A PDF version of this post is available here.
Summary
- Over the last several years, we have written several research notes demonstrating the potential benefits of diversifying “specification risk.”
- Specification risk occurs when an investment strategy is overly sensitive to the outcome of a single investment process or parameter choice.
- Adopting an ensemble approach is akin to creating a virtual fund-of-funds of stylistically similar managers, exhibiting many of the same advantages of traditional multi-manager diversification.
- In this piece, we briefly explore whether model specification choices can be timed using momentum within the context of a naïve trend strategy.
- We find little evidence that momentum-based parameter specification leads to meaningful or consistent improvements beyond a naively diversified approach.
Over the last several years, we’ve advocated on numerous occasions for a more holistic view of diversification: one that goes beyond just what we invest in, but also considers how those decisions are made and when they are made.
We believe that this style of thinking can be applied “all the way down” our process. For example, how-based diversification would advocate for the inclusion of both value and momentum processes, as well as for different approaches to capturing value and momentum.
Unlike correlation-based what diversification, how-based diversification often does little for traditional portfolio risk metrics. For example, in Is Multi-Manager Diversification Worth It? we demonstrated that within most equity categories, allocating across multiple managers does almost nothing to reduce portfolio volatility. It does, however, have a profound impact on the dispersion of terminal wealth that is achieved, often by avoiding manager-specific tail-risks. In other words, our certainty of achieving a given outcome may be dramatically improved by taking a multi-manager approach.
Ensemble techniques to portfolio construction can be thought of as adopting this same multi-manager approach by creating a set of virtual managers to allocate across.
In late 2018, we wrote two notes that touched upon this: When Simplicity Met Fragility and What Do Portfolios and Teacups Have in Common? In both studies we injected a bit of randomness into asset returns to measure the stability of trend-following strategies. We found that highly simplistic models tended to exhibit significant deviations in results with just slightly modified inputs, suggesting that they are highly fragile. Increasing diversification across what, how, and when axes led to a significant improvement in outcome stability.
As empirical evidence, we studied the real-time results of the popular Dual Momentum GEM strategy in our piece Fragility Case Study: Dual Momentum GEM, finding that slight deviations in model specification lead to significantly different allocation conclusions and therefore meaningfully different performance results. This was particularly pronounced over short horizons.
Tying trend-following to option theory, we then demonstrated how an ensemble of trend following models and specifications could be used to increase outcome certainty in Tightening the Uncertain Payout of Trend-Following.
Yet while more diversification appears to make portfolios more consistent in the outcomes they achieve, empirical evidence also suggests that certain specifications can lead to superior results for prolonged periods of time. For example, slower trend following signals appear to have performed much, much better than fast trend following signals over the last two decades.
One of the benefits of being a quant is that it is easy to create thousands of virtual managers, all of whom may follow the same style (e.g. “trend”) but implement with a different model (e.g. prior total return, price-minus-moving-average, etc) and specification (e.g. 10 month, 200 day, 13 week / 34 week cross, etc). An ancillary benefit is that it is also easy to re-allocate capital among these virtual managers.
Given this ease, and knowing that certain specifications can go through prolonged periods of out-performance, we might ask: can we time specification choices with momentum?
Timing Trend Specification
In this research note, we will explore whether momentum signals can help us time out specification choices as it relates to a simple long/flat U.S. trend equity strategy.
Using data from the Kenneth French library, our strategy will hold broad U.S. equities when the trend signal is positive and shift to the risk-free asset when trends are negative. We will develop 1023 different strategies by employing three different models – prior total return, price-minus-moving-average, and dual-moving-average-cross-over – with lookback choices spanning from 20-to-360 days in length.
After constructing the 1023 different strategies, we will then apply a momentum model that ranks the models based upon prior returns and equally-weights our portfolio across the top 10%. These choices are made daily and implemented with 21 overlapping portfolios to reduce the impact of rebalance timing luck.
It should be noted that because the underlying strategies are only allocating between U.S. equities and a risk-free asset, they can go through prolonged periods where they have identical returns or where more than 10% of models share the highest prior return. In these cases, we select all models that have returns equal-to-or-greater-than the model identified at the 10th percentile.
Before comparing performance results, we think it is worthwhile to take a quick look under the hood to see whether the momentum-based approach is actually creating meaningful tilts in specification selection. Below we plot both aggregate model and lookback weights for the 126-day momentum strategy.
Source: Kenneth French Data Library. Calculations by Newfound Research.
We can see that while the model selection remains largely balanced, with the exception of a few periods, the lookback horizon selection is far more volatile. On average, the strategy preferred intermediate-to-long-term signals (i.e. 181-to-360 day), but we can see intermittent periods where short-term models carried favor.
Did this extra effort generate value, though? Below we plot the ratio of the momentum strategies’ equity curves versus the naïve diversified approach.
We see little consistency in relative performance and four of the five strategies end up flat-to-worse. Only the 252-day momentum strategy out-performs by the end of the testing period and this is only due to a stretch of performance from 1950-1964. In fact, since 1965 the relative performance of the 252-day momentum model has been negative versus the naively diversified approach.
Source: Kenneth French Data Library. Calculations by Newfound Research. Past performance is not an indicator of future results. Performance is backtested and hypothetical. Performance figures are gross of all fees, including, but not limited to, manager fees, transaction costs, and taxes. Performance assumes the reinvestment of all distributions.
This analysis suggests that naïve, momentum-based specification selection does not appear to have much merit against a diversified approach for our simple trend equity strategy.
The Potential Benefits of Virtual Rebalancing
One potential benefit of an ensemble approach is that rebalancing across virtual managers can generate growth under certain market conditions. Similar to a strategically rebalanced portfolio, we find that when returns across virtual managers are expected to be similar, consistent rebalancing can harvest excess returns above a buy-and-hold approach.
The trade-off, of course, is that when there is autocorrelation in specification performance, rebalancing creates a drag. However, given that the evidence above suggests that relative performance between specifications is not persistent, we might expect that continuously rebalancing across our ensemble of virtual managers may actually allow us to harvest returns above and beyond what might be possible with just selecting an individual manager.
Source: Kenneth French Data Library. Calculations by Newfound Research. Past performance is not an indicator of future results. Performance is backtested and hypothetical. Performance figures are gross of all fees, including, but not limited to, manager fees, transaction costs, and taxes. Performance assumes the reinvestment of all distributions.
Conclusion
In this study, we explored whether we could time model specification choices in a simple trend equity strategy using momentum signals.
Testing different lookback horizons of 21-through-378 days, we found little evidence of meaningful persistence in the returns of different model specifications. In fact, four of the five momentum models we studied actually under-performed a naïve, diversified. The one model that did out-perform only seemed to do so due to strong performance realized over the 1950-1964 period, actually relatively under-performing ever since.
While this evidence suggests that timing specification with momentum may not be a fruitful approach, it does suggest that the lack of return persistence may benefit diversification for a second reason: rebalancing. Indeed, barring any belief that one specification would necessarily do better than another, consistently re-pooling and distributing resources through rebalancing may actually lead to the growth-optimal solution.1 This potentially implies an even higher hurdle rate for specification-timers to overcome.
Can Managed Futures Offset Equity Losses?
By Corey Hoffstein
On February 3, 2020
In Risk & Style Premia, Risk Management, Trend, Weekly Commentary
This post is available as a PDF download here.
Summary
Shortly after the 2008 crisis, the appetite for risk management strategies exploded. At the forefront of this trend was managed futures, which had already proven itself in the dot-com fallout. With the Societe Generale Trend Index1 returning 20.9% in 2008, the evidence for CTAs to provide “crisis alpha”2 seemed un-debatable. AUM in these strategies sky-rocketed, growing from $200 billion in 2007 to approximately $325 billion by 2012.
Subsequent performance has, unfortunately, been lack-luster. Since 12/31/2011, the SG Trend Index has returned just 14.2% compared to the S&P 500’s 200.8% total return. While this is an unfair, apples-to-oranges comparison, it does capture the dispersion the strategy has exhibited to the benchmark most investors measure performance against during a bull market.
Furthermore, the allocation to managed futures had to come from somewhere. If investors reduced exposure to equities to introduce managed futures, the spread in performance captures the opportunity cost of that decision. There is hope yet: if the S&P 500 fell 50% over the next year, managed futures would have to return just 32% for their full-period performance (2011-2020) to equalize.
Yet how certain are we that managed futures would necessarily generate a positive return in an S&P 500 left-tail environment? Hurst, Ooi, and Pedersen (2017)3 find that managed futures have generated anything from flat to meaningfully positive results during the top 10 largest drawdowns of a 60/40 portfolio since the late 1800s. This evidence makes a strong empirical case, but we should acknowledge the N=10 nature of the data.
Perhaps we can lean into the mechanically convex nature of trend following. Trend following is a close cousin to the trading strategy that delta-hedges a strangle, generating the pay-off profile of a straddle (long an at-the-money put and call). Even without an anomalous premium generated by autocorrelation in the underlying security, the trading strategy itself should – barring trading frictions – generate a convex payoff.
Yet while mechanical convexity may be true on a contract-by-contract basis, it is entirely possible that the convexity we want to see emerge is diluted by trades across other contracts. Consider the scenario where the S&P 500 enters a prolonged and significant drawdown and our managed futures strategy goes short S&P 500 futures contract. While this trade may generate the hedge we were looking for, it’s possible that it is diluted by trades on other contracts such as wheat, the Japanese Yen, or the German Bund.
When we consider that many investors have portfolios dominated by equity risk (recall that equities have historically contributed 90% of the realized volatility for a 60/40 portfolio), it is possible that too much breadth within a managed futures portfolio could actually prevent it from providing negative beta during left-tail equity events.
Replicating Managed Futures
We begin our study by first replicating a generic trend-following CTA index. We adopt an ensemble approach, which is effectively equivalent to holding a basket of managers who each implement a trend-following strategy with a different model and parameterization.
Specifically, we assume each manager implements using the same 47 contracts that represent a diversified basket of equities, rates, commodities, and currencies.4
We implement with three different models (total return, price-minus-moving-average, and dual-moving-average-cross) and five potential lookback specifications (21, 42, 84, 168, and 336 days) for a total of 15 different implementations.
Each implementation begins by calculating an equal-risk contribution (“risk parity”) portfolio. Weights for each contract are then multiplied by their trend signal (which is simply either +1 or -1).
The weights for all 15 implementations are then averaged together to generate our index weights. Notional exposure of the aggregate weights is then scaled to target a 10% annualized volatility level. We assume that the index is fully collateralized using the S&P U.S. Treasury Bill Index.
Below we plot our index versus the SG Trend Index. The correlation of monthly returns between these two indices is 75% suggesting that our simple implementation does a reasonable job approximating the broad trend-following style of CTAs. We can also see that it captures the salient features of the SG Trend Index, including strong performance from 2001-2003, Q4 2008 and Q1 2009, and the 2014-2015 period. We can also see it closely tracks the shape the SG Trend Index equity curve from 2015 onward in all its meandering glory.
Source: Stevens Analytics. Calculations by Newfound Research. Past performance is not an indicator of future results. Performance is backtested and hypothetical. Performance figures are gross of all fees, including, but not limited to, manager fees, transaction costs, and taxes. Performance assumes the reinvestment of all distributions. These results do not reflect the returns of any strategy managed by Newfound Research.
Convexity versus Diversification
To explore the impact of diversification in managed futures versus convexity exhibited against the S&P 500, we will create a number of managed futures strategies and vary the number of contracts included. As we are attempting to create a convex payoff against the S&P 500, the S&P 500 futures contract will always be selected.
For example, a 2-contract strategy will always include S&P 500 futures, but the second contract could be 10-year U.S. Treasuries, the Nikkei, the Australian Dollar, Oil, or any of the other 42 futures contracts. Once selected, however, that pair defines the strategy.
For 2-, 4-, 8-, 16-, and 32- contract systems, we generate the performance of 25 randomly selected strategies. We then generate scatter plots with non-overlapping 6-month returns for the S&P 500 on the x-axis and non-overlapping 6-month returns for the managed futures strategies on the y-axis.5 We then fit a 2nd-degree polynomial line to visualize the realized convexity.
(Note that for the single contract case – i.e. just the S&P 500 futures contract – we plot overlapping 6-month returns.)
Source: Stevens Analytics and Sharadar. Calculations by Newfound Research. Past performance is not an indicator of future results. Performance is backtested and hypothetical. Performance figures are gross of all fees, including, but not limited to, manager fees, transaction costs, and taxes. Performance assumes the reinvestment of all distributions. These results do not reflect the returns of any strategy managed by Newfound Research.
There are two particularly interesting artifacts to note.
First, as the number of contracts goes up, the best-fit model turns from a “smile” to a “smirk,” suggesting that diversification dilutes positive convexity relationships with the S&P 500. This outcome should have been expected, as we generally know how managed futures has done over the 20-year period we’re examining. Namely, managed futures did quite well offsetting losses in 2000-2003 and 2008-2009, but has failed to participate in the 2010s.
Perhaps more interestingly, however, is the increase in left-tail performance of managed futures, climbing from 20% when just trading the S&P 500 futures contract to 150% in the 32-contract case. The subtle reason here is diversification’s impact on total notional exposure.
Consider this trivial example: Asset A and Asset B have constant 10% volatility and are uncorrelated with one another. As they are uncorrelated, any combination of these assets will have a volatility that is less than 10%. Therefore, if we want to achieve 10%, we need to apply leverage. In fact, a 50-50 mix of these assets requires us to apply 1.41x leverage to achieve our volatility target, resulting in 70.7% exposure to each asset.
As a more concrete example, when trading just the S&P 500 futures contract, achieving 10% volatility position in 2008 requires diluting gross notional exposure to just 16%. For the full, 47-contract model, gross notional exposure during 2008 dipped to 90% at its lowest point.
Now consider that trend following tends to transform the underlying distributions of assets to generate positive skewness. Increasing leverage can help push those positive trades even further out in the tails.
But here’s the trade-off: the actual exposure to S&P 500 futures contracts, specifically, still remains much, much higher in the case where we’re trading it alone. In practice, the reason the diversified approach was able to generate increased returns during left-tail equity events – such as 2008 – is due to the fact correlations crashed to extremes (both positive and negative) between global equity indices, rates, commodities, and currencies. This allowed the total notional exposure of directionally similar trades (e.g. short equities, long bonds, and short commodities in 2008) to far exceed the total notional exposure achieved if we were just trading the S&P 500 futures contract alone.
Our confidence in achieving negative convexity versus equity left-tail events, therefore, is inherently tied to our belief that we will see simultaneously trends across a large number of assets during such environments.
Another interpretation of this data is that because negative trends in the S&P 500 have historically coincided with higher volatility, a strategy that seeks to trade just the S&P 500 futures with constant volatility will lose convexity in those tail events. An alternative choice is to vary the volatility of the system to target the volatility of the S&P 500, whose convexity profile we plot below.
Source: Stevens Analytics and Sharadar. Calculations by Newfound Research. Past performance is not an indicator of future results. Performance is backtested and hypothetical. Performance figures are gross of all fees, including, but not limited to, manager fees, transaction costs, and taxes. Performance assumes the reinvestment of all distributions. These results do not reflect the returns of any strategy managed by Newfound Research.
This analysis highlights a variety of trade-offs to consider:
Perhaps, then, we should consider approaching the problem from another angle: given exposure to managed futures, what would be a better core portfolio to hold? Given that most managed futures portfolios start from a risk parity core, the simplest answer is likely risk parity.
As an example, we construct a 10% target volatility risk parity index using equity, rate, and commodity contracts. Below we plot the convexity profile of our managed futures strategy against this risk parity index and see the traditional “smile” emerge. We also plot the equity curves for the risk parity index, the managed futures index, and a 50/50 blend. Both the risk parity and managed futures indices have a realized volatility of level of 10.8%; the blended combination drops this volatility to just 7.6%, achieving a maximum drawdown of just -10.1%.
Source: Stevens Analytics and Sharadar. Calculations by Newfound Research. Past performance is not an indicator of future results. Performance is backtested and hypothetical. Performance figures are gross of all fees, including, but not limited to, manager fees, transaction costs, and taxes. Performance assumes the reinvestment of all distributions. These results do not reflect the returns of any strategy managed by Newfound Research.
Conclusion
Managed futures have historically generated significant gains during left-tail equity events. These returns, however, are by no means guaranteed. While trend following is a mechanically convex strategy, the diversified nature of most managed futures programs can potentially dilute equity-crisis-specific returns.
In this research note, we sought to explore this concept by generating a large number of managed futures strategies that varied in the number of contracts traded. We found that increasing the number of contracts had two primary effects: (1) it reduced realized convexity from a “smile” to a “smirk” (i.e. exhibited less up-side participation with equity markets); and (2) meaningfully increased returns during negative equity markets.
The latter is particularly curious but ultimately the byproduct of two facts. First, increasing diversification allows for increased notional exposure in the portfolio to achieve the same target volatility level. Second, during past crises we witnessed a large number of assets trending simultaneously. Therefore, while increasing the number of contracts reduced notional exposure to S&P 500 futures specifically, the total notional exposure to trades generating positive gains during past crisis events was materially higher.
While the first fact is evergreen, the second may not always be the case. Therefore, employing managed futures specifically as a strategy to provide offsetting returns during an equity market crisis requires the belief that a sufficient number of other exposures (i.e. equity indices, rates, commodities, and currencies) will be exhibiting meaningful trends at the same time.
Given its diversified nature, it should come as no surprise that managed futures appear to be a natural complement to a risk parity portfolio.
Investors acutely sensitive to significant equity losses – e.g. those in more traditional strategic allocation portfolios – might therefore consider strategies designed more specifically with such environments in mind. At Newfound, we believe that trend equity strategies are one such solution, as they overlay trend-following techniques directly on equity exposure, seeking to generate the convexity mechanically and not through correlated assets. When overlaid with U.S. Treasury futures – which have historically provided a “flight-to-safety” premium during equity crises – we believe it is a particularly strong solution.