*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.

*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.

## 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

^{rd}, the S&P 500 fell more than 10%.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 risksof 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

somewhattechnical. 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 changes

^{1}that occur.## Decomposing Dual-Moving-Average-Crossover

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

We assume

mis less thann(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.

## 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.