparity.  For example, the choice to rebalance the portfolio in March versus September would have lead to a 1,000 basis point performance difference in 2009.

This difference was largely driven by the opportunities perceived by the systematic strategy at the time of rebalancing.

This risk is not limited to active portfolios.  In the graph below we plot rolling 1-year return differences between two 60/40 portfolios, one of which is rebalanced at the end of each February and one that is rebalanced at the end of each August.

We can see that the rebalance in early 2009 lead to a 700 basis point gap in performance by spring 2010.

While we believe this has important implications for how research is conducted, benchmarks are constructed, and managers build portfolios, the more practical takeaway for investors is that they might benefit from choosing managers who rebalance on different schedules.

6. Summary

Investors often focus on returns, but it is important to keep in mind why we expect to earn those returns in the first place.  We believe a risk-based mindset can help remind us that we expect to earn excess returns because we are willing to bear risk.

In many ways, we can think of ourselves and our portfolios as insurance companies: we collect premiums for bearing risk.  Yet while we can we can seek to diversify the risks we insure, there are few truly independent risk factor and the premiums aren’t often large enough to offset large losses.

We also believe that there exist theoretical limits to diversification.  If we eliminate risk through diversification, we also eliminate reward.  In other words: no pain, no premium.

This does not inherently mean, however, we should just “suck it up.”  The implications of risk-based thinking is dependent upon where we are in our investment lifecycle.

The primary risk of investors with growth mandates (e.g. investors early in their lifecycle) is “failing slow,” which is the failure to growth their capital sufficiently to outpace inflation or meet future liabilities.  In this case, our aim should be to diversify as much as possible without overly de-risking the portfolio.  With a risk-based mindset, it becomes clear why approaches like risk parity, when targeting an adequate volatility, may be philosophically superior to traditional asset allocation.

For investors taking withdrawals (e.g. those late in their lifecycle or endowments/pensions), the primary risk is “failing fast” from large drawdowns.  Diversification is likely insufficient on its own and de-risking may be prudent.  Diversifying payoff types and introducing positive skew styles – e.g. trend – may also benefit the investment plan by creating a more consistent return stream.

Yet we should acknowledge that even return opportunities available along the how axis appear to be driven largely by skew, re-emphasizing that without potential pain, there should be no premium.

Tightening the Uncertain Payout of Trend-Following

By

On January 28, 2019

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

This post is available as a PDF download here.

Summary­

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

Introduction

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

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

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

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

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

Diversification in Trend-Following

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

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

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

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

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

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

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

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

Source: ReSolve Asset Management.  Reprinted with permission

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

The Math Behind the Diversification

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

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

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

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

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

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

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

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

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

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

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

Source: Global Financial Data and Kenneth French Data Library. Calculation by Newfound. Returns are backtested and hypothetical. Returns assume the reinvestment of all distributions. Returns are gross of all fees. None of the strategies shown reflect any portfolio managed by Newfound Research and were constructed solely for demonstration purposes within this commentary. You cannot invest in an index.

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

What do these parameters mean?

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

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

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

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

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

Source: Global Financial Data and Kenneth French Data Library. Calculation by Newfound. Returns are backtested and hypothetical. Returns assume the reinvestment of all distributions. Returns are gross of all fees. None of the strategies shown reflect any portfolio managed by Newfound Research and were constructed solely for demonstration purposes within this commentary. You cannot invest in an index.

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

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

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

Source: Global Financial Data and Kenneth French Data Library. Calculation by Newfound. Returns are backtested and hypothetical. Returns assume the reinvestment of all distributions. Returns are gross of all fees. None of the strategies shown reflect any portfolio managed by Newfound Research and were constructed solely for demonstration purposes within this commentary. You cannot invest in an index.

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

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

Source: Global Financial Data and Kenneth French Data Library. Calculation by Newfound. Returns are backtested and hypothetical. Returns assume the reinvestment of all distributions.  Returns are gross of all fees. None of the strategies shown reflect any portfolio managed by Newfound Research and were constructed solely for demonstration purposes within this commentary. You cannot invest in an index.

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

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

Source: Global Financial Data and Kenneth French Data Library. Calculation by Newfound. Returns are backtested and hypothetical. Returns assume the reinvestment of all distributions. Returns are gross of all fees. None of the strategies shown reflect any portfolio managed by Newfound Research and were constructed solely for demonstration purposes within this commentary. You cannot invest in an index.

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

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

Expanding the Multitude of Models

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

Source: Global Financial Data and Kenneth French Data Library. Calculation by Newfound. Returns are backtested and hypothetical. Returns assume the reinvestment of all distributions. Returns are gross of all fees. None of the strategies shown reflect any portfolio managed by Newfound Research and were constructed solely for demonstration purposes within this commentary. You cannot invest in an index.

Source: Global Financial Data and Kenneth French Data Library. Calculation by Newfound. Returns are backtested and hypothetical. Returns assume the reinvestment of all distributions. Returns are gross of all fees. None of the strategies shown reflect any portfolio managed by Newfound Research and were constructed solely for demonstration purposes within this commentary. You cannot invest in an index.

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

Source: Global Financial Data and Kenneth French Data Library. Calculation by Newfound. Returns are backtested and hypothetical. Returns assume the reinvestment of all distributions. Returns are gross of all fees. None of the strategies shown reflect any portfolio managed by Newfound Research and were constructed solely for demonstration purposes within this commentary. You cannot invest in an index.

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

Conclusion

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

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

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

A multi-model approach can address both of these.

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

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

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

Fragility Case Study: Dual Momentum GEM

By

On January 14, 2019

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

This post is available as a PDF download here.

Summary­

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

Introduction

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

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

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

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

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

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

Global Equities Momentum (“GEM”)

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

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

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

Source: CSI Analytics.  Calculations by Newfound Research.  Returns are backtested and hypothetical.  Returns assume the reinvestment of all distributions.  Returns are gross of all fees except for underlying ETF expense ratios.  None of the strategies shown reflect any portfolio managed by Newfound Research and were constructed solely for demonstration purposes within this commentary.  You cannot invest in an index.

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

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

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

Source: CSI Analytics.  Calculations by Newfound Research.  Returns are backtested and hypothetical.  Returns assume the reinvestment of all distributions.  Returns are gross of all fees except for underlying ETF expense ratios.  None of the strategies shown reflect any portfolio managed by Newfound Research and were constructed solely for demonstration purposes within this commentary.  You cannot invest in an index.

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

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

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

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

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

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

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

Source: CSI Analytics.  Calculations by Newfound Research.  Returns are backtested and hypothetical.  Returns assume the reinvestment of all distributions.  Returns are gross of all fees except for underlying ETF expense ratios.  None of the strategies shown reflect any portfolio managed by Newfound Research and were constructed solely for demonstration purposes within this commentary.  You cannot invest in an index.

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

Conclusion

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

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

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

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

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

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

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

 

Is Multi-Manager Diversification Worth It?

By

On January 7, 2019

In Popular, Portfolio Construction, Risk Management, Weekly Commentary

This post is available as a PDF download here.

Summary­

  • Portfolio risk is traditionally quantified by volatility.  The benefits of diversification are measured in how portfolio volatility is changed with the addition or subtraction of different investments.
  • Another measure of portfolio risk is the dispersion in terminal wealth: a measure that attempts to capture the potential difference in realized returns. For example, two equity managers that each hold 30 stock portfolios may exhibit similar volatility levels but will likely have very different realized results.
  • In this commentary we explore existing literature covering the potential diversification benefits that can arise from combining multiple managers together.
  • Empirical evidence suggests that in heterogeneous categories (e.g. many hedge fund styles), combining managers can reduce portfolio volatility. Yet even in homogenous categories (e.g. equity style boxes), combining managers can have a pronounced effect on reducing the dispersion in terminal wealth.
  • Finally, we address the question as to whether manager diversification leads to dilution, arguing that a combination of managers will reduce idiosyncratic process risks but maintain overall style exposure.

Introduction

In their 2014 paper The Free Lunch Effect: The Value of Decoupling Diversification and Risk, Croce, Guinn, and Robinson draw a distinction between the risk reduction effects that occur due to de-risking and those that occur due to diversification benefits.

To illustrate the distinction, the authors compare the volatility of an all equity portfolio versus a balanced stock/bond mix.  In the 1984-2014 sample period, they find that the all equity portfolio has an annualized volatility of 15.25% while the balanced portfolio has an annualized volatility of just 9.56%.

Over 75% of this reduction in volatility, however, is due simply to the fact that bonds were much less volatile than stocks over the period.  In fact, of the 568-basis-point reduction, only 124 basis points was due to actual diversification benefits.

Why does this matter?

Because de-risking carries none of the benefits of diversification.  If there is a commensurate trade-off between expected return and risk, then all we have done is reduced the expected return of our portfolio.1

It is only by combining assets of like volatility – and, it is assumed, like expected return – that should allow us to enjoy the free lunch of diversification.

Unfortunately, unless you are willing to apply leverage (e.g. risky parity), the reality of finding such free lunch opportunities across assets is limited. The classic example of inter-asset diversification, though, is taught in Finance 101: as we add more stocks to a portfolio, we drive the contribution of idiosyncratic volatility towards zero.

Yet volatility is only one way to measure risk.  If we build a portfolio of 30 stocks and you build a portfolio of 30 stocks, the portfolios may have nearly identical levels of volatility, but we almost assuredly will end up with different realized results.  This difference between the expected and the realized is captured by a measure known as terminal wealth dispersion, first introduced by Robert Radcliffe in his book Investment: Concepts, Analysis, Strategy.

This form of risk naturally arises when we select between investment managers.  Two managers may both select securities from the same universe using the same investment thesis, but the realized results of their portfolios can be starkly different.  In rare cases, the specific choice of one manager over another can even lead to catastrophic results.

The selection of a manager reflects not only an allocation to an asset class, but also reflects an allocation to a process.  In this commentary, we ask: how much diversification benefit exists in process diversification?

The Theory Behind Manager Diversification

In Factors from Scratch, the research team at O’Shaughnessy Asset Management (OSAM), in partnership with anonymous blogger Jesse Livermore, digs into the driving elements behind value and momentum equity strategies.

They find that value stocks do tend to exhibit negative EPS growth, but this decay in fundamentals is offset by multiple expansion.  In other words, markets do appear to correctly identify companies with contracting fundamentals, but they also exaggerate and over-extrapolate that weakness.  The historical edge for the strategy has been that the re-rating – measured via multiple expansion – tends to overcompensate for the contraction in fundamentals.

For momentum, OSAM finds a somewhat opposite effect.  The strategy correctly identifies companies with strengthening fundamentals, but during the holding period a valuation contraction occurs as the market recognizes that its outlook might have been too optimistic. Historically, however, the growth outweighed the contraction to create a net positive effect.

These are the true, underlying economic and behavioral effects that managers are trying to capture when they implement value and momentum strategies.

These are not, however, effects we can observe directly in the market; they are effects that we have to forecast.  To do so, we have to utilize semi-noisy signals that we believe are correlated. Therefore, every manager’s strategy will be somewhat inefficient at capturing these effects.

For example, there are a number of quantitative measures we may apply in our attempt to identify value opportunities; e.g. price-to-book, price-to-earnings, and EBITDA-to-enterprise-value to name a few. Two different noisy signals might end up with different performance just due to randomness.

This noise between signals is further compounded when we consider all the other decisions that must be made in the portfolio construction process.  Two managers may use the same signals and still end up with very different portfolios based upon how the signals are translated into allocations.

Consider this: Morningstar currently2 lists 1,217 large-cap value funds in its mutual fund universe and trailing 1-year returns ranged from 1.91% to -22.90%. This is not just a case of extreme outliers, either: the spread between the 10th and 90thpercentile returning funds was 871 basis points.

It bears repeating that these are funds that, in theory, are all trying to achieve the same goal: large-cap value exposure.

Yet this result is not wholly surprising to us.  In Separating Ingredients and Recipe in Factor Investing we demonstrated that the performance dispersion between different momentum strategy definitions (e.g. momentum measure, look-back length, rebalance frequency, weighting scheme, et cetera) was larger than the performance dispersion between the traditional Fama-French factors themselves in 90% of rolling 1-year periods.  As it turns out, intra-factor differences can cause greater dispersion than inter-factor differences.

Without an ex-ante view as to the superiority of one signal, one process, or one fund versus another, it seems prudent for a portfolio to have diversified exposure to a broad range of signals that seem plausibly related to the underlying phenomenon.

Literature Review

While foundational literature on modern portfolio diversification extends back to the 1950s, little has been written in the field of manager diversification. While it is a well-established teaching that a portfolio of 25-40 stocks is typically sufficient to reduce idiosyncratic risk, there is no matching rule for how many managers to combine together.

One of the earliest articles on the topic was written by Edward O’Neal in 1997, titled How Many Mutual Funds Constitute a Diversified Mutual Fund Portfolio?

Published in the Financial Analysts Journal, this article explores risk across two different dimensions: the volatility of returns over time and the dispersion in terminal period wealth.  Again, the idea behind the latter measure is that two investors with identical horizons and different investments will achieve different terminal wealth levels, even if those investments have the same volatility.

Exploring equity mutual fund returns from 1986 to 1997, the study adopts a simulation-based approach to constructing portfolios and tracking returns.  Multi-manager portfolios of varying sizes are randomly constructed and compared against other multi-manager portfolios of the same size.

O’Neal finds that while combining managers has little-to-no effect on volatility (manager returns were too homogenous), it had a significant effect upon the dispersion of terminal wealth.  To quote the article,

Holding more than a single mutual fund in a portfolio appears to have substantial diversification benefits. The traditional measure of volatility, the time-series standard deviation, is not greatly influenced by holding multiple funds. Measures of the dispersion in terminal-wealth levels, however, which are arguably more important to long-term investors than time-series risk measures, can be reduced significantly. The greatest portion of the reduction occurs with the addition of small numbers of funds. This reduction in terminal-period wealth dispersion is evident for all holding periods studied. Two out of three downside risk measures are also substantially reduced by including multiple funds in a portfolio. These findings are especially important for investors who use mutual funds to fund fixed-horizon investment goals, such as retirement and college savings.

Allocating to three managers instead of just one could reduce the dispersion in terminal wealth by nearly 50%, an effect found to be quite consistent across the different time horizons measured.

In 1999, O’Neal teamed up with L. Franklin Fant to publish Do You Need More than One Manager for a Given Equity Style? Adopting a similar simulation-based approach, Fant and O’Neal explored multi-manager equity portfolios in the context of the style-box framework.

And, as before, they find that taking a multi-manager approach has little effect upon portfolio volatility.

It does, however, again prove to have a significant effect on the deviation in terminal wealth.

To quote the paper,

Regardless of the style category considered, the variability in terminal wealth levels is significantly reduced by using more managers. The first few additional managers make the most difference, as terminal wealth standard deviation declines at a decreasing rate with the number of managers. Concentrating on the variability of periodic portfolio returns fails to document the advantage of using multiple managers within style categories.

Second, some categories benefit more from additional managers than others. Plan sponsors would do well to allocate relatively more managers to the styles that display the greatest diversification benefits. Growth styles and small-cap styles appear to offer the greatest potential for diversification.

In 2002, François-Serge Lhabitant and Michelle Learned pursued a similar vein of research in the realm of hedge funds in their article Hedge Fund Diversification: How Much is Enough?  They employ the same simulation-based approach but evaluate diversification effects within the different hedge fund styles.

They find that while diversification does little to affect the expected return for a given style, it does appear to help reduce portfolio volatility: sometimes quite significantly so. This somewhat contradictory result to the prior research is likely due to the fact that hedge funds within a given category exhibit far more heterogeneity in process and returns than do equity managers in the same style box.

(Note that while the graphs below only show the period 1990-1993, the paper explores three time periods: 1990-1993, 1994-1997, and 1998-2001 and finds a similar conclusion in all three).

Perhaps most importantly, however, they find a rather significant reduction in risk characteristics like a portfolio’s realized maximum drawdown.

To quote the article,

We find that naively adding more funds to a portfolio tends to leave returns stable, decrease the standard deviation, and reduce downside risk. Thus, diversification should be increased as long as the marginal benefits of adding a new asset to a portfolio exceeds the marginal cost.

…

If a sample of managers is relatively style pure, then a fewer number of managers will minimize the unsystematic risk of that style. On the contrary, if the sample is really heterogeneous, increasing the number of managers may still provide important diversification benefits.

Taken together, this literature paints an important picture:

  • Diversifying across managers in the same category will likely do little to reduce portfolio volatility, except in the cases where categories are broad enough to capture many heterogeneous managers.
  • Diversifying across managers appears to significantly reduce the potential dispersion in terminal wealth.

But why is minimizing “the dispersion of terminal wealth” important?  The answer is the same reason why we diversify in the first place: risk management.

The potential for high dispersion in terminal wealth means that we can have dramatically different outcomes based upon the choices we are making, placing significant emphasis on our skill in manager selection.  Choosing just one manager is more right style thinking rather than our preferred less wrong.

But What About Dilution?

The number one response we hear when we talk about manager diversification is: “when we combine managers, won’t we just dilute our exposure back to the market?”

The answer, as with all things, is: “it depends.”  For the sake of brevity, we’re just going to leave it with, “no.”

No?

No.

If we identify three managers as providing exposure to value, then it makes little logical sense that somehow a combination of them would suddenly remove that exposure.  Subtraction through addition only works if there is a negative involved; i.e. one of the managers would have to provide anti-value exposure to offset the others.

Remember that an active manager’s portfolio can always be decomposed into two pieces: the benchmark and a dollar-neutral long/short portfolio that isolates the active over/under-weights that manager has made.

To “dilute back to the benchmark,” we’d have to identify managers and then weight them such that all of their over/under-weights net out to equal zero.

Candidly, we’d be impressed if you managed to do that.  Especially if you combine managers within the same style who should all be, at least directionally, taking similar bets.  The dilution that occurs is only across those bets which they disagree on and therefore reflect the idiosyncrasies of their specific process.

What a multi-manager implementation allows us to diversify is our selection risk, leading to a return profile more “in-line” with a given style or category.  In fact, Lhabitant and Learned (2002) demonstrated this exact notion with a graph that plots the correlation of multi-manager portfolios with their broad category.  While somewhat tautological, an increase in manager diversification leads to a return profile closer to the given style than to the idiosyncrasies of those managers.

We can also see this with a practical example.  Below we take several available ETFs that implement quantitative value strategies and plot their rolling 52-week return relative to the S&P 500. We also construct a multi-manager index (“MM_IDX”) that is a naïve, equal-weight portfolio.  The only wrinkle to this portfolio is that ETFs are not introduced immediately, but rather slowly over a 12-month period.3

Source: CSI Analytics.  Calculations by Newfound Research.  It is not possible to invest in an index.  Returns are total returns (i.e. assume the reinvestment of all distributions) and are gross of all fees except for underlying expense ratios of ETFs. Past performance does not guarantee future results. 

 

We can see that while the multi-manager blend is never the best performing strategy, it is also never the worst.  Never the hero; never a zero.

It should be noted that while manager diversification may be able to reduce the idiosyncratic returns that result from process differences, it will not prevent losses (or relative underperformance) of the underlying style itself.  In other words, we might avoid the full brunt of losses specific to the Sequoia Fund, but no amount of diversification would prevent the relative drag seen by the quantitative value style in general over the last decade.

We can see this in the graph above by the fact that all the lines generally tend to move together.  2015 was bad for value managers.  2016 was much better.  But we can also see that every once in a while, a specific implementation will hit a rough patch that is idiosyncratic to that approach; e.g. IWD in 2017 and most of 2018.

Multi-manager diversification is the tool that allows us to avoid the full brunt of this risk.

Conclusion

Taken together, the research behind manager diversification suggests:

  • In heterogeneous categories (e.g. many hedge fund styles), manager diversification may reduce portfolio volatility.
  • In more homogenous categories (e.g. equity style boxes), manager diversification may reduce the dispersion in terminal wealth.
  • Multi-manager implementations appear to reduce realized portfolio risk metrics such as maximum drawdown. This is likely partially due to the reduction in portfolio volatility, but also due to a reduction in exposure to funds that exhibit catastrophic losses.
  • Multi-manager implementations do not necessarily “dilute” the portfolio back to market exposure, but rather “dilute” the portfolio back to the style exposure, reducing exposure idiosyncratic process risk.

For advisors and investors, this evidence may cause a sigh of relief.  Instead of having to spend time trying to identify the best manager or the best process, there may be significant advantages to simply “avoiding the brain damage”4 and allocating equally among a few.  In other words, if you don’t know which low-volatility ETF to pick, just buy a couple and move on with your life.

But what are the cons?

  • A multi-manager approach may be tax inefficient, as we will need to rebalance allocations back to parity between the exposures.
  • A multi-manager approach may lead to fund bloat within a portfolio, doubling or tripling the number of holdings we have. While this is merely optical, except possibly in small portfolios, we recognize there exists an aversion to it.
  • By definition, performance will be middling: the cost of avoiding the full brunt of losers is that we also give up the full benefit of winners. We’re reluctant to label this as a con, as it is arguably the whole point of diversification, but it is worth pointing out that the same behavioral biases that emerge in portfolio reviews of asset allocation will likely re-emerge in reviews of manager selection, especially over short time horizons.

For investment managers, a natural interpretation of this research is that approaches blending different signals and portfolio construction methods together should lead to more consistent outcomes.  It should be no surprise, then, that asset managers adopting machine learning are finding significant advantages with ensemble techniques. After all, they invoke the low-hanging fruit of manager diversification.

Perhaps most interesting is that this research suggests that fund-of-funds really are not such bad ideas so long as costs can be kept under control.  As the asset management business continues to be more competitive, perhaps there is an edge – and a better client result – found in cooperation.

 

Dart-Throwing Monkeys and Process Diversification

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On December 24, 2018

In Portfolio Construction, Risk Management, Weekly Commentary

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.

 

 

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