*This post is available as a PDF download here.*

# Summary

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

** Introduction**

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

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

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

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

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

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

**Global Equities Momentum (“GEM”)**

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

**Conclusion**

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

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

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

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

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

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

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

## Decomposing Trend Equity

By Corey Hoffstein

On September 24, 2018

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

This post is available as a PDF download here.## Summary

The Simple Arithmetic of Portfolio ConstructionIn our commentary

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

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

Figure 1No, this is not a trick question. The straightforward answer is that we sell 50% of our exposure in A and buy 50% of our exposure in B. As it turns out, however, this is entirely equivalent to holding our portfolio constant and simply going

short50% exposure in A and using the proceeds to purchase 50% notional portfolio exposure in B (see Figure 2). Operationally, of course, these are very different things. Thinking about the portfolio in this way, however, can be constructive to truly understanding the implications of the trade.The difference in performance between our new portfolio and our old portfolio will be entirely captured by the performance of this long/short overlay. This tells us, for example, that the new portfolio will outperform the old portfolio when asset B outperforms asset A, since the long/short portfolio effectively captures the spread in performance between asset B and asset A.

Figure 2: Portfolio Arithmetic – Long/Short OverlayRelative to our original portfolio, the long/short represents our

active bets.A slightly more nuanced view of this arithmetic requires scaling our active bets such that each leg is equal to 100%, and then only implementing a portion of that overlay. It is important to note that the overlay is “dollar-neutral”: in other words, the dollars allocated to the short leg and the long leg add up to zero. This is also called “self-funding” because it is presumed that we would enter the short position and then use the cash generated to purchase our long exposure, allowing us to enter the trade without utilizing any capital.Figure 3: Portfolio Arithmetic – Scaled Long/Short OverlayIn our prior example, a portfolio that is 50% long B and 50% short A is equivalent to 50% exposure to a portfolio that is 100% long B and 100% short A. The benefit of taking this extra step is that it allows us to decompose our trade into two pieces: the active bets we are making and the sizing of these bets.

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

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

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

Figure 4Strategic PositionTrend StrategyDecompositionPositive TrendNegative TrendFlat/Short Trend Strategy

100% Equity

-100% Equity

100% ST US Treasuries

50% Equity

50% ST US Treasuries

-100% ST US Treasuries

-100% Equity

+100% ST US Treasuries

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

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

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

Figure 5: A Flat/Short U.S. Equity StrategySource: Newfound Research. Return data relies on hypothetical indices and is exclusive of all fees and expenses. Returns assume the reinvestment of all dividends. Flat/Short Equity shorts U.S. Large-Cap Equity when the prior month has a positive 12-1 month total return, investing available capital in 3-month U.S. Treasury Bills. The strategy assumes zero cost of shorting. The Flat/Short Equity strategy does not reflect any strategy offered or managed by Newfound Research and was constructed exclusively for the purposes of this commentary. It is not possible to invest in an index. Past performance does not guarantee future results.The flat/short strategy has historically achieved a payoff structure that looks very much like a put option: positive returns during significantly negative return regimes, and (on average) slight losses otherwise. Of course, unlike a put option where the premium paid is known upfront, the flat/short trading strategy pays its premium in the form of “whipsaw” resulting from trend reversals. These head-fakes cause the strategy to “short low” and “cover high,” creating realized losses.

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

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

minusthe whipsaw costs of the flat/short strategy. The drag in return, however, is payment for the expectation that significant left-tail events will be meaningfully offset. In many ways, this decomposition lends itself nicely to thinking of trend equity as a “defensive equity” allocation.Figure 6: Combination of U.S. Large-Cap Equities and a Flat/Short Trend-Following StrategySource: Newfound Research. Return data relies on hypothetical indices and is exclusive of all fees and expenses. Returns assume the reinvestment of all dividends. Flat/Short Equity shorts U.S. Large-Cap Equity when the prior month has a negative 12-1 month total return, investing available capital in 3-month U.S. Treasury Bills. The strategy assumes zero cost of shorting. The Flat/Short Equity strategy does not reflect any strategy offered or managed by Newfound Research and was constructed exclusively for the purposes of this commentary. It is not possible to invest in an index. Past performance does not guarantee future results.50% Equity/50% Cash + 50% Long/ShortThe second decomposition achieves the long/flat strategy profile by assuming a strategic allocation that is 50% large-cap U.S. equities and 50% short-term U.S. Treasuries. The overlaid trend strategy now goes both long and short U.S. equities depending upon the underlying trend signal, going short and long large-cap U.S. Treasuries to keep the dollar-neutral profile of the overlay.

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

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

Figure 7: A Long/Short Equity Trend-Following StrategySource: Newfound Research. Return data relies on hypothetical indices and is exclusive of all fees and expenses. Returns assume the reinvestment of all dividends. Long/Short Equity goes long U.S. Large-Cap Equity when the prior month has a positive 12-1 month total return, shorting an equivalent amount in 3-month U.S. Treasury Bills. When the prior month has a negative 12-1 month total return, the strategy goes short U.S. Large-Cap Equity, investing available capital in 3-month U.S. Treasury Bills. The strategy assumes zero cost of shorting. The Long/Short Equity strategy does not reflect any strategy offered or managed by Newfound Research and was constructed exclusively for the purposes of this commentary. It is not possible to invest in an index. Past performance does not guarantee future results.We can see the traditional “smile” associated with long/short trend-following strategies. With options, this payoff profile is reminiscent of a straddle, a strategy that combines a position in a put and a call option to profit in both extremely positive and negative environments. The premium paid to buy these options causes the strategy to lose money in more normal environments. We see a similar result with the long/short trend-following approach.

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

50% Equity / 50% Cash: We should expect to earn, over the long run, about half the equity risk premium, but only expect to suffer about half the losses associated with equities.50% Long/Short Equity: The “smile” payoff associated with trend following should increase exposure to equities in the positive tail and help offset losses in the negative tail, at the cost of whipsaw during periods of trend reversals.Taken together, we should expect equity up-capture exceeding 50% in strongly trending years, a down-capture less than 50% in strongly negatively trending years, and a slight drag in more normal environments. We believe that this form of decomposition is most useful when investors are planning to fund their trend equity from both stocks and bonds, effectively using it as a risk pivot within their portfolio.

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

Figure 8Source: Newfound Research. Return data relies on hypothetical indices and is exclusive of all fees and expenses. Returns assume the reinvestment of all dividends. Long/Short Equity goes long U.S. Large-Cap Equity when the prior month has a positive 12-1 month total return, shorting an equivalent amount in 3-month U.S. Treasury Bills. When the prior month has a negative 12-1 month total return, the strategy goes short U.S. Large-Cap Equity, investing available capital in 3-month U.S. Treasury Bills. The strategy assumes zero cost of shorting. The Long/Short Equity strategy does not reflect any strategy offered or managed by Newfound Research and was constructed exclusively for the purposes of this commentary. It is not possible to invest in an index. Past performance does not guarantee future results.## Conclusion

In this commentary, we continued our exploration of trend equity strategies. To gain a better sense of how we should expect trend equity strategies to perform, we introduce the basic arithmetic of portfolio construction that we later use to decompose trend equity into a strategic allocation plus a self-funded trading strategy.

In the first decomposition, we break trend equity into a strategic, passive allocation in large-cap U.S. equities plus a self-funding flat/short trading strategy. The flat/short strategy sits in cash when trends in large-cap U.S. equities are positive and goes short large-cap U.S. equities when trends are negative. In isolating the flat/short trading strategy, we see a return profile that is reminiscent of the payoff of a put option, exhibiting negative returns in positive market environments and large gains during negative market environments.

For investors planning on utilizing trend equity as a form of defensive equity, this decomposition is appropriate. It clearly demonstrates that we should expect returns that are less than passive equity during almost all market environments, with the exception being extreme negative tail events, where the trading strategy aims to hedge against significant losses. While we would expect to be able to measure manager skill by the amount of drag created to equities during positive markets (i.e. the “cost of the hedge”), we can see from the hypothetical example inn Figure 5 that there is considerable variation year-to-year, making short-term analysis difficult.

In our second decomposition, we break trend equity into a strategic portfolio that is 50% large-cap U.S. equity / 50% short-term U.S. Treasury plus a self-funding long/short trading strategy. If the flat/short trading strategy was similar to a put option, the long/short trading strategy is similar to a straddle, exhibiting profit in the wings of the return distribution and losses near the middle.

This particular decomposition is most relevant to investors who plan on funding their trend equity exposure from both stocks and bonds, allowing the position to serve as a risk pivot within their overall allocation. The strategic contribution provides partial exposure to the equity risk premium, but the trading strategy aims to add value in both tails, demonstrating that trend equity can potentially increase returns in both strongly positive and strongly negative environments.

In both cases, we can see that trend equity can be thought of as a strategic allocation to equities – seeking to benefit from the equity risk premium – plus an alternative strategy that seeks to harvest benefits from the trend premium.

In this sense, trend equity strategies help investors achieve capital efficiency. Allocations to the alternative return premia, in this case trend, does not require allocating away from the strategic, long-only portfolio. Rather, exposure to both the strategic holdings and the trend-following alternative strategy can be gained in the same package.