Flirting with Models

The Research Library of Newfound Research

Leverage and Trend Following

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On May 7, 2018

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

This post is available as a PDF download here.

Summary­

  • We typically discuss trend following in the context of risk management for investors looking to diversify their diversifiers.
  • While we believe that trend following is most appropriate for investors concerned about sequence risk, levered trend following may have use for investors pursuing growth.
  • In a simple back-test, a naïve levered trend following considerably increases annualized returns and reduces negative skew and kurtosis (“fat tails”).
  • The introduced leverage, however, significantly increases annualized volatility, meaning that the strategy still exhibits significant and large drawdown profiles.
  • Nevertheless, trend following may be a way to allow for the incorporation of leverage with reduced risk of permanent portfolio impairment that would otherwise occur from large drawdowns.

In an industry obsessed with alpha, our view here at Newfound has long been to take a risk-first approach to investing.  In light of this, when we discuss trend following techniques, it is often with an eye towards explicitly managing drawdowns.  Our aim is to help investors diversify their diversifiers and better manage the potentially devastation that sequence risk can wreak upon their portfolios.

Thus, we often discuss the application of trend following for soon-to-be and recent retirees who are in peak sequence risk years.

  • Empirical evidence suggests that trend following can be a highly effective means of limiting exposure to significant and prolonged drawdowns.
  • Trend following is complementary to other diversifiers like fixed income, which can theoretically increase the Sharpe ratio of the diversification bucket as a whole.
  • Instead of acting as a static hedge, the dynamic approach of trend following can also help investors take advantage of market tailwinds. This may be particularly important if real interest rates remain low.
  • The potential tax inefficiency of trend following is significantly lower when the alternative risk management technique is fixed income.

Despite our focus on using trend following to manage sequence risk, we often receive questions from investors still within their accumulation phase asking whether trend following can be appropriate for them as well.  Most frequently, the question is, “If trend following can manage downside risk, can I use a levered approach to trend following in hopes of boosting returns?”

This commentary explores that idea, specifically in the context of available levered ETFs.

Does Naïve Levered Trend Following Work?

In an effort to avoid overfitting our results to any one particular model or parameterization of trend following, we have constructed our signals employing a model-of-models approach [1] Specifically, we use four different definitions of trend for a given N-period lookback:

  • Price-Minus-Moving-Average: When price is above its N-period simple moving average, invest.Otherwise, divest.
  • EWMA Cross-Over: When the (N/4)-length exponentially-weighted moving average is above the (N/2)-length exponentially-weighted moving average, invest.Otherwise, divest.
  • EWMA Slope: When the (N/2)-length exponentially-weighted moving average is positively sloped, invest. Otherwise, divest.
  • Percentile Channel: When price crossed above the trailing 75thpercentile over the prior N-periods, invest. Stay invested until it crosses below its trailing 25thpercentile over the prior N-periods.  Stay divested until it crosses back above the 75th

For each of these four models, we also run a number of parameterizations covering 6-to-18-month lookbacks.  In grand total, there are 4 models with 5 parameterizations each, giving us 30 variations of trend signals.

Using these signals, we construct three models. In the first model, we simply invest in U.S. equities in proportion to the number of signals that are positive. For example, if 75% of the trend following signals are positive, the portfolio is 75% invested in U.S. equities and 25% in the risk-free asset.

For our leveraged model, we simply multiply the percentage of signals by 2x and invest that proportion of our portfolio in U.S. equities and the remainder in the risk-free asset.  In those cases where the amount invested in U.S. equities exceeds 100% of the portfolio, we assume a negative allocation to the risk-free asset (e.g. if we invest 150% of our assets in U.S. equities, we assume a -50% allocation to the risk-free asset).

With the benefit of hindsight, we should not be surprised at the results.  If we know that trend following is effective at limiting severe and prolonged drawdowns (the kryptonite to levered investors), then it should come as no surprise that a levered trend following strategy does quite well.

It is well worth pointing out, however, that a highly levered strategy can be quickly wiped out by a sudden and immediate drawdown that trend following is unable to sidestep.  Assuming a 2x levered position, our portfolio would be quickly wiped out by a sharp 50% correction.  While such an event did not happen during the 1900s for U.S. equities, that does not mean it cannot happen in the future.  Caveat emptor.

Logarithmically-plotted equity curves can be deceiving, so it is important that we also compare the annual return characteristics.

Source: Kenneth French Data Library. Calculations by Newfound Research. Returns are gross of all fees, including transaction fees, taxes, and any management fees.  Returns assume the reinvestment of all distributions.  Past performance is not a guarantee of future results.

While we can see that a simple trend following approach effectively “clips” the tails of the underlying distribution – giving up both the best and the worst annual returns – the levered strategy still has significant mass in both directions.  Evaluating the first several moments of the distributions, however, we see that both simple and levered trend following significantly reduce the skew and kurtosis of the return distribution.

MeanStandard DeviationSkewKurtosis
U.S. Equities9.4%19%-1.011.36
Trend Following9.5%13%0.09-0.92
Levered Trend Following14.4%26%0.11-0.78

 

Nevertheless, the standard deviation of the levered trend following strategy exceeds even that of the underlying asset, a potential indication that expectations for the approach may be less about, “Can I avoid large drawdowns?” and more about, “Can I use leverage for growth and still avoid catastrophe?”  We can see this by plotting the joint annual log-return distributions.

We can see that for U.S. equity returns between 0% and -20%, the Levered Trend Following strategy can exhibit returns between -20% and -40%.  About 11% of the observations fall into this category, making it an occurrence that a levered trend follower should expect to experience multiple times in their investment lifecycle.  We can even see one year where U.S. equities are slightly positive and the levered model exhibits a near -30% return.  It is in the most extreme U.S. equity years – those exceeding -20% – that the trend following aspect appears to come into play.

We must also ask the question, “can this idea survive associated fees?”  If investors are looking to apply this approach using levered ETFs, they must consider the expense ratios of the ETFs themselves, transaction costs, and bid/ask spreads.  Here we will use the ProShares Ultra S&P 500 ETF (“SSO”) as a data proxy.  The expense ratio is 0.90% and the average bid/ask spread is 0.03%.  Since transactions costs vary, we will assume an added annual 0.20% fee for asset-based pricing.

In comparison, for the naïve model, we will use the SPDR S&P 500 ETF (“SPY”) as the data proxy and assume an expense ratio of 0.09% and an average bid/ask spread 0.004%.  Since most platforms have a vanilla S&P 500 ETF on their no-transaction fee list, we will not add any explicit transaction costs.

We plot the strategy equity curves below net of these assumed fees.

The annualized return for the Levered Trend Following strategy declines from 15.9% to 14.5%, while the unlevered version only falls from 10.1% to 10.0%.  While the overall return of the levered version declines by 140 basis points per year, it still far exceeds the total return performance of the unlevered version. 

Conclusion

Based upon this initial analysis, it would appear that a simple, levered trend following approach may be worth further consideration for investors in the accumulation phase of their investment lifecycle.

Do-it-yourself investors may have no problem implementing this idea on their own using levered ETFs, but other investors may prefer a simple, packaged approach.  Unfortunately, as far as we are aware, no such packaged product exists in the marketplace today.

However, one workaround may be to utilize levered ETFs to “make room” for an unlevered trend following strategy.  For example, if a growth-oriented investor currently holdings an 80/20 stock/bond mix and wanted to introduce a 20% allocation to trend following, they could re-orient their portfolio to be 60% stocks, 10% 2x levered stocks, 10% 2x levered bonds, and 20% trend following.  This would have the effect of being an 80/20 stock/bond portfolio with 20% leverage applied to introduce the trend following strategy.  While there are the nuances of daily reset to consider in the levered ETF solutions, this approach may allow for the modest introduction of levered trend following into the portfolio.

It is worth noting that while we employed up to 2x leverage in this commentary, there is no reason investors could not apply a lower amount, either by mixing levered and unlevered ETFs, or by using a solution like the new Portfolio+ line-up from Direxion, which applies 1.25x leverage to underlying indices.

As we like to say here at Newfound, “risk cannot be destroyed, only transformed.” While this commentary explored levered trend following in comparison to unlevered exposure, a more apt comparison might simply be to levered market exposure.  We suspect that the trend following overlay creates the same transformation: a reduction of the best and worst years at the cost of whipsaw. However, the introduction of leverage further heightens the risk of sudden and immediate drawdowns: the exact loss profile trend following is ill-suited to avoid.

 

 

[1] Nothing in this commentary reflects an actual investment strategy or model managed by Newfound and any investment strategies or investment approaches reflected herein are constructed solely for purposes of analyzing and evaluating the topics herein.

The Importance of Diversification in Trend Following

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On April 30, 2018

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

This post is available as a PDF download here.

Summary­

  • Diversification is a key ingredient to a successful trend following program.
  • While most popular trend following programs take a multi-asset approach (e.g. managed futures programs), we believe that single-asset strategies can play a meaningful role in investor portfolios.
  • We believe that long-term success requires introducing sources of diversification within single-asset portfolios. For example, in our trend equity strategies we employ a sector-based framework.
  • We believe the increased internal diversification allows not only for a higher probability of success, but also increases the degrees of freedom with which we can manage the strategy.
  • Introducing diversification, however, can also introduce tracking error, which can be a source of frustration for benchmark-sensitive investors.

Our friends over at ReSolve Asset Management recently penned a blog post titled Diversification – What Most Novice Investors Miss About Trend Following.  What the team at ReSolve succinctly shows – which we tried to demonstrate in our own piece, Diversifying the What, How, and When of Trend Following– is that diversification is a hugely important component of developing a robust trend following program.

A cornerstone argument of both pieces is that the overwhelming success of a simple trend following approach applied to U.S. equities may be misleading.  The same approach, when applied to a large cross-section of majority international equity indices, shows a large degree of dispersion.

That is not to say that the approach does not work: in fact, it is the robustness across such a large cross-section that gives us confidence that it does. Rather, we see that the relative success seen in applying the approach on U.S. equity markets may be a positive outlier.

ReSolve proposes a diversified, multi-asset trend following approach that is levered to the appropriate target volatility.  In our view, this solution is both theoretically and empirically sound.

That said, here at Newfound we do offer a number of solutions that apply trend following on a single asset class.  Indeed, the approach we are most well-known for (going back to when were founded in August 2008), has been long/flat trend following on U.S. equities.

How do we reconcile the belief that multi-asset trend following likely offers a higher risk-adjusted return, but still offer single-asset trend following strategies?  The answer emerges from our ethos of investing at the intersection of quantitative and behavioral finance.  Specifically, we acknowledge that investors tend to exhibit an aversion to non-transparent strategies that have significant tracking error to their reference benchmarks.

Trend following approaches on single asset classes like U.S. equities (an asset class that tends to dominate the risk profile of most U.S. investors) can therefore potentially offer a more sustainable risk management solution, even if it does so with a lower long-term risk-adjusted return than a multi-asset approach.

Nevertheless, we believe that how a trend following strategy is implemented is critical for long-term success.  This is especially true for approaches that target single asset classes.

Finding Diversification Within Single-Asset Strategies

Underlying Newfound’s trend equity strategies (both our Sector and Factor series) is a sector-based methodology.  The reason for employing this methodology is an effort to maximize internal strategy diversification.  Recalling our three-dimensional framework of diversification – “what” (investments), “how” (process), and “when” (timing) – our goal in using sectors is to increase diversification along the what axis.

As an example, below we plot the correlation between sector-based trend following strategies.  Specifically, we use a simple long/flat 200-day moving average cross-over system.

Correlation matrix of sector-based trend following strategies

Source: Kenneth French Data Library. Calculations by Newfound Research. Trend following strategy is a 200-day simple moving average cross-over approach where the strategy holds the underlying sector long when price is above its 200-day simple moving average and invests in the risk-free asset when price falls below.  Returns are gross of all fees, including transaction fees, taxes, and any management fees.  Returns assume the reinvestment of all distributions.  Past performance is not a guarantee of future results.

While none of the sector strategies offer negative correlation to one another (nor would we expect them to), we can see that many of the cross-correlations are substantially less than one.  In fact, the average pairwise correlation is 0.50.

Average pairwise correlation of sector trend following strategies

Source: Kenneth French Data Library. Calculations by Newfound Research. Trend following strategy is a 200-day simple moving average cross-over approach where the strategy holds the underlying sector long when price is above its 200-day simple moving average and invests in the risk-free asset when price falls below.  Not an actual strategy managed by Newfound. Hypothetical strategy created solely for this commentary and all returns are backtested and hypothetical.  Returns are gross of all fees, including transaction fees, taxes, and any management fees.  Returns assume the reinvestment of all distributions.  Past performance is not a guarantee of future results.

We would expect that we can benefit from this diversification by creating a strategy that trades the underlying sectors, which in aggregate provide us exposure to the entire U.S. equity market, rather than trading a single trend signal on the entire U.S. equity market itself.  Using a simple equal-weight approach among the seconds, we find exactly this.

The increased Sharpe ratio of a diversified trend following strategy

Source: Kenneth French Data Library. Calculations by Newfound Research. Trend following strategy is a 200-day simple moving average cross-over approach where the strategy holds the underlying sector long when price is above its 200-day simple moving average and invests in the risk-free asset when price falls below.  Not an actual strategy managed by Newfound. Hypothetical strategy created solely for this commentary and all returns are backtested and hypothetical.  Returns are gross of all fees, including transaction fees, taxes, and any management fees.  Returns assume the reinvestment of all distributions.  Past performance is not a guarantee of future results.

There are two important things to note.  First is that the simple trend following approach, when applied to broad U.S. equities, offers a Sharpe ratio higher than trend following applied to any of the underlying sectors themselves.  We can choose to believe that this is because there is something special about applying trend following at the aggregate index level, or we can assume that this is simply the result of a single realization of history and that our forward expectations for success should be lower.

We would be more likely to believe the former if we demonstrated the same effect across the globe.  For now, we believe it is prudent to assume the latter.

The most important detail of the chart, however, is that a simple equally-weighted portfolio of the underlying sector strategies not only offered a dramatic increase in the Sharpe ratio compared to the median sector strategy, but also a near 15% boost in Sharpe ratio against that offered by trend following on broad U.S. equities.

Using a sector-based approach also affords us greater flexibility in our portfolio construction.  For example, while a single-signal approach to trend following across broad U.S. equities creates an “all in” or “all out” dynamic, using sectors allows us to either incorporate other signals (e.g. cross-sectional momentum, as popularized in Gary Antonacci’s dual momentum approach) or re-distribute available capital.

For example, below we plot the annualized return versus maximum drawdown for an equal-weight sector strategy that allows for the re-use of capital.  For example, when a trend signal for a sector turns negative, instead of moving the capital to cash, the capital is equally re-allocated across the remaining sectors.  A position limit is then applied, allowing the portfolio to introduce the risk-free asset when a certain number of sectors has turned off.

The trade-off between annualized return and maximum drawdown when capital re-use is allowed

Source: Kenneth French Data Library. Calculations by Newfound Research. Not an actual strategy managed by Newfound.  Hypothetical strategy created solely for this commentary and all returns are backtested and hypothetical.  Returns are gross of all fees, including transaction fees, taxes, and any management fees.  Returns assume the reinvestment of all distributions.  Past performance is not a guarantee of future results.

The annotations on each point in the plot reflect the maximum position size, which can also be interpreted as inversely proportional the number of sectors that have to still be exhibiting a positive trend to remain fully invested.  For example, the point labeled 9.1% does not allow for any re-use of capital, as it requires all 11 sectors to be positive. On the other hand, the point labeled 50% requires just two sectors to exhibit positive trends to remain fully invested.

We can see that the degree to which capital is re-used becomes an axis along which we can trade-off our pursuit of return versus our desire to protect on the downside. Limited re-use decreases both drawdown and annualized return.  We can also see, however, that after a certain amount of capital re-use, the marginal increase in annualized return decreases dramatically while maximum drawdown continues to increase.

Of course, the added internal diversification and the ability to re-use available capital do not come free.  The equal-weight sector framework employed introduces potentially significant tracking error to broad U.S. equities, even without introducing the dynamics of trend following.

Tracking error between U.S. equities and an equal-weight sector portfolio

Source: Kenneth French Data Library. Calculations by Newfound Research. Not an actual strategy managed by Newfound.  Hypothetical strategy created solely for this commentary and all returns are backtested and hypothetical.  Returns are gross of all fees, including transaction fees, taxes, and any management fees.  Returns assume the reinvestment of all distributions.  Past performance is not a guarantee of future results.

We can see that the average long-term tracking error is not insignificant, and at times can be quite extreme.  The dot-com bubble, in particular, stands out as the equal-weight framework would have a significant underweight towards technology.  During the dot-com boom, this would likely represent a significant source of frustration for investors.  Even in less extreme times, annual deviations of plus-or-minus 4% from broad U.S. equities would not be uncommon.

Conclusion

For investors pursuing trend following strategies, diversification is a key ingredient.  Many of the most popular trend following programs – for example, managed futures – take a multi-asset approach.  However, we believe that a single-asset approach can still play a meaningful role for investors who seek to manage specific asset risk or who are looking for a potentially more transparent solution.

Nevertheless, diversification remains a critical consideration for single-asset solutions as well.  In our trend equity strategies here at Newfound, we employ a sector-based framework so as to increase the number of signals that dictate our overall equity exposure.

An ancillary benefit of this process is that the sectors provide us another axis with which to manage our portfolio.  We not only have the means by which to introduce other signals into our allocation process (e.g. overweighting sectors exhibiting favorable value or momentum tilts), but we can also decide how much capital we wish to re-invest when trend signals turn negative.

Unfortunately, these benefits do not come free.  A sector-based framework can also potentially introduce a significant degree of tracking error to standard equity benchmarks.  While we believe that the pros outweigh the cons over the long run, investors should be aware that such an approach can lead to significant relative deviations in performance over the short run.

Risk Ignition with Trend Following

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On April 23, 2018

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

This post is available as a PDF download here.

Summary­

  • While investors are often concerned about catastrophic risks, failing to allocate enough to risky assets can lead investors to “fail slowly” by not maintaining pace with inflation or supporting withdrawal rates.
  • Historically, bonds have acted as the primary means of managing risk.However, historical evidence suggests that investors may carry around a significant allocation to fixed income only to offset the tail risks of a few bad years in equities.
  • Going forward, maintaining a large, static allocation to fixed income may represent a significant opportunity cost for investors.
  • Trend following strategies have historically demonstrated the ability to significantly reduce downside risk, though often give up exposure to the best performing years as well.
  • Despite reducing upside capture, trend following strategies may represent a beneficial diversifier for conservative portfolios going forward, potentially allowing investors to more fully participate with equity market growth without necessarily fully exposing themselves to equity market risk.

In our recent commentary Failing Slow, Failing Fast, and Failing Very Fast, we re-introduced the idea of “risk ignition,” a phrase we first read in Aaron Brown’s book Red Blooded Risk.  To quote the book on the core concept of the idea,

“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 worse outcome, and often leads to complete disaster.”

Risk ignition is about taking sufficient risk to promote growth, but not so much risk as to create a high probability of catastrophe.

Traditionally, financial planners have tried to find the balance of risk in the intersection of an investor’s tolerance for risk and their capacity to bear it.  The former addresses the investor’s personal preferences while the latter addresses their financial requirements.

What capacity fails to capture, in our opinion, is an investor’s need to take risk.  It would be difficult to make the argument that a recent retiree with $1,000,000 saved and a planned 4% inflation-adjusted withdrawal rate should ever be allocated to 100% fixed income in the current interest rate environment, no matter what his risk tolerance is.  Bearing too little risk is precisely how investors end up failing slowly.

The simple fact is that earning a return above the risk-free rate requires bearing risk.  It is why, after all, the excess annualized return that equities earn is known as the “equity risk premium.”  Emphasis on the “risk premium” part.

As more and more Baby Boomers retire, prevailing low interest rates mean that traditionally allocated conservative portfolios may no longer offer enough upside to address longevity risk. However, blindly moving these investors into riskier profiles (which may very well be above their risk tolerance anyway) may be equally imprudent, as higher portfolio volatility increases sensitivity to sequence risk when an investor begins taking distributions.

This is where we believe that tactical strategies can play an important role.

Holding Bonds for Insurance

In the simplest asset allocation framework, investors balance their desire to pursue growth with their tolerance (and even capacity) for risk by blending stocks and bonds.  More conservative investors tend to hold a larger proportion of fixed income instruments, preferring their defined cash flows and maturity dates, while growth investors tilt more heavily towards equities.  Stocks fight the risk of lost purchasing power (i.e. inflation) while bonds fight the risk of capital loss.

The blend between equities and bonds will ultimately be determined by balancing exposure to these two risks.

But why not simply hold just stocks?  A trivial question, but one worth acknowledging.  The answer is found in the graph below, where we plot the distribution fitting the annual returns of a broad U.S. equity index from 1962 to 2017.  What we see is a large negative skew, which implies that the left tail of the distribution is much larger than the right.  In plain English: every once in a while, stocks crash. Hard.

Source: Kenneth French Data Library.  Calculations by Newfound Research.  Returns are gross of all fees, including transaction fees, taxes, and any management fees.  Returns assume the reinvestment of all distributions.  Past performance is not a guarantee of future results.

The large left tail implies a drawdown risk that investors with short time horizons, or who are currently taking distributions from their portfolios, may not be able to bear.  This is evident by plotting the realized excess return of different stock / bond[1] mixes versus their respective realized volatility profiles.  We can see that volatility is largely driven by the equity allocation in the portfolio.

This left tail, and long-term equity realized equity volatility in general, is driven by just a few outlier events.  To demonstrate, we will remove the worst performing years for U.S. equities from the dataset.  For the sake of fairness, we’ll also drop an equal number of best years (acknowledging that the best years often follow the worse, and vice versa). Despite losing the best years, the worst years are so bad that we still see a tremendous shift up-and-to-the-left in the realized frontier, indicating higher realized returns with less risk.

Consider that the Sharpe optimal portfolio moves from the 50% stocks / 50% bonds mixture when the full data set is used to an 80% stock / 20% bond split when the best and worst three years are dropped.

Source: Kenneth French Data Library.  Calculations by Newfound Research.  Returns are gross of all fees, including transaction fees, taxes, and any management fees.  Returns assume the reinvestment of all distributions.  Past performance is not a guarantee of future results.

Note that in the full-sample frontier, achieving a long-term annualized volatility of 10% requires holding somewhere between 40-50% of our portfolio in 10-year U.S. Treasuries.  When we drop the best and worst 3 years of equity returns, the same risk level can be achieved with just a 20-30% allocation to bonds.

If we go so far as to drop the best and worst five years?  We would only need 10% of our portfolio in bonds to hit that long-term volatility target.

One interpretation of this data is that investors carry a very significant allocation to bonds in their portfolio simply in effort to hedge the left-tail risks of equities.  For a “balanced” investor (i.e. one around the 10% volatility level of a 60/40 portfolio), the worst three years of equity returns increases the recommended allocation to bonds by 20-30%!

Why is this important?  Consider that forward bond forecasts heavily rely on current interest rates.  Despite the recent increase in the short-end of the U.S. Treasury yield curve, intermediate term rates remain well-below long-term averages.  This has two major implications:

  • If a bear market were to emerge, bonds may not provide the same protection they did in prior bear environments. (See our commentary Bond Returns: Don’t Be Jealous, Be Worried)
  • The opportunity cost for holding bonds versus equities may be quite elevated (if the term premium has eroded while the equity risk premium has remained constant).

Enter trend following.

Cutting the Tails with Trend Following

At its simplest, trend following says to remain invested while an investment is still appreciating in value and divest (or, potentially, even short) when an investment begins to depreciate.

(Since we’ve written at length about trend following in the past, we’ll spare the details in this commentary.  For those keen on learning more about the history and theory of trend following, we would recommend our commentaries Two Centuries of Momentum and Protect and Participate: Managing Drawdowns with Trend Following.)

How, exactly, trend is measured is part of the art. The science, however, largely remains the same: trend following has a long, documented trail of empirical evidence suggesting that it may be an effective means of reducing drawdown risk in a variety of asset classes around the globe.

We can see in the example below that trend following applied to U.S. equities over the last 50+ years is no exception.

(In this example, we have applied a simple price-minus-moving-average trend following strategy.  When price is above the 200-day moving average, we invest in broad U.S. equities.  When price falls below the 200-day moving average, we divest into the risk-free asset. The model is evaluated daily after market close and trades are assumed to be executed at the close of the following day.)

 

Source: Kenneth French Data Library and Federal Reserve of St. Louis. Calculations by Newfound Research. Returns are gross of all fees, including transaction fees, taxes, and any management fees.  Returns assume the reinvestment of all distributions.  Past performance is not a guarantee of future results. 

While the long-term equity curve tells part of the story – nearly matching long-term returns while avoiding many of the deepest – we believe that a more nuanced conversation can be had by looking at the joint distribution of annual returns between U.S. equities and the trend following strategy.

Source: Kenneth French Data Library.  Calculations by Newfound Research.  Scatter plot shows the joint distribution of annual returns from 1962 to 2017 for a broad U.S. equity index and a trend following strategy.  Returns are gross of all fees, including transaction fees, taxes, and any management fees.  Returns assume the reinvestment of all distributions.  Past performance is not a guarantee of future results.

We can see that when U.S. equity returns are positive, the trend following strategy tends to have positive returns as well (albeit slightly lower ones).  When returns are near zero, the trend following strategy has slightly negative returns.  And when U.S. equity returns are highly negative, the trend following strategy significantly limits these returns.

In many ways, one might argue that the return profile of a trend following strategy mirrors that of a long call option (or, alternatively, index plus a long put option).  The strategy has historically offered protection against large drawdowns, but there is a “premium” that is paid in the form of whipsaw.

We can also see this by plotting the annual return distribution of U.S. equities with the distribution of the trend strategy superimposed on top.

Source: Kenneth French Data Library.  Calculations by Newfound Research.  Returns are gross of all fees, including transaction fees, taxes, and any management fees.  Returns assume the reinvestment of all distributions.  Past performance is not a guarantee of future results.

The trend strategy exhibits significantly less skew than U.S. equities, but loses exposure in both tails.  This means that while trend following has historically been able to reduce exposure to significant losses, it has also meant giving up the significant gains.  This makes sense, as many of the market’s best years come off the heels of the worst, when trend following may be slower to reinvest.

In fact, we can see that as we cut off the best and worst years, the distribution of equity returns converges upon the distribution of the trend following strategy.

Source: Kenneth French Data Library.  Calculations by Newfound Research.  Returns are gross of all fees, including transaction fees, taxes, and any management fees.  Returns assume the reinvestment of all distributions.  Past performance is not a guarantee of future results.

Our earlier analysis of changes to the realized efficient frontier when the best and worst years are dropped indicates that the return profile of trend following may be of significant benefit to investors.  Specifically, conservative investors may be able to hold a larger allocation to trend following than naked equities.  This allows them to tilt their exposure towards equities in positive trending periods without necessarily invoking a greater level of portfolio volatility and drawdown due to the negative skew equities exhibit.

In the table below, we find the optimal mix of stocks, bonds, and the trend strategy that would have maximized excess annualized return for the same level of volatility of a given stock/bond blend.

 TargetU.S. Equities10-Year Treasury IndexTrend Strategy
0/1007.4%34.7%58.0%
10/909.7%48.4%41.9%
20/8011.5%59.5%29.0%
30/7010.9%56.4%32.7%
40/608.9%43.8%47.3%
50/506.6%29.9%63.6%
60/4037.2%25.0%37.8%
70/3045.4%14.0%40.7%
80/2053.9%3.1%43.1%
90/1075.9%0.0%24.1%
100/0100.0%0.0%0.0%

We can see that across the board, the optimal portfolio would have had a significant allocation to the trend following strategy. Below, we plot excess annualized return versus volatility for each of these portfolios (in orange) as well as the target mixes (in blue).

In all but the most aggressive cases (where trend following simply was not volatile enough to match the required volatility of the benchmark allocation), trend following creates a lift in excess annualized return.  This is because trend following has historically allowed investors to simultaneously decrease overall portfolio risk in negative trending environments and increaseexposure to equities in positive trending ones.

Consider, for example, the optimal mixture that targets the same risk profile of the 30/70 stock/bond blend.  The portfolio holds 9.7% in stocks, 48.4% in bonds and 41.9% in the trend strategy.  This means that in years where stocks are exhibiting a positive trend, the portfolio is a near 50/50 stock/bond split.  In years where stocks are exhibiting a negative trend, the portfolio tilts towards a 10/90 split.  Trend following allows the portfolio to both be far more aggressive as well as far more defensive than the static benchmark.

Used in this manner, even if the trend following strategy underperforms stocks in positive trending years, so long as it outperforms bonds, it can add value in the context of the overall portfolio! While bonds have, historically, acted as a static insurance policy, trend following acts in a far more dynamic capacity, allowing investors to try to maximize their exposure to the equity risk premium.

Source: Kenneth French Data Library and Federal Reserve of St. Louis. Calculations by Newfound Research. Returns are gross of all fees, including transaction fees, taxes, and any management fees.  Returns assume the reinvestment of all distributions.  Past performance is not a guarantee of future results.

Conclusion

Historically, stocks and bonds have acted as the building blocks of asset allocation.  Investors pursuing a growth mandate have tilted towards stocks, while those focused on capital preservation have tilted more heavily towards bonds.

For conservative investors, the need to employ a large bond position is mainly driven by the negative skew exhibited by equity returns.  However, this means that investors are significantly under-allocated to equities, and therefore sacrifice significant growth potential, during non-volatile years.

With low forecasted returns in fixed income, the significant allocation to bonds carried around by most conservative investors may represent a significant opportunity cost, heightening the risk offailing slow.

Trend following strategies, however, offer a simple alternative.  The return profile of these strategies has historically mimicked that of a call option: meaningful upside participation with limited downside exposure.  While not contractually guaranteed, this dynamic exposure may offer investors a way to reduce their allocation to fixed income without necessarily increasing their exposure to left-tail equity risk.

 

 

[1]  We use a constant maturity 10-year U.S. Treasury index for bonds.

Failing Slow, Failing Fast, and Failing Very Fast

By

On April 9, 2018

In Risk Management, Sequence Risk, Weekly Commentary

This post is available as a PDF download here. 

Summary

  • For most investors, long-term “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 his 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 worse outcome, and often leads to complete disaster.”
  • A third type of failure, failing very fast, occurs when we allow behavioral biases to compound the impact of market volatility (i.e. panicked selling near the bottom of a bear market).
  • In the aftermath of the global financial crisis, risk management was often used synonymously with risk reduction. In actuality, a sound risk management plan is not just about reducing risk, but rather about calibrating risk appropriately as a means of minimizing the risk of both slow and fast failure.

On the way back from a recent trip, I ran across a fascinating article in Vanity Fair: “The Clock is Ticking: Inside the Worst U.S. Maritime Disaster in Decades.”  The article details the saga of the SS El Faro, a U.S. flagged cargo ship that sunk in October 2015 at the hands of Hurricane Joaquin.  Quoting from the beginning of the article:

“In the darkness before dawn on Thursday, October 1, 2015, an American merchant captain named Michael Davidson sailed a 790-foot U.S.-flagged cargo ship, El Faro, into the eye wall of a Category 3 hurricane on the exposed windward side of the Bahama Islands.  El Faro means “the lighthouse” in Spanish.

 The hurricane, named Joaquin, was one of the heaviest to ever hit the Bahamas.  It overwhelmed and sank the ship.  Davidson and the 32 others aboard drowned. 

They had been headed from Jacksonville, Florida, on a weekly run to San Juan, Puerto Rico, carrying 391 containers and 294 trailers and cars.  The ship was 430 miles southwest of Miami in deep water when it went down.

Davidson was 53 and known as a stickler for safety.  He came from Windham, Maine, and left behind a wife and two college age daughters.  Neither his remains nor those of his shipmates were ever recovered. 

Disasters at sea do not get the public attention that aviation accidents do, in part because the sea swallows the evidence.  It has been reported that a major merchant ship goes down somewhere in the world every two or three days; most ships are sailing under flags of convenience, with underpaid crews and poor safety records. 

The El Faro tragedy attracted immediate attention for several reasons.  El Faro was a U.S.-flagged ship with a respected captain – and it should have been able to avoid the hurricane.  Why didn’t it?  Add to the mystery this sample fact: the sinking of the El Faro was the worst U.S. maritime disaster in three decades.”

From the beginning, Hurricane Joaquin was giving forecasters fits.  A National Hurricane Center release from September 29th said, “The track forecast remains highly uncertain, and if anything, the spread in the track model guidance is larger now beyond 48 hours…”  Joaquin was so hard to predict that FiveThirtyEight wrote an article about it.  The image below shows just how much variation there was in projected paths for the storm as of September 30th.

Davidson knew all of this.  Initially, he had two options.  The first option was the standard course: a 1,265-mile trip directly through open ocean toward San Juan.   The second was the safe play, a less direct route that would use a number of islands as protection from the storm.  This option would add 184 miles and six plus hours to the trip.

Davidson faced a classic risk management problem.  Should he risk failing fast or failing slow?

Failing fast would mean taking the standard course and suffering damage or disaster at the hands of the storm.  In this scenario – which tragically ended up playing out – Davidson paid the fatal price by taking too much risk.

Failing slow, on the other hand, would be playing it safe and taking the less direct route.  The risk here would be wasting the company’s time and money.  By comparison, this seems like the obvious choice.  However, the article suggests that Davidson may have been particularly sensitive to this risk as he had been gunning for a captain position on a new vessel that would soon replace El Faro on the Jacksonville to San Juan route.  In this scenario, Davidson would fail by taking too little risk.

This dichotomy between taking too little risk and failing slow and taking too much risk and failing fast is central to portfolio risk management.

Aaron Brown summed this idea up nicely in his book Red Blooded Risk, where he wrote, “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 worse outcome, and often leads to complete disaster.”

Failing Slow

In the investing context, failing slow happens when portfolio returns are insufficient to generate the growth needed to meet one’s objectives.  No one event causes this type of failure.  Rather, it slowly builds over time.  Think death by a thousand papercuts or your home slowly being destroyed from the inside by termites.

Traditionally, this was probably the result of taking too little risk.  Oversized allocations to cash, which as an asset class has barely kept up with inflation over the last 90 years, are particularly likely to be a culprit in this respect.

Data Source: http://pages.stern.nyu.edu/~adamodar/New_Home_Page/datafile/histretSP.html. Calculations by Newfound Research. Past performance does not guarantee future results.

 

Take your average 60% stock / 40% bond investor as an example.  Historically, such an investor would see a $100,000 investment grow to $1,494,003 over a 30-year horizon. Add a 5% cash allocation to that portfolio and the average end result drops to $1,406,935, an $87k cash drag.  Double the cash bucket to 10% and the average drag increases to nearly $170k.  This pattern continues as each additional 5% cash increment lowers ending wealth by approximately $80k.

Data Source: http://pages.stern.nyu.edu/~adamodar/New_Home_Page/datafile/histretSP.html. Calculations by Newfound Research. Past performance does not guarantee future results.

 

Fortunately, there are ways to manage funds earmarked for near-term expenditures or as a safety net without carrying excessive amounts of cash.  For one example, see the Betterment article: Safety Net Funds: Why Traditional Advice Is Wrong.

Unfortunately, today’s investors face a more daunting problem.  Low returns may not be limited to cash.  Below, we present medium term (5 to 10 year) expected returns on U.S. equities, U.S. bonds, and a 60/40 blend from seven different firms/individuals.  The average expected return on the 60/40 portfolio is less than 1% per year after inflation.  Even if we exclude the outlier, GMO, the average expected return for the 60/40 is still only 1.3%.  Heck, even the most optimistic forecast from AQR is downright depressing relative to historical experience.

 

Expected return forecasts are the views of the listed firms, are uncertain, and should not be considered investment advice. Nominal returns are adjusted by subtracting 2.2% assumed inflation.

 

And the negativity is far from limited to U.S. markets.  For example, Research Affiliates forecasts a 5.7% real return for emerging market equities.  This is their highest projected return asset class and it still falls well short of historical experience for the U.S. equity markets, which have returned 6.5% after inflation over the last 90 years.

One immediate solution that may come to mind is just to take more risk.  For example, a 4% real return may still be technically achievable[1]. Assuming that Research Affiliates’ forecasts are relatively accurate, this still requires buying into and sticking with a portfolio that holds around 40% in emerging market securities, more than 20% in real assets/alternatives, and exactly 0% large-cap U.S. equity exposure[2].

This may work for those early in the accumulation phase, but it certainly would require quite a bit of intestinal fortitude.  For those nearing, or in, retirement, the problem is more daunting.  We’ve written quite a bit recently about the problems that low forward returns pose for retirement planning[3][4] and what can be done about it[5][6].

And obviously, one of the main side effects of taking more risk is increasing the portfolio’s exposure to large losses and fast failure, very much akin to Captain Davidson sailing way too close to the eye of the hurricane.

Failing Fast

At its core, failing fast in investing is about realizing large losses at the wrong time.  Think your house burning down or being leveled by a tornado instead of being destroyed slowly by termites.

Note that large losses are a necessary, but not sufficient condition for fast failure[7].  After all, for long-term investors, experiencing a bear market eventually is nearly inevitable.  For example, there has never been a 30-year period in the U.S. equity markets without at least one year-over-year loss of greater than 20%.  79% of historical 30-year periods have seen at least one year-over-year loss greater than 40%.

Fast failure is really about being unfortunate enough to realize a large loss at the wrong time.  This is called “sequence risk” and is particularly relevant for individuals nearing or in the early years of retirement.

We’ve used the following simple example of sequence risk before.  Consider three investments:

  • Portfolio A: -30% return in Year 1 and 6% returns for Years 2 to 30.
  • Portfolio B: 6% returns for Years 1 to 14, a -30% return in Year 15, and 6% returns for Years 16 to 30.
  • Portfolio C: 6% returns in Years 1 to 29 and a -30% return in Year 30.

Over the full 30-year period, all three investments have an identical geometric return of 4.54%.

Yet, the experience of investing in each of the three portfolios will be very different for a retiree taking withdrawals[8].  We see that Portfolio C fares the best, ending the 30-year period with 12% more wealth than it began with.  Portfolio B makes it through the period, ending with 61% of the starting wealth, but not without quite a bit more stress.  Portfolio A, however, ends in disaster, running out of money prematurely.

 

One way we can measure sequence risk is to compare historical returns from a particular investment with and without withdrawals.  The larger this gap, the more sequence risk was realized.

We see that sequence risk peaks in periods where large losses were realized early in the 10-year period.  To highlight a few periods:

  • The period ending in 2009 started with the tech bubble and ended with the global financial crisis.
  • The period ending in 1982 started with losses of 14.3% in 1973 and 25.9% in 1974.
  • The period ending in 1938 started off strong with a 43.8% return in 1928, but then suffered four consecutive annual losses as the Great Depression took hold.

Data Source: http://pages.stern.nyu.edu/~adamodar/New_Home_Page/datafile/histretSP.html. Calculations by Newfound Research. Past performance does not guarantee future results.

 

A consequence of sequence risk is that asset classes or strategies with strong risk-adjusted returns, especially those that are able to successfully avoid large losses, can produce better outcomes than investments that may outperform them on a pure return basis.

For example, consider the period from August 2000, when the equity market peaked prior to the popping of the tech bubble, to March 2018.  Over this period, two common risk management tools – U.S. Treasuries (proxied by the Bloomberg Barclays 7-10 Year U.S. Treasury Index and iShares 7-10 Year U.S. Treasuries ETF “IEF”) and Managed Futures (proxied by the Salient Trend Index) – delivered essentially the same return as the S&P 500 (proxied by the SPDR S&P 500 ETF “SPY”).  Both risk management tools have significantly underperformed during the ongoing bull market (16.6% return from March 2009 to March 2018 for SPY compared to 3.1% for IEF and 0.7% for the Salient Trend Index).

Data Source: CSI, Salient. Calculations by Newfound Research. Past performance does not guarantee future results. Returns include no fees except underlying ETF fees. Returns include the reinvestment of dividends.

 

Yet, for investors withdrawing regularly from their portfolio, bonds and managed futures would have been far superior options over the last two decades.  The SPY-only investor would have less than $45k of their original $100k as of March 2018.  On the other hand, both the bond and managed futures investors would have growth their account balance by $34k and $29k, respectively.

Data Source: CSI, Salient. Calculations by Newfound Research. Past performance does not guarantee future results. Returns include no fees except underlying ETF fees. Returns include the reinvestment of dividends.

 

Failing Really Fast

Hurricanes are an unfortunate reality of sea travel.  Market crashes are an unfortunate reality of investing.  Both have the potential to do quite a bit of damage on their own.  However, what plays out over and over again in times of crisis is that human errors compound the situation.  These errors turn bad situations into disasters.  We go from failing fast to failing really fast.

In the case of El Faro, the list of errors can be broadly classified into two categories:

  1. Failures to adequately prepare ahead of time. For example, El Faro had two lifeboats, but they were not up to current code and were essentially worthless on a hobbled ship in the midst of a Category 4 hurricane.
  2. Poor decisions in the heat of the moment. Decision making in the midst of a crisis is very difficult.   The Coast Guard and NTSB put most of the blame on Davidson for poor decision making, failure to listen to the concerns of the crew, and relying on outdated weather information.

These same types of failures apply to investing.  Imagine the retiree that sells all of his equity exposure in early 2009 and sits out of the market for a few years during the first few years of the bull market or maybe the retiree that goes all-in on tech stocks in 2000 after finally getting frustrated with hearing how much money his friend had made off of Pets.com.  Taking a 50%+ loss on your equity exposure is bad, panicking and making rash decisions can throw your financial plans off track for good.

Compounding bad events with bad decisions is a recipe for fast failure.  Avoiding this fate means:

  1. Having a plan in place ahead of time.
  2. If you plan on actively making decisions during a crisis (instead of simply holding), systematize your process. Lay out ahead of time how you will react to various triggers.
  3. Sticking to your plan, even when it may feel a bit uncomfortable.
  4. Diversify, diversify, diversify.

On that last point, the benefits of diversifying your diversifiers cannot be overstated.

For example, take the following four common risk management techniques:

  1. Static allocation to fixed income (60% SPY / 40% IEF blend)
  2. Risk parity (Salient Risk Parity Index)
  3. Managed futures (Salient Trend Index)
  4. Tactical equity with trend-following (binary SPY or IEF depending on 10-month SPY return).

We see that a simple equal-weight blend of the four strategies delivers risk-adjusted returns that are in line with the best individual strategy.  In other words, the power of diversification is so significant that an equal-weight portfolio performs nearly the same as someone who had a crystal ball at the beginning of the period and could foresee which strategy would do the best.

Data Source: CSI, Salient, Bloomberg. Calculations by Newfound Research. Past performance does not guarantee future results. Returns include no fees except underlying ETF fees. Returns include the reinvestment of dividends. Blend is an equal-weight portfolio of the four strategies that is rebalanced on a monthly basis.

 

Achieving Risk Ignition

In the wake of the tech bubble and the global financial crisis, lots of attention has (rightly) been given to portfolio risk management.  Too often, however, we see risk management used as a synonym for risk reduction.  Instead, we believe that risk management is ultimately taking the right amount of risk, not too little or too much.  We call this achieving risk ignition[9] (a phrase we stole from Aaron Brown), where we harness the power of risk to achieve our objectives.

In our opinion, a key part of achieving risk ignition is utilizing changes that can dynamically adapt the amount of risk in the portfolio to any given market environment.

As an example, take an investor that wants to target 10% volatility using a stock/bond mix.  Using historical data going back to the 1980s, this would require holding 55% in stocks and 45% in bonds.  Yet, our research shows that 20% of that bond position is held simply to offset the worst 3 years of equity returns. With 10-year Treasuries yielding only 2.8%, the cost of re-allocating this 20% of the portfolio from stocks to bonds just to protect against market crashes is significant.

This is why we advocate using tactical asset allocation as a pivot around a strategic asset allocation core.  Let’s continue to use the 55/45 stock/bond blend as a starting point.  We can take 30% of the portfolio and put it into a tactical strategy that has the flexibility to move between 100% stocks and 100% bonds.  We fund this allocation by taking half of the capital (15%) from stocks and the other half from bonds.  Now our portfolio has 40% in stocks, 30% in bonds, and 30% in tactical.  When the market is trending upwards, the tactical strategy will likely be fully invested and the entire portfolio will be tilted 70/30 towards stocks, taking advantage of the equity market tailwinds.  When trends turn negative, the tactical strategy will re-allocate towards bonds and in the most extreme configuration tilt the entire portfolio to a 40/60 stock/bond mix.

In this manner, we can use a dynamic strategy to dial the overall portfolio’s risk up and down as market risk ebbs and flows.

Summary

For most investors, 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 and fast failure results from taking too much risk.

While slow failure has typically resulted from allocating too conservatively or holding excessive cash balances, the current low return environment means that even investors doing everything by the book may not be able to achieve the growth necessary to meet their goals.

Fast failure, on the other hand, is always a reality for investors.  Market crashes will happen eventually.  The biggest risk for investors is that they are unlucky enough to experience a market crash at the wrong time.  We call this sequence risk.

A robust risk management strategy should seek to manage the risk of both slow failure and fast failure.  This means not simply seeking to minimize risk, but rather calibrating it to both the objective and the market environment.

 

 

[1] Using Research Affiliates’ asset allocation tool, the efficient portfolio that delivers an expected real return of 4% means taking on estimated annualized volatility of 12%.  This portfolio has more than double the volatility of a 40% U.S. large-cap / 60% intermediate Treasuries portfolio, which not coincidently returned 4% after inflation going back to the 1920s.

[2] The exact allocations are 0.5% U.S. small-cap, 14.1% foreign developed equities, 24.6% emerging market equities, 12.0% long-term Treasuries, 5.0% intermediate-term Treasuries, 0.8% high yield, 4.5% bank loans, 2.5% emerging market bonds (USD), 8.1% emerging market bonds (local currency), 4.4% emerging market currencies, 3.2% REITs, 8.6% U.S. commercial real estate, 4.2% commodities, and 7.5% private equity.

[3] https://blog.thinknewfound.com/2017/08/impact-high-equity-valuations-safe-retirement-withdrawal-rates/

[4] https://blog.thinknewfound.com/2017/09/butterfly-effect-retirement-planning/

[5] https://blog.thinknewfound.com/2017/09/addressing-low-return-forecasts-retirement-tactical-allocation/

[6] https://blog.thinknewfound.com/2017/12/no-silver-bullets-8-ideas-financial-planning-low-return-environment/

[7] Obviously, there are scenarios where large losses alone can be devastating.  One example are losses that are permanent or take an investment’s value to zero or negative (e.g. investments that use leverage).  Another are large losses that occur in portfolios that are meant to fund short-term objectives/liabilities.

[8] We assume 4% withdrawals increased for 2% annual inflation.

[9] https://blog.thinknewfound.com/2015/09/achieving-risk-ignition/

Diversifying the What, How, and When of Trend Following

By

On April 2, 2018

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

This post is available as a PDF download here.

Summary

  • Naïve and simple long/flat trend following approaches have demonstrated considerable consistency and success in U.S. equities.
  • While there are many benefits to simplicity, an overly simplistic implementation can leave investors naked to unintended risks in the short run.
  • We explore how investors can think about introducing greater diversification across the three axes of what, how, and when in effort to build a more robust tactical solution.

In last week’s commentary – Protect & Participate: Managing Drawdowns with Trend Following – we explored the basics of trend following and how a simple “long/flat” investing approach, when applied to U.S. equities, has historically demonstrated considerable ability to limit extreme drawdowns.

While we always preach the benefits of simplicity, an evaluation of the “long run” can often overshadow many of the short-run risks that can materialize when a model is overly simplistic.  Most strategies look good when plotted over a 100-year period in log-scale and drawn with a fat enough marker.

With trend following in particular, a naïve implementation can introduce uncompensated risk factors that, if left unattended, can lead to performance gremlins.

We should be clear, however, that left unattended, nothing could happen at all.  You could get lucky.  That’s the funny thing about risk: sometimes it does not materialize and correcting for it can actually leave you worse off.

But hope is not a strategy and without a crystal ball at our disposal, we feel that managing uncompensated risks is critical for creating more consistent performance and aligning with investor expectations.

In light of this, the remainder of this commentary will be dedicated to exploring how we can tackle several of the uncompensated risks found in naïve implementations by using the three axes of diversification: what, how, and when. 

The What: Asset Diversification

The first axis of diversification is “what,” which encompasses the question, “what are we allocating across?”

As a tangent, we want to point out that there is a relationship between tactical asset allocation and underlying opportunities to diversify, which we wrote about in a prior commentary Rising Correlations and Tactical Asset Allocation.  The simple take is that when there are more opportunities for diversification, the accuracy hurdle rate that a tactical process has to overcome increases.  While we won’t address that concept explicitly here, we do think it is an important one to keep in mind.

Specifically as it relates to developing a robust trend following strategy, however, what we wish to discuss is “what are we generating signals on?”

A backtest of a naively implemented trend following approach on U.S. equities over the last century has been exceptionally effective.  Perhaps deceivingly so.  Consider the following cumulative excess return results from 12/1969 to present for a 12-1 month time-series momentum strategy.

 

Source: Kenneth French Data Library.  Calculations by Newfound Research.  Past performance is not an indication of future returns.  All performance information is backtested and hypothetical.  Performance is gross of all fees, including manager fees, transaction costs, and taxes.  Performance is net of withholding taxes.  Performance assumes the reinvestment of all dividends.  Benchmark is 50% U.S. equity index / 50% risk-free rate.

While the strategy exhibits a considerable amount of consistency, this need not be the case.

Backtests demonstrate that trend following has worked in a variety of international markets “over the long run,” but the realized performance can be much more volatile than we have seen with U.S. equities.  Below we plot the growth of $1 in standard 12-1 month time-series momentum strategies for a handful of randomly selected international equity markets minus their respective benchmark (50% equity / 50% cash).

Note: Things can get a little whacky when working with international markets.  You ultimately have to consider whose perspective you are investing from.  Here, we assumed a U.S. investor that uses U.S. dollar-denominated foreign equity returns and invests in the U.S. risk-free rate.  Note that this does, by construction, conflate currency trends with underlying trends in the equity indices themselves.  We will concede that whether the appropriate measure of trend should be local-currency based or not is debatable.  In this case, we do not think it affects our overall point.

Source: MSCI.  Calculations by Newfound Research.  Past performance is not an indication of future returns.  All performance information is backtested and hypothetical.  Performance is gross of all fees, including manager fees, transaction costs, and taxes.  Performance is net of withholding taxes.  Performance assumes the reinvestment of all dividends.  Benchmark is 50% respective equity index / 50% U.S. risk-free rate.

The question to ask ourselves, then, is, “Do we believe U.S. equities are special and naive trend following will continue to work exceptionally well, or was U.S. performance an unusual outlier?”

We are rarely inclined to believe that exceptional, outlier performance will continue.  One approach to providing U.S. equity exposure while diversifying our investments is to use the individual sectors that comprise the index itself.  Below we plot the cumulative excess returns of a simple 12-1 time-series momentum strategy applied to a random selection of underlying U.S. equity sectors.

Source: Kenneth French Data Library.  Calculations by Newfound Research.  Past performance is not an indication of future returns.  All performance information is backtested and hypothetical.  Performance is gross of all fees, including manager fees, transaction costs, and taxes.  Performance is net of withholding taxes.  Performance assumes the reinvestment of all dividends.  Benchmark is 50% respective sector index / 50% U.S. risk-free rate.

While we can see that trend following was successful in generating excess returns, we can also see that when it was successful varies depending upon the sector in question.  For example, Energy (blue) and Telecom (Grey) significantly diverge from one another in the late 1950s / early 1960s as well as in the late 1990s / early 2000s.

If we simply equally allocate across sector strategies, we end up with a cumulative excess return graph that is highly reminiscent of the of the results seen in the naïve U.S. equity strategy, but generated with far more internal diversification.

Source: Kenneth French Data Library.  Calculations by Newfound Research.  Past performance is not an indication of future returns.  All performance information is backtested and hypothetical.  Performance is gross of all fees, including manager fees, transaction costs, and taxes.  Performance is net of withholding taxes.  Performance assumes the reinvestment of all dividends.

A potential added benefit of this approach is that we are now afforded the flexibility to vary sector weights depending upon our objective.  We could potentially incorporate other factors (e.g. value or momentum), enforce diversification limits, or even re-invest capital from sectors exhibiting negative trends back into those exhibiting positive trends.

The How: Process Diversification

The second axis of diversification is “how”: the process in which decisions are made.  This axis can be a bit of a rabbit hole: it can start with high-level questions such as, “value or momentum?” and then go deeper with, “which value measure are you using?” and then even more nuanced with questions such as, “cross-market or cross-industry measures?”  Anecdotally, the diversification “bang for your buck” decreases as the questions get more nuanced.

With respect to trend following, the obvious question is, “how are you measuring the trend?”

One Signal to Rule Them All?

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)

One question we often receive is, “is there one approach that is better than another?”  Research over the last decade, however, actually shows that they are highly related approaches.

Bruder, Dao, Richard, and Roncalli (2011) united moving-average-double-crossover strategies and time-series momentum by showing that cross-overs were really just an alternative weighting scheme for returns in time-series momentum.[1] To quote,

“The weighting of each return … forms a triangle, and the biggest weighting is given at the horizon of the smallest moving average. Therefore, depending on the horizon n2 of the shortest moving average, the indicator can be focused toward the current trend (if n2 is small) or toward past trends (if n2 is as large as n1/2 for instance).”

Marshall, Nguyen and Visaltanachoti (2012) proved that time-series momentum is related to moving-average-change-in-direction.[2] In fact, time-series momentum signals will not occur until the moving average changes direction.  Therefore, signals from a price-minus-moving-average strategy are likely to occur before a change in signal from time-series momentum.

Levine and Pedersen (2015) showed that time-series momentum and moving average cross-overs are highly related.[3] It also found that time-series momentum and moving-average cross-over strategies perform similarly across 58 liquid futures and forward contracts.

Beekhuizen and Hallerbach (2015) also linked moving averages with returns, but further explored trend rules with skip periods and the popular MACD rule.[4] Using the implied link of moving averages and returns, it showed that the MACD is as much trend following as it is mean-reversion.

Zakamulin (2015) explored price-minus-moving-average, moving-average-double-crossover, and moving-average-change-of-direction technical trading rules and found that they can be interpreted as the computation of a weighted moving average of momentum rules with different lookback periods.[5]

These studies are important because they help validate the approach of traditional price-based systems (e.g. moving averages) with the growing body of academic literature on time-series momentum.

The other interpretation, however, is that all of the approaches are simply a different way of trying to tap into the same underlying factor.  The realized difference in their results, then, will likely have to do more with the inefficiencies in capturing that factor and which specific environments a given approach may underperform.  For example, below we plot the maximum return difference over rolling 5-year periods between four different trend following approaches: (1) moving-average change-in-direction (12-month), (2) moving-average double-crossover (3-month / 12-month), (3) price-minus-moving-average (12-month), and (4) time-series momentum (12-1 month).

We can see that during certain periods, the spread between approaches can exceed several hundred basis points.  In fact, the long-term average spread was 348 basis points (“bps”) and the median was 306 bps.  What is perhaps more astounding is that no approach was a consistent winner or loser: relative performance was highly time-varying.  In fact, when ranked 1-to-4 based on prior 5-year realized returns, the average long-term ranks of the strategies were 2.09, 2.67, 2.4, and 2.79 respectively, indicating that no strategy was a clear perpetual winner or loser.

 Source: Kenneth French Data Library.  Calculations by Newfound Research.  Past performance is not an indication of future returns.  All performance information is backtested and hypothetical.  Performance is gross of all fees, including manager fees, transaction costs, and taxes.  Performance assumes the reinvestment of all dividends. 

Without the ability to forecast which model will do best and when, model choice represents an uncompensated risk that we bear as a manager.  Using multiple methods, then, is likely a prudent course of action.

Identifying the Magic Parameter

The academic and empirical evidence for trend following (and, generally, momentum) tends to support a formation (“lookback”) period of 6-to-12 months.  Often we see moving averages used that align with this time horizon as well.

Intuition is that shorter horizons tend to react to market changes more quickly since new information represents a larger proportion of the data used to derive the signal.  For example, in a 6-month momentum measure a new monthly data point represents 16.6% of the data, whereas it only represents 8.3% of a 12-month moving average.

A longer horizon, therefore, is likely to be more “stable” and therefore less susceptible to whipsaw.

Which particular horizon achieves the best performance, then, will likely be highly regime dependent.  To get a sense of this, we ran six time-series momentum strategies, with look-back periods ranging from 6-months to 12-months.  Again, we plot the spread between the best and worst performing strategies over rolling 5-year periods.

 Source: Kenneth French Data Library.  Calculations by Newfound Research.  Past performance is not an indication of future returns.  All performance information is backtested and hypothetical.  Performance is gross of all fees, including manager fees, transaction costs, and taxes.  Performance assumes the reinvestment of all dividends. 

Ignoring the Great Depression for a moment, we can see that 5-year annualized returns between parameterizations frequently deviate by more than 500 bps.  If we dig under the hood, we again see that the optimal parameterization is highly regime dependent.

For example, coming out of the Great Depression, the longer-length strategies seemed to perform best.  From 8/1927 to 12/1934, an 11-1 time-series momentum strategy returned 136% while a 6-1 time-series momentum strategy returned -25%.  Same philosophy; very different performance.

Conversely, from 12/1951 to 12/1971, the 6-1 strategy returned 723% while the 11-1 strategy returned 361%.

Once again, without evidence that we can time our parameter choice, we end up bearing unnecessary parameterization risk, and diversification is a prudent action.

Source: Kenneth French Data Library.  Calculations by Newfound Research.  Past performance is not an indication of future returns.  All performance information is backtested and hypothetical.  Performance is gross of all fees, including manager fees, transaction costs, and taxes.  Performance assumes the reinvestment of all dividends. 

Source: Kenneth French Data Library.  Calculations by Newfound Research.  Past performance is not an indication of future returns.  All performance information is backtested and hypothetical.  Performance is gross of all fees, including manager fees, transaction costs, and taxes.  Performance assumes the reinvestment of all dividends. 

The When: Timing Luck

Long-time readers of our commentary will be familiar with this topic.  For those unfamiliar, we recommend a quick glance over our commentary Quantifying Timing Luck (specifically, the section What is “Timing Luck”?).

The simple description of the problem is that investment strategies can be affected by the investment opportunities they see at the point at which they rebalance.  For example, if we rebalance our tactical strategies at the end of each month, our results will be subject to what our signals say at that point.  We can easily imagine two scenarios where this might work against us:

  1. Our signals identify no change and we remain invested; the market sells off dramatically over the next month.
  2. The market sells off dramatically prior to our rebalance, causing us to move to cash. After we trade, the market rebounds significantly, causing us to miss out on potential gains.

As it turns out, these are not insignificant risks.  Below we plot four identically managed tactical strategies that each rebalance on a different week of the month.  While one of the strategies turned $1 into $4,139 another turned it into $6,797.  That is not an insignificant difference.

Source: Kenneth French Data Library.  Calculations by Newfound Research.  Past performance is not an indication of future returns.  All performance information is backtested and hypothetical.  Performance is gross of all fees, including manager fees, transaction costs, and taxes.  Performance assumes the reinvestment of all dividends. 

Fortunately, the cure for this problem is simple: diversification.  Instead of picking a week to rebalance on, we can allocate to multiple variations of the strategy, each rebalancing at a different point in time.  One variation may rebalance on the 1st week of the month, another on the 2nd week, et cetera.  This technique is called “overlapping portfolios” or “tranching” and we have proven in past commentaries that it can dramatically reduce the impact that timing luck can have on realized results.

Conclusion

Basic, naïve implementations of long/flat trend following exhibit considerable robustness and consistency over the long run when applied to U.S. equities.  The short run, however, is a different story.  While simple implementations can help ensure that we avoid overfitting our models to historical data, it can also leave us exposed to a number of unintended bets and uncompensated risks.

Instead of adding more complexity, we believe that the simple solution to combat these risks is diversification.

Specifically, we explore diversification across three axes.

The first axis is “what” and represents “what we invest across.”  We saw that while trend following worked well on U.S. equities, the approach had less consistency when applied to international indices.  Instead of presuming that the U.S. represents a unique candidate for this type of strategy, we explored a sector-based implementation that may allow for greater internal diversification.

The second axis is “how” and captures “how we implement the strategy.”  There are a variety of approaches practitioners use to measure and identify trends, and each comes with its own pros and cons.  We explore four popular methods and find that none consistently reigns supreme, indicating once again that diversification of process is likely a prudent approach.

Similarly, when it comes to parameterizing these models, we find that a range of lookback periods are successful in the long run, but have varying performance in the short run.  A prudent solution once again, is diversification.

The final axis is “when” and represents “when we rebalance our portfolio.”  Long-time readers recognize this topic as one we frequently write about: timing luck.  We demonstrate that merely shifting what week of the month we rebalance on can have considerable long-term effects.  Again, as an uncompensated risk, we would argue that it is best diversified away.

While a naïve trend following process is easy to implement, we believe that a robust one requires thinking along the many dimensions of risk and asking ourselves which risks are worth bearing (hopefully those that are compensated) and which risks we should seek to hedge or diversify away.

 

 

[1] Bruder, Benjamin and Dao, Tung-Lam and Richard, Jean-Charles and Roncalli, Thierry, Trend Filtering Methods for Momentum Strategies (December 1, 2011). Available at SSRN: http://ssrn.com/abstract=2289097

[2] Marshall, Ben R. and Nguyen, Nhut H. and Visaltanachoti, Nuttawat, Time-Series Momentum versus Moving Average Trading Rules (December 22, 2014). Available at SSRN: http://ssrn.com/abstract=2225551

[3] Levine, Ari and Pedersen, Lasse Heje, Which Trend Is Your Friend? (May 7, 2015). Financial Analysts Journal, vol. 72, no. 3 (May/June 2016). Available at SSRN: https://ssrn.com/abstract=2603731

[4] Beekhuizen, Paul and Hallerbach, Winfried G., Uncovering Trend Rules (May 11, 2015). Available at SSRN: http://ssrn.com/abstract=2604942

[5] Zakamulin, Valeriy, Market Timing with Moving Averages: Anatomy and Performance of Trading Rules (May 13, 2015). Available at SSRN: http://ssrn.com/abstract=2585056

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