This post is available as a PDF download here.

Summary­

• We explore a representative multi-asset momentum model that is similar to many bank-based indexes behind structured products and market-linked CDs.
• With a monthly rebalance cycle, we find substantial timing luck risk.
• Using the same basic framework, we build a simple ensemble approach, diversifying both process and rebalance timing risk.
• We find that the virtual strategy-of-strategies is able to harvest diversification benefits, realizing a top-quartile Sharpe ratio with a bottom-quartile maximum drawdown.

Early in the 2010s, a suite of index-linked products came to market that raised billions of dollars.  These products – offered by just about every major bank – sought to simultaneously exploit the diversification benefits of modern portfolio theory and the potential for excess returns from the momentum anomaly.

While each index has its own bells and whistles, they generally follow the same approach:

• A global, multi-asset universe covering equities, fixed income, and commodities.
• Implemented using highly liquid ETFs.
• Asset class and position-level allocation limits.
• A monthly rebalance schedule.
• A portfolio optimization that seeks to maximize weighted prior returns (e.g. prior 6 month returns) while limiting portfolio volatility to some maximum threshold (e.g. 5%).

And despite their differences, we can see in plotting their returns below that these indices generally share a common return pattern, indicating a common, driving style.

Source: Bloomberg.

Frequent readers will know that “monthly rebalance” is an immediate red flag for us here at Newfound: an indicator that timing luck is likely lurking nearby.

Replicating Multi-Asset Momentum

To test the impact of timing luck, we replicate a simple multi-asset momentum strategy based upon available index descriptions.

We rebalance the portfolio at the end of each month.  Our optimization process seeks to identify the portfolio with a realized volatility less than 5% that would have maximized returns over the prior six months, subject to a number of position and asset-level limits.  If the 5% volatility target is not achievable, the target is increased by 1% until a portfolio can be constructed that satisfies our constraints.

We use the following ETFs and asset class limits:

As a naïve test for timing luck, rather than assuming the index rebalances at the end of each month, we will simply assume the index rebalances every 21 trading days. In doing so, we can construct 21 different variations of the index, each representing the results from selecting a different rebalance date.

Source: CSI Analytics; Calculations by Newfound Research.  Results are backtested and hypothetical.  Results assume the reinvestment of all distributions.  Results are gross of all fees, including, but not limited to, manager fees, transaction costs, and taxes, with the exception of underlying ETF expense ratios.  Past performance is not an indicator of future results. 

As expected, the choice of rebalance date has a meaningful impact.  Annualized returns range from 4.7% to 5.5%, Sharpe ratios range from 0.6 to 0.9, and maximum drawdowns range from 9.9% to 20.8%.

On a year-by-year basis, the only thing that is consistent is the large spread between the worst and best-performing rebalance date.  On average, the yearly spread exceeds 400 basis points.

* Partial year starting 7/22/2018

We’ve said it in the past and we’ll say it again: timing luck can be the difference between hired and fired.  And while we’d rather be on the side of good luck, the lack of control means we’d rather just avoid this risk all together.

If it isn’t nailed down for a reason, diversify it

The choice of when to rebalance is certainly not the only free variable of our multi-asset momentum strategy.  Without an explicit view as to why a choice is made, our preference is always to diversify so as to avoid specification risk.

We will leave the constraints (e.g. volatility target and weight constraints) well enough alone in this example, but we should consider the process by which we’re measuring past returns as well as the horizon over which we’re measuring it.  There is plenty of historical efficacy to using prior 6-month total returns for momentum, but no lack of evidence supporting other lookback horizons or measurements.

Therefore, we will use three models of momentum: prior total return, the distance of price from its moving average, and the distance of a short-term moving average from a longer-term moving average.  We will vary the parameterization of these signals to cover horizons ranging from 3- to 15-months in length.

We will also vary which day of the month the portfolio rebalances on.

By varying the signal, the lookback horizon, and the rebalance date, we can generate hundreds of different portfolios, all supported by the same theoretical evidence but having slightly different realized results due to their particular specification.

Our robust portfolio emerges by calculating the weights for all these different variations and averaging them together, in many ways creating a virtual strategy-of-strategies.

Below we plot the result of this –ensemble approach– as compared to a –random sample of the underlying specifications–.  We can see that while there are specifications that do much better, there are also those that do much worse.  By employing an ensemble approach, we forgo the opportunity for good luck and avoid the risk of bad luck.   Along the way, though, we may pick up some diversification benefits: the Sharpe ratio of the ensemble approach fell in the top quartile of specifications and its maximum drawdown was in the bottom quartile (i.e. lower drawdown).

Source: CSI Analytics; Calculations by Newfound Research.  Results are backtested and hypothetical.  Results assume the reinvestment of all distributions.  Results are gross of all fees, including, but not limited to, manager fees, transaction costs, and taxes, with the exception of underlying ETF expense ratios.  Past performance is not an indicator of future results.

Conclusion

In this commentary, we again demonstrate the potential risk of needless specification and the potential power of diversification.

Using a popular multi-asset momentum model as our example, we again find a significant amount of timing luck lurking in a monthly rebalance specification.  By building a virtual strategy-of-strategies, we are able to manage this risk by partially rebalancing our portfolio on different days.

We go a step further, acknowledging that processrepresents another axis of risk. Specifically, we vary both how we measure momentum and the horizon over which it is measured.  Through the variation of rebalance days, model specifications, and lookback horizons, we generate over 500 different strategy specifications and combine them into a virtual strategy-of-strategies to generate our robust multi-asset momentum model.

As with prior commentaries, we find that the robust model is able to effectively reduce the risk of both specification and timing luck.  But perhaps most importantly, it was able to harvest the benefits of diversification, realizing a Sharpe ratio in the top quartile of specifications and a maximum drawdown in the lowest quartile.

Corey Hoffstein

Corey is co-founder and Chief Investment Officer of Newfound Research. Corey holds a Master of Science in Computational Finance from Carnegie Mellon University and a Bachelor of Science in Computer Science, cum laude, from Cornell University. You can connect with Corey on LinkedIn or Twitter.