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Fragility Case Study: Dual Momentum GEM

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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.

 

Decomposing Trend Equity

By

On September 24, 2018

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

This post is available as a PDF download here.

Summary­

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

The Simple Arithmetic of Portfolio Construction

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

First, what do we mean by “decompose”?

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

Figure 1

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

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

Figure 2: Portfolio Arithmetic – Long/Short Overlay

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

Figure 3: Portfolio Arithmetic – Scaled Long/Short Overlay

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

Decomposing Trend Equity

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

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

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

Figure 4

Strategic Position

Trend Strategy

Decomposition

Positive Trend

Negative Trend

Strategic +
Flat/Short Trend Strategy

100% Equity

No Position

-100% Equity
100% ST US Treasuries

Strategic + 50% Long/Short Trend Strategy

50% Equity
50% ST US Treasuries

100% Equity
-100% ST US Treasuries

-100% Equity
+100% ST US Treasuries

Equity + Flat/Short

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

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

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

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

Source: Newfound Research.  Return data relies on hypothetical indices and is exclusive of all fees and expenses.  Returns assume the reinvestment of all dividends.  Flat/Short Equity shorts U.S. Large-Cap Equity when the prior month has a positive 12-1 month total return, investing available capital in 3-month U.S. Treasury Bills.  The strategy assumes zero cost of shorting.   The Flat/Short Equity strategy does not reflect any strategy offered or managed by Newfound Research and was constructed exclusively for the purposes of this commentary.  It is not possible to invest in an index.  Past performance does not guarantee future results.

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

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

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

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

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

Source: Newfound Research.  Return data relies on hypothetical indices and is exclusive of all fees and expenses.  Returns assume the reinvestment of all dividends.  Flat/Short Equity shorts U.S. Large-Cap Equity when the prior month has a negative 12-1 month total return, investing available capital in 3-month U.S. Treasury Bills.  The strategy assumes zero cost of shorting.   The Flat/Short Equity strategy does not reflect any strategy offered or managed by Newfound Research and was constructed exclusively for the purposes of this commentary.  It is not possible to invest in an index.  Past performance does not guarantee future results.

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

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

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

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

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

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

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

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

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

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

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

Figure 8

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.

A Trend Equity Primer

By

On September 17, 2018

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

This post is available as a PDF download here.

Summary­

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

A Balance of Risks

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

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

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

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

The Potential Hedging Properties of Trend Following

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

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

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

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

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

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

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

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

What is Trend Equity?

Trend equity strategies rely upon the empirical evidence2 that performance tends to persist in the short-run: positive performance tends to beget further positive performance and negative performance tends to beget further negative performance.  The theory behind the evidence is that behavioral biases exhibited by investors lead to the emergence of trends.

In an efficient market, changes in the underlying value of an investment should be met by an immediate, commensurate change in the price of that investment. The empirical evidence of trends suggests that investors may not be entirely efficient at processing new information.  Behavioral theory suggests that investors anchor their views on prior beliefs, causing price to underreact to new information.  As price continues to drift towards fair value, herding behavior occurs, causing price to overreact and extend beyond fair value.  Combined, these effects cause a trend.

Trend equity strategies seek to capture this potential inefficiency by systematically investing in equities when they are exhibiting positively trending characteristics and divesting when they exhibit negative trends.  The potential benefit of this approach is that it can try to exploit two sources of return: (1) the expected long-term risk premium associated with equities, and (2) the convex payoff structure typically associated with trend-following strategies.

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

Figure 2

Figure 3

U.S. Large-Cap EquitiesTrend Equity
Annualized Return11.1%11.6%
Volatility16.9%11.3%
Skewness-1.40.0
Excess Kurtosis2.2-1.0

 Source: Newfound Research.  Return data relies on hypothetical indices and is exclusive of all fees and expenses.  Returns assume the reinvestment of all dividends.  Trend Equity invests in U.S. Large-Cap Equity when the prior month has a positive 12-1 month total return and in 3-month U.S. Treasury Bills otherwise.  The Trend Equity strategy does not reflect any strategy offered or managed by Newfound Research and was constructed exclusively for the purposes of this commentary.  It is not possible to invest in an index.  Past performance does not guarantee future results.

Implementing Trend Equity

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

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

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

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

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

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

Figure 4

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

 

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

Original
Glidepath		Same Return,
Decrease Risk		Increase Return,
Same Risk
Annual Return8.20%8.25%8.60%
Volatility8.58%8.17%8.59%
Maximum Drawdown-28.55%-24.71%-23.80%
Sharpe Ratio0.610.640.65

 Source: Newfound Research.  Return data relies on hypothetical indices and is exclusive of all fees and expenses.  Returns assume the reinvestment of all dividends.  Trend Equity invests in U.S. Large-Cap Equity when the prior month has a positive 12-1 month total return and in 3-month U.S. Treasury Bills otherwise.  The Trend Equity strategy does not reflect any strategy offered or managed by Newfound Research and was constructed exclusively for the purposes of this commentary.  It is not possible to invest in an index.  Past performance does not guarantee future results.

 

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

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

A Discussion of Trade-Offs

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

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

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

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

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

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

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

Figure 7Source: Newfound Research.  Return data relies on hypothetical indices and is exclusive of all fees and expenses. Returns assume the reinvestment of all dividends.  Trend Equity invests in U.S. Large-Cap Equity when the prior month has a positive 12-1 month total return and in 3-month U.S. Treasury Bills otherwise.   The Trend Equity strategy does not reflect any strategy offered or managed by Newfound Research and was constructed exclusively for the purposes of this commentary.  It is not possible to invest in an index.  Past performance does not guarantee future results.

Figure 8

Source: Newfound Research.  Return data relies on hypothetical indices and is exclusive of all fees and expenses. Returns assume the reinvestment of all dividends.  Trend Equity invests in U.S. Large-Cap Equity when the prior month has a positive 12-1 month total return and in 3-month U.S. Treasury Bills otherwise.   The Trend Equity strategy does not reflect any strategy offered or managed by Newfound Research and was constructed exclusively for the purposes of this commentary.  It is not possible to invest in an index.  Past performance does not guarantee future results.

Conclusion

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

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

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

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

Bibliography

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

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

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

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

The State of Risk Management

By

On August 20, 2018

In Portfolio Construction, Risk Management, Weekly Commentary

This post is available as PDF download here. 

Summary

  • We compare and contrast different approaches to risk managing equity exposure; including fixed income, risk parity, managed futures, tactical equity, and options-based strategies; over the last 20 years.
  • We find that all eight strategies studied successfully reduce risk, while six of the eight strategies improve risk-adjusted returns. The lone exceptions are two options-based strategies that involve being long volatility and therefore are on the wrong side of the volatility risk premium.
  • Over time, performance of the risk management strategies varies significantly both relative to the S&P 500 and compared to the other strategies. Generally, risk-managed strategies tend to behave like insurance, underperforming on the upside and outperforming on the downside.
  • Diversifying your diversifiers by blending a number of complementary risk-managed strategies together can be a powerful method of improving long-term outcomes. The diversified approach to risk management shows promise in terms of reducing sequence risk for those investors nearing or in retirement.

I was perusing Twitter the other day and came across this tweet from Jim O’Shaughnessy, legendary investor and author of What Works on Wall Street.

As always. Jim’s wisdom is invaluable.  But what does this idea mean for Newfound as a firm?  Our first focus is on managing risk.  As a result, one of the questions that we MUST know the answer to is how to get more investors comfortable with sticking to a risk management plan through a full market cycle.

Unfortunately, performance chasing seems to us to be just as prevalent in risk management as it is in investing as a whole.  The benefits of giving up some upside participation in exchange for downside protection seemed like a no brainer in March of 2009.  After 8+ years of strong equity market returns (although it hasn’t always been as smooth of a ride as the market commentators may make you think), the juice may not quite seem worth the squeeze.

While we certainly don’t profess to know the answer to our burning question from above, we do think the first step towards finding one is a thorough understanding on the risk management landscape.  In that vein, this week we will update our State of Risk Management presentation from early 2016.

We examine eight strategies that roughly fit into four categories:

  • Diversification Strategies: strategic 60/40 stock/bond mix1 and risk parity2
  • Options Strategies: equity collar3, protective put4, and put-write5
  • Equity Strategies: long-only defensive equity that blends a minimum volatility strategy6, a quality strategy7, and a dividend growth strategy8 in equal weights
  • Trend-Following Strategies: managed futures9 and tactical equity10

The Historical Record

We find that over the period studied (December 1997 to July 2018) six of the eight strategies outperform the S&P 500 on a risk-adjusted basis both when we define risk as volatility and when we define risk as maximum drawdown.  The two exceptions are the equity collar strategy and the protective put strategy.  Both of these strategies are net long options and therefore are forced to pay the volatility risk premium.  This return drag more than offsets the reduction of losses on the downside.

Data Source: Bloomberg, CSI. Calculations by Newfound Research. Past performance does not guarantee future results. Volatility is a statistical measure of the amount of variation around the average returns for a security or strategy. All returns are hypothetical index returns. You cannot invest directly in an index and unmanaged index returns do not reflect any fees, expenses, sales charges, or trading expenses. Index returns include the reinvestment of dividends. No index is meant to measure any strategy that is or ever has been managed by Newfound Research. The Tactical Equity strategy was constructed by Newfound in August 2018 for purposes of this analysis and is therefore entirely backtested and not an investment strategy that is currently managed and offered by Newfound.

 

Data Source: Bloomberg, CSI. Calculations by Newfound Research. Past performance does not guarantee future results. Drawdown is a statistical measure of the losses experienced by a security or strategy relative to its historical maximum. The maximum drawdown is the largest drawdown over the security or strategy’s history. All returns are hypothetical index returns. You cannot invest directly in an index and unmanaged index returns do not reflect any fees, expenses, sales charges, or trading expenses. Index returns include the reinvestment of dividends. No index is meant to measure any strategy that is or ever has been managed by Newfound Research. The Tactical Equity strategy was constructed by Newfound in August 2018 for purposes of this analysis and is therefore entirely backtested and not an investment strategy that is currently managed and offered by Newfound.

 

Not Always a Smooth Ride

While it would be nice if this outperformance accrued steadily over time, reality is quite a bit messier.  All eight strategies exhibit significant variation in their rolling one-year returns vs. the S&P 500.  Interestingly, the two strategies with the widest ranges of historical one-year performance vs. the S&P 500 are also the two strategies that have delivered the most downside protection (as measured by maximum drawdown).  Yet another reminder that there is no free lunch in investing.  The more aggressively you wish to reduce downside capture, the more short-term tracking error you must endure.

Relative 1-Year Performance vs. S&P 500 (December 1997 to July 2018)

Data Source: Bloomberg, CSI. Calculations by Newfound Research. Past performance does not guarantee future results. All returns are hypothetical index returns. You cannot invest directly in an index and unmanaged index returns do not reflect any fees, expenses, sales charges, or trading expenses. Index returns include the reinvestment of dividends. No index is meant to measure any strategy that is or ever has been managed by Newfound Research. The Tactical Equity strategy was constructed by Newfound in August 2018 for purposes of this analysis and is therefore entirely backtested and not an investment strategy that is currently managed and offered by Newfound.

 

Thinking of Risk Management as (Uncertain) Portfolio Insurance

When we examine this performance dispersion across different market environments, we find a totally intuitive result: risk management strategies generally underperform the S&P 500 when stocks advance and outperform the S&P 500 when stocks decline.  The hit rate for the risk management strategies relative to the S&P 500 is 81.2% in the four years that the S&P 500 was down (2000, 2001, 2002, and 2008) and 19.8% in the seventeen years that the S&P was up.

In this way, risk management strategies are akin to insurance.  A premium, in the form of upside capture ratios less than 100%, is paid in exchange for a (hopeful) reduction in downside capture.

With this perspective, it’s totally unsurprising that these strategies have underperformed since the market bottomed during the global market crisis.   Seven of the eight strategies (with the long-only defensive equity strategy being the lone exception) underperformed the S&P 500 on an absolute return basis and six of the eight strategies (with defensive equity and the 60/40 stock/bond blend) underperformed on a risk-adjusted basis.

Annual Out/Underperformance Relative to S&P 500 (December 1997 to July 2018)

Data Source: Bloomberg, CSI. Calculations by Newfound Research. Past performance does not guarantee future results. All returns are hypothetical index returns. You cannot invest directly in an index and unmanaged index returns do not reflect any fees, expenses, sales charges, or trading expenses. Index returns include the reinvestment of dividends. No index is meant to measure any strategy that is or ever has been managed by Newfound Research. The Tactical Equity strategy was constructed by Newfound in August 2018 for purposes of this analysis and is therefore entirely backtested and not an investment strategy that is currently managed and offered by Newfound.

 

Diversifying Your Diversifiers

The good news is that there is significant year-to-year variation in the performance across strategies, as evidenced by the periodic table of returns above, suggesting there are diversification benefits to be harvested by allocating to multiple risk management strategies.  The average annual performance differential between the best performing strategy and the worst performing strategy is 20.0%.  This spread was less than 10% in only 3 of the 21 years studied.

We see the power of diversifying your diversifiers when we test simple equal-weight blends of the risk management strategies.  Both blends have higher Sharpe Ratios than 7 of the 8 individual strategies and higher excess return to drawdown ratios than 6 of the eight individual strategies.

This is a very powerful result, indicating that naïve diversification is nearly as good as being able to pick the best individual strategies with perfect foresight.

Data Source: Bloomberg, CSI. Calculations by Newfound Research. Past performance does not guarantee future results. All returns are hypothetical index returns. You cannot invest directly in an index and unmanaged index returns do not reflect any fees, expenses, sales charges, or trading expenses. Index returns include the reinvestment of dividends. No index is meant to measure any strategy that is or ever has been managed by Newfound Research. The Tactical Equity strategy was constructed by Newfound in August 2018 for purposes of this analysis and is therefore entirely backtested and not an investment strategy that is currently managed and offered by Newfound.

 

Why Bother with Risk Management in the First Place?

As we’ve written about previously, we believe that for most investors investing “failure” means not meeting one’s financial objectives.  In the portfolio management context, failure comes in two flavors.  “Slow” failure results from taking too little risk, while “fast” failure results from taking too much risk.

In this book, Red Blooded Risk, Aaron Brown summed up this idea nicely: “Taking less risk than is optimal is not safer; it just locks in a worse outcome.  Taking more risk than is optimal also results in a worst outcome, and often leads to complete disaster.”

Risk management is not synonymous with risk reduction.  It is about taking the right amount of risk, not too much or too little.

Having a pre-defined risk management plan in place before a crisis can help investors avoid panicked decisions that can turn a bad, but survivable event into catastrophe (e.g. the retiree that sells all of his equity exposure in early 2009 and then stays out of the market for the next five years).

It’s also important to remember that individuals are not institutions.  They have a finite investment horizon.  Those that are at or near retirement are exposed to sequence risk, the risk of experiencing a bad investment outcome at the wrong time.

We can explore sequence risk using Monte Carlo simulation.  We start by assessing the S&P 500 with no risk management overlay and assume a 30-year retirement horizon.  The simulation process works as follows:

  1. Randomly choose a sequence of 30 annual returns from the set of actual annual returns over the period we studied (December 1998 to July 2018).
  2. Adjust returns for inflation.
  3. For the sequence of returns chosen, calculate the perfect withdrawal rate (PWR). Clare et al, 2016 defines the PWR as “the withdrawal rate that effectively exhausts wealth at death (or at the end of a fixed period, known period) if one had perfect foresight of all returns over the period.11
  4. Return to #1, repeating 1000 times in total.

We plot the distribution of PWRs for the S&P 500 below.  While the average PWR is a respectable 5.7%, the range of outcomes is very wide (0.6% to 14.7%).  The 95 percent confidence interval around the mean is 2.0% to 10.3%.  This is sequence risk.  Unfortunately, investors do not have the luxury of experiencing the average, they only see one draw.  Get lucky and you may get to fund a better lifestyle than you could have imagined with little to no financial stress.  Get unlucky and you may have trouble paying the bills and will be sweating every market move.

Calculations by Newfound Research. Past performance does not guarantee future results. All returns are hypothetical index returns. You cannot invest directly in an index and unmanaged index returns do not reflect any fees, expenses, sales charges, or trading expenses. Index returns include the reinvestment of dividends.

 

Next, we repeat the simulation, replacing the pure S&P 500 exposure with the equal-weight blend of risk management strategies excluding the equity collar and the protective put.  We see quite a different result.  The average PWR is similar (6.2% to 5.7%), but the range of outcomes is much smaller (95% confidence interval from 4.4% to 8.1%).  At its very core, this is what implementing a risk management plan is all about.  Reducing the role of investment luck in financial planning.  We give up some of the best outcomes (in the right tail of the S&P 500 distribution) in exchange for reducing the probability of the very worst outcomes (in the left tail).

Calculations by Newfound Research. Past performance does not guarantee future results. All returns are hypothetical index returns. You cannot invest directly in an index and unmanaged index returns do not reflect any fees, expenses, sales charges, or trading expenses. Index returns include the reinvestment of dividends.

Conclusion

There is no holy grail when it comes to risk management.  While a number of approaches have historically delivered strong results, each comes with its own pros and cons.

In an uncertain world where we cannot predict exactly what the next crisis will look like, diversifying your diversifiers by combining a number of complementary risk-managed strategies may be a prudent course of action. We believe that this type of balanced approach has the potential to deliver compelling results over a full market cycle while managing the idiosyncratic risk of any one manager or strategy.

Diversification can also help to increase the odds of an investor sticking with their risk management plan as the short-term performance lows won’t be quite as low as they would be with a single strategy (conversely, the highs won’t be as high either).

That being said, having the discipline to stick with a risk management plan also requires being realistic.  While it would be great to build a strategy with 100% upside and 0% downside, such an outcome is unrealistic.  Risk-managed strategies tend to behave a lot like uncertain insurance for the portfolio.  A premium, in the form of upside capture ratios less than 100%, is paid in exchange for a (hopeful) reduction in downside capture.  This upside underperformance is a feature, not a bug.  Trying too hard to correct it may lead to overfit strategies fail to deliver adequate protection on the downside.

Measuring Process Diversification in Trend Following

By

On July 30, 2018

In Craftsmanship, Portfolio Construction, Risk Management, Weekly Commentary

This post is available as a PDF download here.

Summary­

  • We prefer to think about diversification in a three-dimensional framework: what, how, and when.
  • The “how” axis covers the process with which an investment decision is made.
  • There are a number of models that trend-followers might use to capture a trend. For example, trend-followers might employ a time-series momentum model, a price-minus moving average model, or a double moving average cross-over model.
  • Beyond multiple models, each model can have a variety of parameterizations. For example, a time-series momentum model can just as equally be applied with a 3-month formation period as an 18-month period.
  • In this commentary, we attempt to measure how much diversification opportunity is available by employing multiple models with multiple parameterizations in a simple long/flat trend-following process.

When investors talk about diversification, they typically mean across different investments.  Do not just by a single stock, for example, buy a basket of stocks in order to diversify away the idiosyncratic risk.

We call this “what” diversification (i.e. “what are you buying?”) and believe this is only one of three meaningful axes of diversification for investors.  The other two are “how” (i.e. “how are you making your decision?”) and “when” (i.e. “when are you making your decision?”).  In recent years, we have written a great deal about the “when” axis, and you can find a summary of that research in our commentary Quantifying Timing Luck.

In this commentary, we want to discuss the potential benefits of diversifying across the “how” axis in trend-following strategies.

But what, exactly, do we mean by this?  Consider that there are a number of ways investors can implement trend-following signals.  Some popular methods include:

  • Prior total returns (“time-series momentum”)
  • Price-minus-moving-average (e.g. price falls below the 200-day moving average)
  • Moving-average double cross-over (e.g. the 50-day moving average crosses the 200-day moving average)
  • Moving-average change-in-direction (e.g. the 200-day moving average slope turns positive or negative)

As it turns out, these varying methodologies are actually cousins of one another.  Recent research has established that these models can, more or less, be thought of as different weighting schemes of underlying returns.  For example, a time-series momentum model (with no skip month) derives its signal by averaging daily log returns over the lookback period equally.

With this common base, a number of papers over the last decade have found significant relationships between the varying methods.  For example:

 

Evidence
Bruder, Dao, Richard, and Roncalli (2011)Moving-average-double-crossover is just an alternative weighting scheme for time-series momentum.
Marshall, Nguyen and Visaltanachoti (2014)Time-series momentum is related to moving-average-change-in-direction.
Levine and Pedersen (2015)Time-series-momentum and moving-average cross-overs are highly related; both methods perform similarly on 58 liquid futures contracts.
Beekhuizen and Hallerbach (2015)Mathematically linked moving averages with prior returns.
Zakamulin (2015)Price-minus-moving-average, moving-average-double-cross-over, and moving-average-change-of-direction can all be interpreted as a computation of a weighted moving average of momentum rules.

 

As we have argued in past commentaries, we do not believe any single method is necessarily superior to another.  In fact, it is trivial to evaluate these methods over different asset classes and time-horizons and find an example that proves that a given method provides the best result.

Without a crystal ball, however, and without any economic interpretation why one might be superior to another, the choice is arbitrary.  Yet the choice will ultimately introduce randomness into our results: a factor we like to call “process risk.”  A question we should ask ourselves is, “if we have no reason to believe one is better than another, why would we pick one at all?”

We like to think of it this way: ex-post, we will know whether the return over a given period is positive or negative.  Ex-ante, all we have is a handful of trend-following signals that are forecasting that direction.  If, historically, all of these trend signals have been effective, then there may be no reason to necessarily believe on over another.

Combining them, in many ways, is sort of like trying to triangulate on the truth. We have a number of models that all look at the problem from a slightly different perspective and, therefore, provide a slightly different interpretation.  A (very) loose analogy might be using the collective information from a number of cell towers in effort to pinpoint the geographic location of a cellphone.

We may believe that all of the trend models do a good job of identifying trends over the long run, but most will prove false from time-to-time in the short-run. By using them together, we can potentially increase our overall confidence when the models agree and decrease our confidence when they do not.

With all this in mind, we want to explore the simple question: “how much potential benefit does process diversification bring us?”

The Setup

To answer this question, we first generate a number of long/flat trend following strategies that invest in a broad U.S. equity index or the risk-free rate (both provided by the Kenneth French database and ranging from 1926 to 2018). There are 48 strategy variations in total constructed through a combination of four difference processes – time-series momentum, price-minus-moving-average, and moving-average double cross-over– and 16 different lookback periods (from the approximate equivalent of 3-to-18 months).

We then treat each of the 64 variations as its own unique asset.

To measure process diversification, we are going to use the concept of “independent bets.” The greater the number of independent bets within a portfolio, the greater the internal diversification. Below are a couple examples outlining the basic intuition for a two-asset portfolio:

  • If we have a portfolio holding two totally independent assets with similar volatility levels, a 50% allocation to each would maximize our diversification.Intuitively, we have equally allocated across two unique bets.
  • If we have a portfolio holding two totally independent assets with similar volatility levels, a 90% allocation to one asset and a 10% allocation to another would lead us to a highly concentrated bet.
  • If we have a portfolio holding two highly correlated assets, no matter the allocation split, we have a large, concentrated bet.
  • If we have a portfolio of two assets with disparate volatility levels, we will have a large concentrated bet unless the lower volatility asset comprises the vast majority of the portfolio.

To measure this concept mathematically, we are going to use the fact that the square of the “diversification ratio” of a portfolio is equal to the number of independent bets that portfolio is taking.1

Diversifying Parameterization Risk

Within process diversification, the first variable we can tweak is the formation period of our trend signal.  For example, if we are using a time-series momentum model that simply looks at the sign of the total return over the prior period, the length of that period may have a significant influence in the identification of a trend.  Intuition tells us that shorter formation periods might identify short-term trends as well as react to long-term trend changes more quickly but may be more sensitive to whipsaw risk.

To explore the diversification opportunities available to us simply by varying our formation parameterization, we build equal-weight portfolios comprised of two strategies at a time, where each strategy utilizes the same trend model but a different parameterization.  We then measure the number of independent bets in that combination.

We run this test for each trend following process independently.  As an example, we compare using a shorter lookback period with a longer lookback period in the context of time-series momentum in isolation. We will compare across models in the next section.

In the graphs below, L0 through L15 represent the lookback periods, with L0 being the shortest lookback period and L15 representing the longest lookback period.

As we might suspect, the largest increase in available bets arises from combining shorter formation periods with longer formation periods.  This makes sense, as they represent the two horizons that share the smallest proportion of data and therefore have the least “information leakage.” Consider, for example, a time-series momentum signal that has a 4-monnth lookback and one with an 8-month lookback. At all times, 50% of the information used to derive the latter model is contained within the former model.  While the technical details are subtler, we would generally expect that the more informational overlap, the less diversification is available.

We can see that combining short- and long-term lookbacks, the total number of bets the portfolio is taking from 1.0 to approximately 1.2.

This may not seem like a significant lift, but we should remember Grinold and Kahn’s Fundamental Law of Active Management:

Information Ratio = Information Coefficient x SQRT(Independent Bets)

Assuming the information coefficient stays the same, an increase in the number of independent bets from 1.0 to 1.2 increases our information ratio by approximately 10%.  Such is the power of diversification.

Another interesting way to approach this data is by allowing an optimizer to attempt to maximize the diversification ratio.  In other words, instead of only looking at naïve, equal-weight combinations of two processes at a time, we can build a portfolio from all available lookback variations.

Doing so may provide two interesting insights.

First, we can see how the optimizer might look to combine different variations to maximize diversification.  Will it barbell long and short lookbacks, or is there benefit to including medium lookbacks? Will the different processes have different solutions?  Second, by optimizing over the full history of data, we can find an upper limit threshold to the number of independent bets we might be able to capture if we had a crystal ball.

A few takeaways from the graphs above:

  • Almost all of the processes barbell short and long lookback horizons to maximize diversification.
  • The optimizer finds value, in most cases, in introducing medium-term lookback horizons as well. We can see for Time-Series MOM, the significant weights are placed on L0, L1, L6, L10, and L15.  While not perfectly spaced or equally weighted, this still provides a strong cross-section of available information.  Double MA Cross-Over, on the other hand, finds value in weighting L0, L8, and L15.
  • While the optimizer increases the number of independent bets in all cases versus a naïve, equal-weight approach, the pickup is not incredibly dramatic. At the end of the day, a crystal ball does not find a meaningfully better solution than our intuition may provide.

Diversifying Model Risk

Similar to the process taken in the above section, we will now attempt to quantify the benefits of cross-process diversification.

For each trend model, we will calculate the number of independent bets available by combining it with another trend model but hold the lookback period constant. As an example, we will combine the shortest lookback period of the Time-Series MOM model with the shortest lookback period of the MA Double Cross-Over.

We plot the results below of the number of independent bets available through a naïve, equal-weight combination.

We can see that model combinations can lift the number of independent bets from by 0.05 to 0.1.  Not as significant as the theoretical lift from parameter diversification, but not totally insignificant.

Combining Model and Parameterization Diversification

We can once again employ our crystal ball in an attempt to find an upper limit to the diversification available to trend followers, as well as the process / parameterization combinations that will maximize this opportunity.  Below, we plot the results.

We see a few interesting things of note:

  • The vast majority of models and parameterizations are ignored.
  • Time-Series MOM is heavily favored as a model, receiving nearly 60% of the portfolio weight.
  • We see a spread of weight across short, medium, and long-term weights. Short-term is heavily favored, with Time-Series MOM L0 and Price-Minus MA L0 approaching nearly 45% of model weight.
  • All three models are, ultimately, incorporated, with approximately 10% being allocated to Double MA Cross-Over, 30% to Price-Minus MA, and 60% to Time-Series MOM.

It is worth pointing out that naively allocating equally across all 48 models creates 1.18 independent bets while the full-period crystal ball generated 1.29 bets.

Of course, having a crystal ball is unrealistic.  Below, we look at a rolling window optimization that looks at the prior 5 years of weekly returns to create the most diversified portfolio.  To avoid plotting a graph with 48 different components, we have plot the results two ways: (1) clustered by process and (2) clustered by lookback period.

Using the rolling window, we see similar results as we saw with the crystal ball. First, Time-Series MOM is largely favored, often peaking well over 50% of the portfolio weights.  Second, we see that a barbelling approach is frequently employed, balancing allocations to the shortest lookbacks (L0 and L1) with the longest lookbacks (L14 and L15).  Mid-length lookbacks are not outright ignored, however, and L5 through L11 combined frequently make up 20% of the portfolio.

Finally, we can see that the rolling number of bets is highly variable over time, but optimization frequently creates a meaningful impact over an equal-weight approach.2

Conclusion

In this commentary, we have explored the idea of process diversification.  In the context of a simple long/flat trend-following strategy, we find that combining strategies that employ different trend identification models and different formation periods can lead to an increase in the independent number of bets taken by the portfolio.

As it specifically pertains to trend-following, we see that diversification appears to be maximized by allocating across a number of lookback horizons, with an optimizer putting a particular emphasis on barbelling shorter and longer lookback periods.

We also see that incorporating multiple processes can increase available diversification as well.  Interestingly, the optimizer did not equally diversify across models.  This may be due to the fact that these models are not truly independent from one another than they might seem.  For example, Zakamulin (2015) demonstrated that these models can all be decomposed into a different weighted average of the same general momentum rules.

Finding process diversification, then, might require moving to a process that may not have a common basis.  For example, trend followers might consider channel methods or a change in basis (e.g. constant volume bars instead of constant time bars).

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