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.
Ensembles and Rebalancing
By Corey Hoffstein
On February 24, 2020
In Portfolio Construction, Weekly Commentary
This post is available as a PDF download here.
Summary
Two weeks ago, we wrote about the idea of payoff diversification. The notion is fairly trivial, though we find it is often overlooked. Put simply, any and all trading decisions – even something as trivial as rebalancing – create a “payoff profile.” These profiles often fall into two categories: concave strategies that do well in stable environments is maintained and convex strategies that do better in the tails.
For example, we saw that rebalancing a 60/40 stock/bond portfolio earned a premium against a buy-and-hold approach when the spread between stock and bond returns remained narrow. Conversely, when the spread in return between stocks and bonds was wide, rebalancing created a drag on returns. This is a fairly trivial and obvious conclusion, but we believe it is important for investors to understand these impacts and why payoff is a meaningful axis of diversification.
In our prior study, we compared two different approaches to investing: strategic rebalancing and momentum investing. In this (very brief) study, we want to demonstrate that these results are also applicable when applied to different variations of the same strategy.
Specifically, we will look at two long/short trend following strategies applied to broad U.S. equities. When trend signals are positive, the strategy will be long U.S. equities and short the risk-free rate; when trend signals are negative the strategy will be short U.S. equities and long the risk-free rate. We will use a simple time-series momentum signal. The first model (“21D”) will evaluate trailing 21-day returns and hold for 1 day and the second model (“168D”) will evaluate trailing 168-day returns and holds for 14 days (with 14 overlapping portfolios).1 Both strategies implement a full skip day before allocating and assuming implementation at closing prices.
So, what happens if we create a portfolio that holds both of these strategies, allocating 50% of our capital to each? Readers of our prior note will likely be able to guess the answer easily: we create a concave payoff profile that depends upon the relative performance between the two strategies. How, specifically, that concave shape manifests will be path dependent, but will also depend upon the rebalance frequency. For example, below we plot the payoff profiles for the 50/50 blend rebalanced weekly and monthly.
If we stop thinking of these as two strategies applied to the same asset and just think of them as two assets, the results are fairly standard and intuitive. What is potentially appealing, however, is that the same literature and research that applies to the potential to create a rebalancing premium between assets can apply to a portfolio of strategies (whether a combination of distinct strategies, such as value and momentum, or an ensemble of the same strategy).
Below, we plot the annualized return of weekly rebalanced portfolios with different fixed-mix allocations to the 21D and 168D strategies. We can see that the curve peaks at approximately 45%, suggesting that a 45% allocation to the 21D strategy and a 55% allocation to the 168D strategy actually maximizes the compound annualized growth rate of the portfolio.
If we follow the process of Dubikovsky and Susinno (2017)2 to derive the optimal blend of these two assets – using the benefit of hindsight to measure their annualized returns (7.28% and 7.61% respectively), volatility (17.55% and 17.97% respectively), and correlation (0.1318) – we derive an optimal weight of 45.33%.
Perhaps somewhat surprisingly, even if the correlation between these two strategies was 0.9, the optimal blend would still recommend about 10% to the 21D variation. And, as extreme as it may seem, even if the annualized return of the 21D strategy was just 5.36% – a full 225 basis points below the 168D strategy – the optimal blend would still recommend about 10%. Diversification can create interesting opportunities to harvest return; at least, in expectation.
And, as we would expect, if we have no view as to a difference in return or volatility between the two specifications, we would end up with a recommended allocation of 50% to each.
Conclusion
While most studies on rebalancing consider the potential benefits of combining assets, we believe that these benefits are trivially extended to strategies. Not just different strategies, however, but even strategies of the same style.
In this brief note, we explore the payoff profile created by combining two naïve long/short trend following strategies applied to broad U.S. equities. Unsurprisingly, rebalancing a simple mixture of the two specifications creates a concave payoff that generally profits when the spread between the two strategies is narrow and loses when the spread is wide.
More interestingly, however, we demonstrate that by rebalancing a fixed-mix of the two strategies, we can generate a return that is greater than either strategy individually. We believe that this potential benefit of ensemble approaches has been mostly overlooked by existing literature and deserves further analysis.