Tag: time-series momentum Page 1 of 2

Why Trend Models Diverge

By Corey Hoffstein

On March 9, 2020

In Risk & Style Premia, Trend, Weekly Commentary

This post is available as a PDF download here.

Summary

During the week of February 23^rd, the S&P 500 fell more than 10%.
After a prolonged bullish period in equities, this tumultuous decline caused many trend-following signals to turn negative.
As we would expect, short-term signals across a variety of models turned negative. However, we also saw that price-minus-moving-average models turned negative across a broad horizon of lookbacks where the same was not true for other models.
In this brief research note, we aim to explain why common trend-following models are actually mathematically linked to one another and differ mainly in how they place weight on recent versus prior price changes.
We find that price-minus-moving-average models place the greatest weight on the most recent price changes, whereas models like time-series momentum place equal-weight across their lookback horizon.

In a market note we sent out last weekend, the following graphic was embedded:

What this table intends to capture is the percentage of trend signals that are on for a given model and lookback horizon (i.e. speed) on U.S. equities. The point we were trying to establish was that despite a very bearish week, trend models remained largely mixed. For frequent readers of our commentaries, it should come as no surprise that we were attempting to highlight the potential specification risks of selecting just one trend model to implement with (especially when coupled with timing luck!).

But there is a potentially interesting second lesson to learn here which is a bit more academic. Why does it look like the price-minus (i.e. price-minus-moving-average) models turned off, the time series momentum models partially turned off, and the cross-over (i.e. dual-moving-average-cross) signals largely remained positive?

While this note will be short, it will be somewhat technical. Therefore, we’ll spoil the ending: these signals are all mathematically linked.

They can all be decomposed into a weighted average of prior log-returns and the primary difference between the signals is the weighting concentration. The price-minus model front-weights, the time-series model equal weights, and the cross-over model tends to back-weight (largely dependent upon the length of the two moving averages). Thus, we would expect a price-minus model to react more quickly to large, recent changes.

If you want the gist of the results, just jump to the section The Weight of Prior Evidence, which provides graphical evidence of these weighting schemes.

Before we begin, we want to acknowledge that absolutely nothing in this note is novel. We are, by in large, simply re-stating work pioneered by Bruder, Dao, Richard, and Roncalli (2011); Marshall, Nguyen and Visaltanachoti (2012); Levine and Pedersen (2015); Beekhuizen and Hallerbach (2015); and Zakamulin (2015).

Decomposing Time-Series Momentum

We will begin by decomposing a time-series momentum value, which we will define as:

We will begin with a simple substitution:

Which implies that:

Simply put, time-series momentum puts equal weight on all the past price changes¹ that occur.

Decomposing Dual-Moving-Average-Crossover

We define the dual-moving-average-crossover as:

We assume m is less than n (i.e. the first moving average is “faster” than the second). Then, re-writing:

Here, we can make a cheeky transformation where we add and subtract the current price, P_t:

What we find is that the double-moving-average-crossover value is the difference in two weighted averages of time-series momentum values.

Decomposing Price-Minus-Moving-Average

This decomposition is trivial given the dual-moving-average-crossover. Simply,

The Weight of Prior Evidence

We have now shown that these decompositions are all mathematically related. Just as importantly, we have shown that all three methods are simply re-weighting schemes of prior price changes. To gain a sense of how past returns are weighted to generate a current signal, we can plot normalized weightings for different hypothetical models.

For TSMOM, we can easily see that shorter lookback models apply more weight on less data and therefore are likely to react faster to recent price changes.
PMAC models apply weight in a linear, declining fashion, with the most weight applied to the most recent price changes. What is interesting is that PMAC(50) puts far more weight on recent prices changes than the TSMOM(50) model does. For equivalent lookback periods, then, we would expect PMAC to react much more quickly. This is precisely why we saw PMAC models turn off in the most recent sell-off when other models did not: they are much more front-weighted.
DMAC models create a hump-shaped weighting profile, with increasing weight applied up until the length of the shorter lookback period, and then descending weight thereafter. If we wanted to, we could even create a back-weighted model, as we have with the DMAC(150, 200) example. In practice, it is common to see that m is approximately equal to n/4 (e.g. DMAC(50, 200)). Such a model underweights the most recent information relative to slightly less recent information.

Conclusion

In this brief research note, we demonstrated that common trend-following signals – namely time-series momentum, price-minus-moving-average, and dual-moving-average-crossover – are mathematically linked to one another. We find that prior price changes are the building blocks of each signal, with the primary differences being how those prior price changes are weighted.

Time-series momentum signals equally-weight prior price changes; price-minus-moving-average models tend to forward-weight prior price changes; and dual-moving-average-crossovers create a hump-like weighting function. The choice of which model to employ, then, expresses a view as to the relative importance we want to place on recent versus past price changes.

These results align with the trend signal changes seen over the past week during the rapid sell-off in the S&P 500. Price-minus-moving-average models appeared to turn negative much faster than time-series momentum or dual-moving-average-crossover signals.

By decomposing these models into their most basic and shared form, we again highlight the potential specification risks that can arise from electing to employ just one model. This is particularly true if an investor selects just one of these models without realizing the implicit choice they have made about the relative importance they would like to place on recent versus past returns.

The Importance of Diversification in Trend Following

By Corey Hoffstein

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.

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.

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.

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.

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.

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

By Corey Hoffstein

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.

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.

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.

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.

Target	U.S. Equities	10-Year Treasury Index	Trend Strategy
0/100	7.4%	34.7%	58.0%
10/90	9.7%	48.4%	41.9%
20/80	11.5%	59.5%	29.0%
30/70	10.9%	56.4%	32.7%
40/60	8.9%	43.8%	47.3%
50/50	6.6%	29.9%	63.6%
60/40	37.2%	25.0%	37.8%
70/30	45.4%	14.0%	40.7%
80/20	53.9%	3.1%	43.1%
90/10	75.9%	0.0%	24.1%
100/0	100.0%	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.

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.

Diversifying the What, How, and When of Trend Following

By Corey Hoffstein

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.

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.

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.

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.

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.

**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:

Our signals identify no change and we remain invested; the market sells off dramatically over the next month.
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.

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 1^st week of the month, another on the 2^nd 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

Protect & Participate: Managing Drawdowns with Trend Following

By Corey Hoffstein

On March 26, 2018

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

This post is available as PDF download here.

Summary

Trend following is an investment strategy that buys assets exhibiting strong absolute performance and sells assets exhibiting negative absolute performance.
Despite its simplistic description, trend following has exhibited considerable empirical robustness as a strategy, having been found to work in equity indices, bonds, commodities, and currencies.
A particularly interesting feature about trend following is its potential ability to avoid significant losses. Evidence suggests that trend following approaches can be used as alternative risk management techniques.
However, if investors expect to fully participate with asset growth while receiving significant protection, they are likely to be disappointed.
Relative to other risk management techniques, even very simple trend following strategies have exhibited very attractive return profiles.

What is Trend Following?

At its core, trend following – also called “absolute” or “time-series” momentum – is a very basic investment thesis: investments exhibiting positive returns tend to keep exhibiting positive returns and those exhibiting negative returns tend to keep exhibiting negative returns.

While the approach may sound woefully simplistic, the empirical and academic evidence that supports it extends back nearly two centuries. Lempérière, Deremble, Seager, Potters, and Bouchard (2014), for example, test trend following approaches on commodities, currencies, stock indices, and bonds going back to 1800 and find that “the existence of trends [is] one of the most statistically significant anomalies in financial markets.”[1]

While LDSPB (2014) may have one of the longest backtests to date, a variety of other authors have demonstrated the existence of trends, and the success of trend following, in a variety of environments and markets. We won’t list them here, but for those interested, a more thorough history can be found in our own paper Two Centuries of Momentum.

The driving theory behind trend following is that investor (mis-)behavior causes the emergence of trends. When new information enters the market, investors underreact due to an anchoring bias that causes them to overweight prior information. As price begins to drift towards fair value, herding takes over and causes investors to overreact. This under and subsequent over-reaction is what causes a trend to emerge.

While somewhat contradictory to the notion that investors should not “chase performance” or “time markets,” evidence suggests that when systematically applied, trend following approaches can create a potentially significant return premium and potentially help investors avoid significant losses.

The Basic Trend Following Setup

In our experience, the two most popular methods of implementing a trend following signal are (1) a simple moving average cross-over system and (2) a measure of trailing total return.

In a simple moving average system cross-over system, when price is above the simple moving average, the system stays invested. When price falls below, the strategy divests (usually into a risk-free asset, like U.S. Treasury Bills). This sort of “in-or-out” system is often called “long/flat.” For example, below we show a 12-month simple moving average and highlight when the system would buy and sell based upon when price crosses over.

The second form of trend following is more commonly referred to as “time-series momentum.” In this approach, prior realized returns are calculated and the signal is generated depending upon whether returns were positive or negative. For example, a popular academic approach is to use a “12-1” model, which takes the prior 12-month returns and subtracts the most recent month’s return (to avoid short-term mean reversion effects). If this value is positive, the system invests and if the value is negative, it divests.

By looking at the example graphs, we can see that while these systems are similar, they are not exactly equal. Nor are they the only way trend following approaches are implemented by practitioners. What is important here is not the specific methodology, but that these methodologies attempt to capture the same underlying dynamics.

Empirical Evidence: Trend Following in a Crisis

To explore how a simple 12-1 time-series momentum system has worked in the past, we will apply the process to a broad U.S. equity index. At the end of each month, we will calculate the trend following signal. If the signal is positive, we will remain invested in the index (i.e. we are “long”). If the signal is negative, we will divest into U.S. Treasury Bills (i.e. we are “flat”).

To explore the potential risk management capabilities of trend following, we will define a “crisis” as any period over which the broad U.S. equity market suffers a drawdown exceeding 25% from a recent market high. We will then measure the maximum peak-to-trough drawdown of U.S. equities over the period and compare it to the maximum peak-to-trough drawdown of the 12-1 time series momentum strategy.

Since the early 1900s, we identify eight such scenarios.

Source: Kenneth French Data Library. Calculations by Newfound Research. Past performance is not indicative of future returns. All performance is hypothetical and backtested. Performance assumes the reinvestment of all distributions. Returns are gross of all fees, including management fees, transaction costs, and taxes.

A few important takeaways:

Trend following is not a risk panacea. Even with trend following applied, drawdowns in excess of 15% occurred in each of these cases. This is the cost of market participation, which will address a bit later.
Trend following did not limit losses in all cases. The market sell-off in October 1987 was so rapid that there was not sufficient time for trends to emerge and the system to be able to exit. When trend following ends up protecting from quick sell-offs, it is more likely a function of luck than skill.
In many cases, trend following did help cut losses significantly. In the bear markets of the 1970s and 2000s, trend following helped reduce realized losses by over 50%.

Of course, the experience of these losses is very different than the summary numbers. Below we plot the actual returns of equities versus a trend following overlay for several of the scenarios.

We can see that the in many cases, when the trend following system got out, the market subsequently rallied, meaning that a trend follower would have a larger drawdown. For example, in the Great Depression after the trend following system divested into U.S. Treasury Bills, the equity market rallied significantly. This left the trend follower with a realized loss of -32% while a buy-and-hold investor would only be down -19%.

It is only with the benefit of hindsight that we can see that markets continued to fall and the patient trend follower was rewarded.

Ex-Ante Expectations About Participation

Of course, protecting capital is only half of the equation. If we only cared about capital preservation, we could invest in short-term inflation-protected Treasuries and, barring a default by the U.S. government, sleep very well at night.

Before we demonstrate any empirical evidence about trend following’s ability to participate in growth, we want to use one of our favorite exercises – a coin flip game – to help establish reasonable expectations.

Imagine that we approach you with the offer to play a game. We are going to flip a coin and you are going to try to guess how it lands. If the coin lands on heads and you guess heads, the game is a push. If it lands on tails and you guess tails, we give you $1. If you guess wrong, you give us $1.

Does this sound like a game you would want to play? Our guess is “no.”

Yet when we talk to many investors about their expectations for trend following strategies, this is the game they have created by choosing the U.S. equity market as a benchmark.

Consider the four scenarios that can happen:

The market goes up and trend following participates.
The market goes down and trend following goes down.
The market goes up and trend following is in cash.
The market goes down and trend following is in cash.

In the first scenario, even though trend following got the call right, we created a mental “push.” In the middle two scenarios, trend following was incorrect and either participates on the downside or fails to participate on the upside (i.e. we “lose”). It is only in the last scenario that trend following adds value.

In other words, by choosing U.S. equities as our benchmark for a long/flat trend following strategy, the strategy can only add value when the market is going down. If we believe that the market will go up over the long run, that leaves very few scenarios for trend following to add value and plenty of scenarios for it to be a detractor.

Which is, unsurprisingly, exactly what you see if you plot the growth of a buy-and-hold investor versus a time-series momentum strategy: success in periods of significant market drawdown and relative underperformance in other periods.

We can see, for example, that the trend following strategy lost its entire lead to the buy-and-hold investor from 1942 to 1962. That is a frustratingly long period of underperformance for any investor to weather.

Determining the appropriate benchmark, however, is often a matter of preference. We believe the appropriate way to address the problem is by asking whether trend following materially outperforms U.S. equities on a risk-adjusted basis.

To answer this question, we calculate the strategy’s full-period sensitivity to the U.S. equity index (i.e. its “beta”) and then re-create a new index that is comprised of a mixture U.S. equities and U.S. Treasury Bills that shares the same beta. In this case, that index is 50% U.S. equities and 50% U.S. Treasury Bills.

We can see that compared to a risk-adjusted benchmark, trend following exhibits a significant return premium without necessarily materializing significant excess downside risk.

Our take away from this is simple: investors who expect long/flat trend following strategies to keep up with equities are sure to be disappointed eventually. However, if we use a benchmark that allows both “in” and “flat” decisions to add value (e.g. a 50% U.S. equity index + 50% U.S. Treasury Bill portfolio), trend following has historically added significant value.

One interpretation may be that trend following may be best suited as a “risk pivot” within the portfolio, rather than as an outright replacement for U.S. equity. For example, if an investor has a 60% equity and 40% bond portfolio, rather than replacing equity with a trend strategy, the investor could replace a mix of both stocks and bonds. By taking 10% from stocks and 10% from bonds to give to the trend allocation, the portfolio now has the ability to pivot between a 70/30 and a 50/50. You can read more about this idea in our whitepaper Achieving Risk Ignition.

Another potential interpretation of this data is that long/flat trend following is a risk management technique and should be compared in light of alternative means of managing risk.

Pre-2008 versus Post-2008 Experience

Unfortunately, many investors have had their expectations for long/flat trend following strategies set by the period leading up to the 2008 financial crisis as well as the crisis itself, only to find themselves disappointed by subsequent performance.

Several years of whipsaws (including 2011, 2015 and 2016) leading to relative underperformance have caused many to ask, “is trend following broken?”

When we evaluate the data, however, we see that it is not the post-2008 period that is unique, but rather the pre-2008 period.

In fact, the pre-2008 period is unique in how calm a market environment it was, with drawdowns rarely eclipsing 10%. While the post-2008 period has had its calm years (e.g. 2013 and 2017), it has also been punctuated by periods of volatility. We can see the difference by plotting the drawdowns over the two periods.

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

The unfortunate reality is that the calm period of pre-2008 and the strong performance of trend following in 2008 gave investors the false confidence that trend following had the ability to nearly fully participate on the upside and protect almost entirely on the downside.

Unfortunately, this simply is not true. As we have said many times in the past, “risk cannot be destroyed, only transformed.” While trend following tends to do well in environments where trends persist, it does poorly in those periods that exhibit sharp and sudden price reversals.

However, if we compare our trend following system against the more appropriate long-term risk-adjusted benchmark, we still see a significant return premium earned.

One question we may ask ourselves is, “if we are using trend following to manage risk, how did other risk management techniques perform over the same period?”

	Annualized Return (2009 – 2017)	Annualized Volatility (2009 – 2017)	Maximum Drawdown (2007 – 2009)
S&P 500	14.4%	12.0%	-52.3%
12-1 TS Momentum	11.7%	12.3%	-10.9%
80/20	12.3%	9.4%	-42.5%
60/40	10.1%	6.9%	-32.0%
CBOE S&P 500 5% Put Protection Index	10.2%	10.1%	-36.6%
Salient Trend Index (Managed Futures)	1.2%	10.3%	-14.3%
Salient Risk Parity Index	6.6%	8.7%	-30.8%
HFRX Global Hedge Fund Index	1.5%	4.0%	-23.4%

Source: Kenneth French Data Library, CSI, Salient, HFRI, CBOE. Calculations by Newfound Research. Past performance is not indicative of future returns. Performance assumes the reinvestment of all distributions. Returns are gross of all fees, including management fees, transaction costs, and taxes. 60/40 and 80/20 portfolios are mixtures of the SPDR S&P 500 ETF (“SPY”) and iShares Core U.S. Bond ETF (“AGG”) in 60%/40% and 80%/20% proportional allocations, rebalanced annually.

We can see that while trend following has failed to keep up with U.S. equities in the post-crisis period (again, we would expect this), it has kept up much better than other potential risk management alternatives while providing significantly more protection during the crisis period.

Another important takeaway is that during the post crisis period, the trend following strategy had the highest volatility of any of the strategies measured. In other words, while we might be able to rely on trend following for crisis risk management (i.e. avoiding the large left tail of returns), it is not necessarily going to reduce volatility during a bull market.

Conclusion

As an investment strategy, trend following has a long history of academic and empirical support. Evidence suggests that trend following can be an effective means of avoiding large negative returns that coincide with traditional bear markets.

However, trend following is not a panacea. In line with our philosophy that “risk cannot be destroyed, only transformed,” the risk management benefit often seen in trend following strategies comes with higher risks in other environments (i.e. “whipsaw”).

Investors who have relied upon the realized participation of trend following strategies during the pre-crisis period (2003-2007), as well as the protection afforded during the 2008 crisis itself, may have unrealistic expectations for forward performance. Simply put: long/flat trend following strategies are very likely to underperform the underlying asset during strong bull markets. In this case, replacing traditional equity exposure with a long/flat trend following strategy will likely lead to long-term underperformance.

However, when compared against other means of risk management, trend following has historically exhibited considerable downside protection for the upside participation it has realized. Compared to a risk-adjusted benchmark, a long/flat U.S. equity trend following strategy exhibits an annualized excess return of 2.89%.

For investors looking to diversify how they manage risk, we believe the trend following represents a high transparent, and historically effective, alternative.

[1] https://arxiv.org/pdf/1404.3274.pdf

Tag: time-series momentum Page 1 of 2

Why Trend Models Diverge

Summary

Decomposing Time-Series Momentum

Decomposing Dual-Moving-Average-Crossover

Decomposing Price-Minus-Moving-Average

The Weight of Prior Evidence

Conclusion

The Importance of Diversification in Trend Following

Summary­

Finding Diversification Within Single-Asset Strategies

Conclusion

Risk Ignition with Trend Following

Summary­

Holding Bonds for Insurance

Cutting the Tails with Trend Following

Conclusion

Diversifying the What, How, and When of Trend Following

Summary

The What: Asset Diversification

The How: Process Diversification

One Signal to Rule Them All?

Identifying the Magic Parameter

The When: Timing Luck

Conclusion

Protect & Participate: Managing Drawdowns with Trend Following

Summary

What is Trend Following?

The Basic Trend Following Setup

Empirical Evidence: Trend Following in a Crisis

Ex-Ante Expectations About Participation

Pre-2008 versus Post-2008 Experience

Conclusion

Summary

Summary

**The What: Asset Diversification**

**The How: Process Diversification**

**The When: Timing Luck**