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The Dumb (Timing) Luck of Smart Beta

By

On November 18, 2019

In Craftsmanship, Defensive, Momentum, Popular, Portfolio Construction, Risk & Style Premia, Value, Weekly Commentary

This post is available as a PDF download here.

Summary

  • In past research notes we have explored the impact of rebalance timing luck on strategic and tactical portfolios, even using our own Systematic Value methodology as a case study.
  • In this note, we generate empirical timing luck estimates for a variety of specifications for simplified value, momentum, low volatility, and quality style portfolios.
  • Relative results align nicely with intuition: higher concentration and less frequent rebalancing leads to increasing levels of realized timing luck.
  • For more reasonable specifications – e.g. 100 stock portfolios rebalanced semi-annually – timing luck ranges between 100 and 400 basis points depending upon the style under investigation, suggesting a significant risk of performance dispersion due only to when a portfolio is rebalanced and nothing else.
  • The large magnitude of timing luck suggests that any conclusions drawn from performance comparisons between smart beta ETFs or against a standard style index may be spurious.

We’ve written about the concept of rebalance timing luck a lot.  It’s a cowbell we’ve been beating for over half a decade, with our first article going back to August 7th, 2013.

As a reminder, rebalance timing luck is the performance dispersion that arises from the choice of a particular rebalance date (e.g. semi-annual rebalances that occur in June and December versus March and September).

We’ve empirically explored the impact of rebalance timing luck as it relates to strategic asset allocation, tactical asset allocation, and even used our own Systematic Value strategy as a case study for smart beta.  All of our results suggest that it has a highly non-trivial impact upon performance.

This summer we published a paper in the Journal of Index Investing that proposed a simple solution to the timing luck problem: diversification.  If, for example, we believe that our momentum portfolio should be rebalanced every quarter – perhaps as an optimal balance of cost and signal freshness – then we proposed splitting our capital across the three portfolios that spanned different three-month rebalance periods (e.g. JAN-APR-JUL-OCT, FEB-MAY-AUG-NOV, MAR-JUN-SEP-DEC).  This solution is referred to either as “tranching” or “overlapping portfolios.”

The paper also derived a formula for estimating timing luck ex-ante, with a simplified representation of:

Where L is the timing luck measure, T is turnover rate of the strategy, F is how many times per year the strategy rebalances, and S is the volatility of a long/short portfolio that captures the difference of what a strategy is currently invested in versus what it could be invested in if the portfolio was reconstructed at that point in time.

Without numbers, this equation still informs some general conclusions:

  • Higher turnover strategies have higher timing luck.
  • Strategies that rebalance more frequently have lower timing luck.
  • Strategies with a less constrained universe will have higher timing luck.

Bullet points 1 and 3 may seem similar but capture subtly different effects.  This is likely best illustrated with two examples on different extremes.  First consider a very high turnover strategy that trades within a universe of highly correlated securities.  Now consider a very low turnover strategy that is either 100% long or 100% short U.S. equities.  In the first case, the highly correlated nature of the universe means that differences in specific holdings may not matter as much, whereas in the second case the perfect inverse correlation means that small portfolio differences lead to meaningfully different performance.

L, in and of itself, is a bit tricky to interpret, but effectively attempts to capture the potential dispersion in performance between a particular rebalance implementation choice (e.g. JAN-APR-JUL-OCT) versus a timing-luck-neutral benchmark.

After half a decade, you’d would think we’ve spilled enough ink on this subject.

But given that just about every single major index still does not address this issue, and since our passion for the subject clearly verges on fever pitch, here comes some more cowbell.

Equity Style Portfolio Definitions

In this note, we will explore timing luck as it applies to four simplified smart beta portfolios based upon holdings of the S&P 500 from 2000-2019:

  • Value: Sort on earnings yield.
  • Momentum: Sort on prior 12-1 month returns.
  • Low Volatility: Sort on realized 12-month volatility.
  • Quality: Sort on average rank-score of ROE, accruals ratio, and leverage ratio.

Quality is a bit more complicated only because the quality factor has far less consistency in accepted definition.  Therefore, we adopted the signals utilized by the S&P 500 Quality Index.

For each of these equity styles, we construct portfolios that vary across two dimensions:

  • Number of Holdings: 50, 100, 150, 200, 250, 300, 350, and 400.
  • Frequency of Rebalance: Quarterly, Semi-Annually, and Annually.

For the different rebalance frequencies, we also generate portfolios that represent each possible rebalance variation of that mix.  For example, Momentum portfolios with 50 stocks that rebalance annually have 12 possible variations: a January rebalance, February rebalance, et cetera.  Similarly, there are 12 possible variations of Momentum portfolios with 100 stocks that rebalance annually.

By explicitly calculating the rebalance date variations of each Style x Holding x Frequency combination, we can construct an overlapping portfolios solution.  To estimate empirical annualized timing luck, we calculate the standard deviation of monthly return dispersion between the different rebalance date variations of the overlapping portfolio solution and annualize the result.

Empirical Timing Luck Results

Before looking at the results plotted below, we would encourage readers to hypothesize as to what they expect to see.  Perhaps not in absolute magnitude, but at least in relative magnitude.

For example, based upon our understanding of the variables affecting timing luck, would we expect an annually rebalanced portfolio to have more or less timing luck than a quarterly rebalanced one?

Should a more concentrated portfolio have more or less timing luck than a less concentrated variation?

Which factor has the greatest risk of exhibiting timing luck?

Source: Sharadar.  Calculations by Newfound Research.

To create a sense of scale across the styles, below we isolate the results for semi-annual rebalancing for each style and plot it.

Source: Sharadar.  Calculations by Newfound Research.

In relative terms, there is no great surprise in these results:

  • More frequent rebalancing limits the risk of portfolios changing significantly between rebalance dates, thereby decreasing the impact of timing luck.
  • More concentrated portfolios exhibit larger timing luck.
  • Faster-moving signals (e.g. momentum) tend to exhibit more timing luck than more stable, slower-moving signals (e.g. low volatility).

What is perhaps the most surprising is the sheer magnitude of timing luck.  Consider that the S&P 500 Enhanced Value, Momentum, Low Volatility, and Quality portfolios all hold 100 securities and are rebalanced semi-annually.  Our study suggests that timing luck for such approaches may be as large as 2.5%, 4.4%, 1.1%, and 2.0% respectively.

But what does that really mean?  Consider the realized performance dispersion of different rebalance date variations of a Momentum portfolio that holds the top 100 securities in equal weight and is rebalanced on a semi-annual basis.

Source: 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. 

The 4.4% estimate of annualized timing luck is a measure of dispersion between each underlying variation and the overlapping portfolio solution.  If we isolate two sub-portfolios and calculate rolling 12-month performance dispersion, we can see that the difference can be far larger, as one might exhibit positive timing luck while the other exhibits negative timing luck.  Below we do precisely this for the APR-OCT and MAY-NOV rebalance variations.

Source: 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. 

In fact, since these variations are identical in every which way except for the date on which they rebalance, a portfolio that is long the APR-OCT variation and short the MAY-NOV variation would explicitly capture the effects of rebalance timing luck.  If we assume the rebalance timing luck realized by these two portfolios is independent (which our research suggests it is), then the volatility of this long/short is approximately the rebalance timing luck estimated above scaled by the square-root of two.

Derivation: For variations vi and vj and overlapping-portfolio solution V, then:

Thus, if we are comparing two identically-managed 100-stock momentum portfolios that rebalance semi-annually, our 95% confidence interval for performance dispersion due to timing luck is +/- 12.4% (2 x SQRT(2) x 4.4%).

Even for more diversified, lower turnover portfolios, this remains an issue.  Consider a 400-stock low-volatility portfolio that is rebalanced quarterly.  Empirical timing luck is still 0.5%, suggesting a 95% confidence interval of 1.4%.

S&P 500 Style Index Examples

One critique of the above analysis is that it is purely hypothetical: the portfolios studied above aren’t really those offered in the market today.

We will take our analysis one step further and replicate (to the best of our ability) the S&P 500 Enhanced Value, Momentum, Low Volatility, and Quality indices.  We then created different rebalance schedule variations.  Note that the S&P 500 Low Volatility index rebalances quarterly, so there are only three possible rebalance variations to compute.

Source: 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. 

We see a meaningful dispersion in terminal wealth levels, even for the S&P 500 Low Volatility index, which appears at first glance in the graph to have little impact from timing luck.

Minimum Terminal Wealth

Maximum Terminal Wealth

Enhanced Value

$4.45

$5.45

Momentum

$3.07

$4.99

Low Volatility

$6.16

$6.41

Quality

$4.19

$5.25

 

We should further note that there does not appear to be one set of rebalance dates that does significantly better than the others.  For Value, FEB-AUG looks best while JUN-DEC looks the worst; for Momentum it’s almost precisely the opposite.

Furthermore, we can see that even seemingly closely related rebalances can have significant dispersion: consider MAY-NOV and JUN-DEC for Momentum. Here is a real doozy of a statistic: at one point, the MAY-NOV implementation for Momentum is down -50.3% while the JUN-DEC variation is down just -13.8%.

These differences are even more evident if we plot the annual returns for each strategy’s rebalance variations.   Note, in particular, the extreme differences in Value in 2009, Momentum in 2017, and Quality in 2003.

Source: 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. 

Conclusion

In this study, we have explored the impact of rebalance timing luck on the results of smart beta / equity style portfolios.

We empirically tested this impact by designing a variety of portfolio specifications for four different equity styles (Value, Momentum, Low Volatility, and Quality).  The specifications varied by concentration as well as rebalance frequency.  We then constructed all possible rebalance variations of each specification to calculate the realized impact of rebalance timing luck over the test period (2000-2019).

In line with our mathematical model, we generally find that those strategies with higher turnover have higher timing luck and those that rebalance more frequently have less timing luck.

The sheer magnitude of timing luck, however, may come as a surprise to many.  For reasonably concentrated portfolios (100 stocks) with semi-annual rebalance frequencies (common in many index definitions), annual timing luck ranged from 1-to-4%, which translated to a 95% confidence interval in annual performance dispersion of about +/-1.5% to +/-12.5%.

The sheer magnitude of timing luck calls into question our ability to draw meaningful relative performance conclusions between two strategies.

We then explored more concrete examples, replicating the S&P 500 Enhanced Value, Momentum, Low Volatility, and Quality indices.  In line with expectations, we find that Momentum (a high turnover strategy) exhibits significantly higher realized timing luck than a lower turnover strategy rebalanced more frequently (i.e. Low Volatility).

For these four indices, the amount of rebalance timing luck leads to a staggering level of dispersion in realized terminal wealth.

“But Corey,” you say, “this only has to do with systematic factor managers, right?”

Consider that most of the major equity style benchmarks are managed with annual or semi-annual rebalance schedules.  Good luck to anyone trying to identify manager skill when your benchmark might be realizing hundreds of basis points of positive or negative performance luck a year.

 

The Limit of Factor Timing

By

On November 11, 2019

In Craftsmanship, Momentum, Risk & Style Premia, Weekly Commentary

This post is available as a PDF download here.

Summary­

  • We have shown previously that it is possible to time factors using value and momentum but that the benefit is not large.
  • By constructing a simple model for factor timing, we examine what accuracy would be required to do better than a momentum-based timing strategy.
  • While the accuracy required is not high, finding the system that achieves that accuracy may be difficult.
  • For investors focused on managing the risks of underperformance – both in magnitude and frequency – a diversified factor portfolio may be the best choice.
  • Investors seeking outperformance will have to bear more concentration risk and may be open to more model risk as they forego the diversification among factors.

A few years ago, we began researching factor timing – moving among value, momentum, low volatility, quality, size etc. – with the hope of earning returns in excess not only of the equity market, but also of buy-and-hold factor strategies.

To time the factors, our natural first course of action was to exploit the behavioral biases that may create the factors themselves. We examined value and momentum across the factors and used these metrics to allocate to factors that we expected to outperform in the future.

The results were positive. However, taking into account transaction costs led to the conclusion that investors were likely better off simply holding a diversified factor portfolio.

We then looked at ways to time the factors using the business cycle.

The results in this case were even less convincing and were a bit too similar to a data-mined optimal solution to instill much faith going forward.

But this evidence does not necessarily remove the temptation to take a stab at timing the factors, especially since explicit transactions costs have been slashed for many investors accessing long-only factors through ETFs.Source: Kenneth French Data Library, AQR. 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. 

After all, there is a lot to gain by choosing the right factors. For example, in the first 9 months of 2019, the spread between the best (Quality) and worst (Value) performing factors was nearly 1,000 basis points (“bps”). One month prior, that spread had been double!

In this research note, we will move away from devising a systematic approach to timing the factors (as AQR asserts, this is deceptively difficult) and instead focus on what a given method would have to overcome to achieve consistent outperformance.

Benchmarking Factor Timing

With all equity factor strategies, the goal is usually to outperform the market-cap weighted equity benchmark.

Since all factor portfolios can be thought of as a market cap weighted benchmark plus a long/short component that captures the isolated factor performance, we can focus our study solely on the long/short portfolio.

Using the common definitions of the factors (from Kenneth French and AQR), we can look at periods over which these self-financing factor portfolios generate positive returns to see if overlaying them on a market-cap benchmark would have added value over different lengths of time.1

We will also include the performance of an equally weighted basket of the four factors (“Blend”).

Source: Kenneth French Data Library, AQR. 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. Data from July 1957 – September 2019.

The persistence of factor outperformance over one-month periods is transient. If the goal is to outperform the most often, then the blended portfolio satisfies this requirement, and any timing strategy would have to be accurate enough to overcome this already existing spread.

Source: Kenneth French Data Library, AQR. 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. Data from July 1957 – September 2019.

The results for the blended portfolio are so much better than the stand-alone factors because the factors have correlations much lower than many other asset classes, allowing even naïve diversification to add tremendous value.

The blended portfolio also cuts downside risk in terms of returns. If the timing strategy is wrong, and chooses, for example, momentum in an underperforming month, then it could take longer for the strategy to climb back to even. But investors are used to short periods of underperformance and often (we hope) realize that some short-term pain is necessary for long-term gains.

Looking at the same analysis over rolling 1-year periods, we do see some longer periods of factor outperformance. Some examples are quality in the 1980s, value in the mid-2000s, momentum in the 1960s and 1990s, and size in the late-1970s.

However, there are also decent stretches where the factors underperform. For example, the recent decade for value, quality in the early 2010s, momentum sporadically in the 2000s, and size in the 1980s and 1990s. If the timing strategy gets stuck in these periods, then there can be a risk of abandoning it.

Source: Kenneth French Data Library, AQR. 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. Data from July 1957 – September 2019.

Again, a blended portfolio would have addressed many of these underperforming periods, giving up some of the upside with the benefit of reducing the risk of choosing the wrong factor in periods of underperformance.

Source: Kenneth French Data Library, AQR. 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. Data from July 1957 – September 2019.

And finally, if we extend our holding period to three years, which may be used for a slower moving signal based on either value or the business cycle, we see that the diversified portfolio still exhibits outperformance over the most rolling periods and has a strong ratio of upside to downside.

Source: Kenneth French Data Library, AQR. 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. Data from July 1957 – September 2019.

The diversified portfolio stands up to scrutiny against the individual factors but could a generalized model that can time the factors with a certain degree of accuracy lead to better outcomes?

Generic Factor Timing

To construct a generic factor timing model, we will consider a strategy that decides to hold each factor or not with a certain degree of accuracy.

For example, if the accuracy is 50%, then the strategy would essentially flip a coin for each factor. Heads and that factor is included in the portfolio; tails and it is left out. If the accuracy is 55%, then the strategy will hold the factor with a 55% probability when the factor return is positive and not hold the factor with the same probability when the factor return is negative. Just to be clear, this strategy is constructed with look-ahead bias as a tool for evaluation.

All factors included in the portfolio are equally weighted, and if no factors are included, then the returns is zero for that period.

This toy model will allow us to construct distributions to see where the blended portfolio of all the factors falls in terms of frequency of outperformance (hit rate), average outperformance, and average underperformance. The following charts show the percentiles of the diversified portfolio for the different metrics and model accuracies using 1,000 simulations.2

Source: Kenneth French Data Library, AQR. 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. Data from July 1957 – September 2019.

In terms of hit rate, the diversified portfolio behaves in the top tier of the models over all time periods for accuracies up to about 57%. Even with a model that is 60% accurate, the diversified portfolio was still above the median.

Source: Kenneth French Data Library, AQR. 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. Data from July 1957 – September 2019.

For average underperformance, the diversified portfolio also did very well in the context of these factor timing models. The low correlation between the factors leads to opportunities for the blended portfolio to limit the downside of individual factors.

Source: Kenneth French Data Library, AQR. 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. Data from July 1957 – September 2019.

For average outperformance, the diversified portfolio did much worse than the timing model over all time horizons. We can attribute this also to the low correlation between the factors, as choosing only a subset of factors and equally weighting them often leads to more extreme returns.

Overall, the diversified portfolio manages the risks of underperformance, both in magnitude and in frequency, at the expense of sacrificing outperformance potential. We saw this in the first section when we compared the diversified portfolio to the individual factors.

But if we want to have increased return potential, we will have to introduce some model risk to time the factors.

Checking in on Momentum

Momentum is one model-based way to time the factors. Under our definition of accuracy in the toy model, a 12-1 momentum strategy on the factors has an accuracy of about 56%. While the diversified portfolio exhibited some metrics in line with strategies that were even more accurate than this, it never bore concentration risk: it always held all four factors.

Source: Kenneth French Data Library, AQR. 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. Data from July 1957 – September 2019.

For the hit rate percentiles of the momentum strategy, we see a more subdued response. Momentum does not win as much as the diversified portfolio over the different time periods.

But not winning as much can be fine if you win bigger when you do win.

The charts below show that momentum does indeed have a higher outperformance percentile but with a worse underperformance percentile, especially for 1-month periods, likely due to mean reversionary whipsaw.

Source: Kenneth French Data Library, AQR. 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. Data from July 1957 – September 2019.

While momentum is definitely not the only way to time the factors, it is a good baseline to see what is required for higher average outperformance.

Now, turning back to our generic factor timing model, what accuracy would you need to beat momentum?

Sharpening our Signal

The answer is: not a whole lot. Most of the time, we only need to be about 53% accurate to beat the momentum-based factor timing.

Source: Kenneth French Data Library, AQR. 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. 

The caveat is that this is the median performance of the simulations. The accuracy figure climbs closer to 60% if we use the 25th percentile as our target.

While these may not seem like extremely high requirements for running a successful factor timing strategy, it is important to observe that not many investors are doing this. True accuracy may be hard to discover, and sticking with the system may be even harder when the true accuracy can never be known.

Conclusion

If you made it this far looking for some rosy news on factor timing or the Holy Grail of how to do it skillfully, you may be disappointed.

However, for most investors looking to generate some modest benefits relative to market-cap equity, there is good news. Any signal for timing factors does not have to be highly accurate to perform well, and in the absence of a signal for timing, a diversified portfolio of the factors can lead to successful results by the metrics of average underperformance and frequency of underperformance.

For those investors looking for higher outperformance, concentration risk will be necessary.

Any timing strategy on low correlation investments will generally forego significant diversification in the pursuit of higher returns.

While this may be the goal when constructing the strategy, we should always pause and determine whether the potential benefits outweigh the costs. Transaction costs may be lower now. However, there are still operational burdens and the potential stress caused by underperformance when a system is not automated or when results are tracked too frequently.

Factor timing may be possible, but timing and tactical rotation may be better suited to scenarios where some of the model risk can be mitigated.

Harvesting the Bond Risk Premium

By

On August 5, 2019

In Craftsmanship, Portfolio Construction, Risk & Style Premia, Risk Management, Term, Weekly Commentary

This post is available as a PDF download here.

Summary­

  • The bond risk premium is the return that investors earn by investing in longer duration bonds.
  • While the most common way that investors can access this return stream is through investing in bond portfolios, bonds often significantly de-risk portfolios and scale back returns.
  • Investors who desire more equity-like risk can tap into the bond risk premium by overlaying bond exposure on top of equities.
  • Through the use of a leveraged ETP strategy, we construct a long-only bond risk premium factor and investigate its characteristics in terms of rebalance frequency and timing luck.
  • By balancing the costs of trading with the risk of equity overexposure, investors can incorporate the bond risk premium as a complementary factor exposure to equities without sacrificing return potential from scaling back the overall risk level unnecessarily.

The discussion surrounding factor investing generally pertains to either equity portfolios or bond portfolios in isolation. We can calculate value, momentum, carry, and quality factors for each asset class and invest in the securities that exhibit the best characteristics of each factor or a combination of factors.

There are also ways to use these factors to shift allocations between stocks and bonds (e.g. trend and standardizing based on historical levels). However, we do not typically discuss bonds as their own standalone factor.

The bond risk premium – or term premium – can be thought of as the premium investors earn from holding longer duration bonds as opposed to cash. In a sense, it is a measure of carry. Its theoretical basis is generally seen to be related to macroeconomic factors such as inflation and growth expectations.1

While timing the term premium using factors within bond duration buckets is definitely a possibility, this commentary will focus on the term premium in the context of an equity investor who wants long-term exposure to the factor.

The Term Premium as a Factor

For the term premium, we can take the usual approach and construct a self-financing long/short portfolio of 100% intermediate (7-10 year) U.S. Treasuries that borrows the entire portfolio value at the risk-free rate.

This factor, shown in bold in the chart below, has exhibited a much tamer return profile than common equity factors.

Source: CSI Analytics, AQR, and Bloomberg. Calculations by Newfound Research. Data from 1/31/1992 to 6/28/2019. Results are 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. Past performance is not an indicator of future results.  

Source: CSI Analytics, AQR, and Bloomberg. Calculations by Newfound Research. Data from 1/31/1992 to 6/28/2019. Results are 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. Past performance is not an indicator of future results.  

But over the entire time period, its returns have been higher than those of both the Size and Value factors. Its maximum drawdown has been less than 40% of that of the next best factor (Quality), and it is worth acknowledging that its volatility – which is generally correlated to drawdown for highly liquid assets with non-linear payoffs – has also been substantially lower.

The term premium also has exhibited very low correlation with the other equity factors.

Source: CSI Analytics, AQR, and Bloomberg. Calculations by Newfound Research. Data from 1/31/1992 to 6/28/2019. Results are 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. Past performance is not an indicator of future results.  

A Little Free Lunch

Whether we are treating bonds as factor or not, they are generally the primary way investors seek to diversify equity portfolios.

The problem is that they are also a great way to reduce returns during most market environments through their inherently lower risk.

Anytime that an asset with lower volatility is added to a portfolio, the risk will be reduced. Unless the asset class also has a particularly high Sharpe ratio, maintaining the same level of return is virtually impossible even if risk-adjusted returns are improved.

In a 2016 paper2, Salient broke down this reduction in risk into two components: de-risking and the “free lunch” affect.

The reduction in risk form the free lunch effect is desirable, but the risk reduction from de-risking may or may not be desirable, depending on the investor’s target risk profile.

The following chart shows the volatility breakdown of a range of portfolios of the S&P 500 (IVV) and 7-10 Year U.S. Treasuries (IEF).

Source: CSI Analytics and Bloomberg. Calculations by Newfound Research. Data from 1/31/1992 to 6/28/2019. Results are 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. Past performance is not an indicator of future results.  

Moving from an all equity portfolio to a 50/50 equity reduces the volatility from 14.2% to 7.4%. But only 150 bps of this reduction is from the free lunch effect that stems from the lower correlation between the two assets (-0.18). The remaining 530 bps of volatility reduction is simply due to lower risk.

In this case, annualized returns were dampened from 9.6% to 7.8%. While the Sharpe ratio climbed from 0.49 to 0.70, an investor seeking higher risk would not benefit without the use of leverage.

Despite the strong performance of the term premium factor, risk-seeking investors (e.g. those early in their careers) are generally reluctant to tap into this factor too much because of the de-risking effect.

How do investors who want to bear risk commensurate with equities tap into the bond risk premium without de-risking their portfolio?

One solution is using leveraged ETPs.

Long-Only Term Premium

By taking a 50/50 portfolio of the 2x Levered S&P 500 ETF (SSO) and the 2x Levered 7-10 Year U.S. Treasury ETF (UST), we can construct a portfolio that has 100% equity exposure and 100% of the term premium factor.3

But managing this portfolio takes some care.

Left alone to drift, the allocations can get very far away from their target 50/50, spanning the range from 85/15 to 25/75. Periodic rebalancing is a must.

Source: CSI Analytics and Bloomberg. Calculations by Newfound Research. Data from 1/31/1992 to 6/28/2019. Results are 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. Past performance is not an indicator of future results.  

Of course, now the question is, “How frequently should we rebalance the portfolio?”

This boils down to a balancing act between performance and costs (e.g. ticket charges, tax impacts, operational burden, etc.).

On one hand, we would like to remain as close to the 50/50 allocation as possible to maintain the desired exposure to each asset class. However, this could require a prohibitive amount of trading.

From a performance standpoint, we see improved results with longer holding periods (take note of the y-axes in the following charts; they were scaled to highlight the differences).

Source: CSI Analytics and Bloomberg. Calculations by Newfound Research. Data from 1/31/1992 to 6/28/2019. Results are 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. Past performance is not an indicator of future results.  

The returns do not show a definitive pattern based on rebalance frequency, but the volatility decreases with increasing time between rebalances. This seems like it would point to waiting longer between rebalances, which would be corroborated by a consideration of trading costs.

The issues with waiting longer between the rebalance are twofold:

  1. Waiting longer is essentially a momentum trade. The better performing asset class garners a larger allocation as time progresses. This can be a good thing – especially in hindsight with how well equities have done – but it allows the portfolio to become overexposed to factors that we are not necessarily intending to exploit.
  2. Longer rebalances are more exposed to timing luck. For example, a yearly rebalance may have done well from a performance perspective, but the short-term performance could vary by as much as 50,000 bps between the best performing rebalance month and the worst! The chart below shows the performance of each iteration relative to the median performance of the 12 different monthly rebalance strategies.

Source: CSI Analytics and Bloomberg. Calculations by Newfound Research. Data from 1/31/1992 to 6/28/2019. Results are 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. Past performance is not an indicator of future results.  

As the chart also shows, tranching can help mitigate timing luck. Tranching also gives the returns of the strategies over the range of rebalance frequencies a more discernible pattern, with longer rebalance period strategies exhibiting slightly higher returns due to their higher average equity allocations.

Under the assumption that we can tranche any strategy that we choose, we can now compare only the tranched strategies at different rebalance frequencies to address our concern with taking bets on momentum.

Pausing for a minute, we should be clear that we do not actually know what the true factor construction should be; it is a moving target. We are more concerned with robustness than simply trying to achieve outperformance. So we will compare the strategies to the median performance of the previously monthly offset annual rebalance strategies.

The following charts shows the aggregate risk of short-term performance deviations from this benchmark.

The first one shows the aggregate deviations, both positive and negative, and the second focuses on only the downside deviation (i.e. performance that is worse than the median).4

Both charts support a choice of rebalance frequency somewhere in the range of 3-6 months.

Source: CSI Analytics and Bloomberg. Calculations by Newfound Research. Data from 1/31/1992 to 6/28/2019. Results are 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. Past performance is not an indicator of future results.  

With the rebalance frequency set based on the construction of the factor, the last part is a consideration of costs.

Unfortunately, this is more situation-specific (e.g. what commissions does your platform charge for trades?).

From an asset manager point-of-view, where we can trade with costs proportional to the size of the trade, execute efficiently, and automate much of the operational burden, tranching is our preferred approach.

We also prefer this approach over simply rebalancing back to the static 50/50 allocation more frequently.

In our previous commentary on constructing value portfolios to mitigate timing luck, we described how tranching monthly is a different decision than rebalancing monthly and that tranching frequency and rebalance frequency are distinct decisions.

We see the same effect here where we plot the monthly tranched annually rebalanced strategy (blue line) and the strategy rebalanced back to 50/50 every month (orange line).

Source: CSI Analytics and Bloomberg. Calculations by Newfound Research. Data from 1/31/1992 to 6/28/2019. Results are 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. Past performance is not an indicator of future results.  

Tranching wins out.

However, since the target for the term premium factor is a 50/50 static allocation, running a simple allocation filter to keep the portfolio weights within a certain tolerance can be a way to implement a more dynamic rebalancing model while reducing costs.

For example, rebalancing when the allocations for SSO and UST we outside a 5% band (i.e. the portfolio was beyond a 55/45 or 45/55) achieved better performance metrics than the monthly rebalanced version with an average of only 3 rebalances per year.

Conclusion

The bond term premium does not have to be reserved for risk-averse investors. Investors desiring portfolios tilted heavily toward equities can also tap into this diversifying return stream as a factor within their portfolio.

Utilizing leveraged ETPs is one way to maintaining exposure to equities while capturing a significant portion of the bond risk premium. However, it requires more oversight than investing in other factors such as value, momentum, and quality, which are typically packaged in easy-to-access ETFs.

If a fixed frequency rebalance approach is used, tranching is an effective way to reduce timing risk, especially when markets are volatile. Aside from tranching, we find that, historically, holding periods between 3 and 6 months yield results close in line with the median rolling short-term performance of the individual strategies. Implementing a methodology like this can reduce the risk of poor luck in choosing the rebalance frequency or starting the strategy at an unfortunate time.

If frequent rebalances – like those seen with tranching – are infeasible, a dynamic schedule based on a drift in allocations is also a possibility.

Leveraged ETPs are often seen as risk trading instruments that are not fit for retail investors who are more focused on buy-and-hold systems. However, given the right risk management, these investment vehicles can be a way for investors to access the bond term premium, getting a larger free lunch, and avoiding undesired de-risking along the way.

Timing Luck and Systematic Value

By

On July 29, 2019

In Craftsmanship, Risk & Style Premia, Value, Weekly Commentary

This post is available as a PDF download here.

Summary­

  • We have shown many times that timing luck – when a portfolio chooses to rebalance – can have a large impact on the performance of tactical strategies.
  • However, fundamental strategies like value portfolios are susceptible to timing luck, as well.
  • Once the rebalance frequency of a strategy is set, we can mitigate the risk of choosing a poor rebalance date by diversifying across all potential variations.
  • In many cases, this mitigates the risk of realizing poor performance from an unfortunate choice of rebalance date while achieving a risk profile similar to the top tier of potential strategy variations.
  • By utilizing strategies that manage timing luck, the investors can more accurately assess performance differences arising from luck and skill.

On August 7th, 2013 we wrote a short blog post titled The Luck of Rebalance Timing.  That means we have been prattling on about the impact of timing luck for over six years now (with apologies to our compliance department…).

(For those still unfamiliar with the idea of timing luck, we will point you to a recent publication from Spring Valley Asset Management that provides a very approachable introduction to the topic.1)

While most of our earliest studies related to the impact of timing luck in tactical strategies, over time we realized that timing luck could have a profound impact on just about any strategy that rebalances on a fixed frequency.  We found that even a simple fixed-mix allocation of stocks and bonds could see annual performance spreads exceeding 700bp due only to the choice of when they rebalanced in a given year.

In seeking to generalize the concept, we derived a formula that would estimate how much timing luck a strategy might have.  The details of the derivation can be found in our paper recently published in the Journal of Index Investing, but the basic formula is:

Here T is strategy turnover, F is how many times per year the strategy rebalances, and S is the volatility of a long/short portfolio capturing the difference between what the strategy is currently invested in versus what it could be invested in.

We’re biased, but we think the intuition here works out fairly nicely:

  • The higher a strategy’s turnover, the greater the impact of our choice of rebalance dates. For example, if we have a value strategy that has 50% turnover per year, an implementation that rebalances in January versus one that rebalances in July might end up holding very different securities.  On the other hand, if the strategy has just 1% turnover per year, we don’t expect the differences in holdings to be very large and therefore timing luck impact would be minimal.
  • The more frequently we rebalance, the lower the timing luck. Again, this makes sense as more frequent rebalancing limits the potential difference in holdings of different implementation dates.  Again, consider a value strategy with 50% turnover.  If our portfolio rebalances every other month, there are two potential implementations: one that rebalances January, March, May, etc. and one that rebalances February, April, June, etc. We would expect the difference in portfolio holdings to be much more limited than in the case where we rebalance only annually.2
  • The last term, S, is most easily explained with an example. If we have a portfolio that can hold either the Russell 1000 or the S&P 500, we do not expect there to be a large amount of performance dispersion regardless of when we rebalance or how frequently we do so.  The volatility of a portfolio that is long the Russell 1000 and short the S&P 500 is so small, it drives timing luck near zero.  On the other hand, if a portfolio can hold the Russell 1000 or be short the S&P 500, differences in holdings due to different rebalance dates can lead to massive performance dispersion. Generally speaking, S is larger for more highly concentrated strategies with large performance dispersion in their investable universe.

Timing Luck in Smart Beta

To date, we have not meaningfully tested timing luck in the realm of systematic equity strategies.3  In this commentary, we aim to provide a concrete example of the potential impact.

A few weeks ago, however, we introduced our Systematic Value portfolio, which seeks to deliver concentrated exposure to the value style while avoiding unintended process and timing luck bets.

To achieve this, we implement an overlapping portfolio process.  Each month we construct a concentrated deep value portfolio, selecting just 50 stocks from the S&P 500.  However, because we believe the evidence suggests that value is a slow-moving signal, we aim for a holding period between 3-to-5 years.  To achieve this, our capital is divided across the prior 60 months of portfolios.4

Which all means that we have monthly snapshots of deep value5 portfolios going back to November 2012, providing us data to construct all sorts of rebalance variations.

The Luck of Annual Rebalancing

Given our portfolio snapshots, we will create annually rebalanced portfolios.  With monthly portfolios, there are twelve variations we can construct: a portfolio that reconstitutes each January; one that reconstitutes each February; a portfolio that reconstitutes each March; et cetera.

Below we plot the equity curves for these twelve variations.

Source: CSI Analytics.  Calculations by Newfound Research.  Results are 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.  Past performance is not an indicator of future results.  

We cannot stress enough that these portfolios are all implemented using a completely identical process.  The only difference is when they run that process.  The annualized returns range from 9.6% to 12.2%.  And those two portfolios with the largest disparity rebalanced just a month apart: January and February.

To avoid timing luck, we want to diversify when we rebalance.  The simplest way of achieving this goal is through overlapping portfolios.  For example, we can build portfolios that rebalance annually, but allocate to two different dates.  One portfolio could place 50% of its capital in the January rebalance index and 50% in the July rebalance index.

Another variation could place 50% of its capital in the February index and 50% in the August index.6  There are six possible variations, which we plot below.

The best performing variation (January and July) returned 11.7% annualized, while the worst (February and August) returned 9.7%.  While the spread has narrowed, it would be dangerous to confuse 200bp annualized for alpha instead of rebalancing luck.

Source: CSI Analytics.  Calculations by Newfound Research.  Results are 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.  Past performance is not an indicator of future results.  

We can go beyond just two overlapping portfolios, though.  Below we plot the three variations that contain four overlapping portfolios (January-April-July-October, February-May-August-November, and March-June-September-December).  The best variation now returns 10.9% annualized while the worst returns 10.1% annualized.  We can see how overlapping portfolios are shrinking the variation in returns.

Finally, we can plot the variation that employs 12 overlapping portfolios.  This variation returns 10.6% annualized; almost perfectly in line with the average annualized return of the underlying 12 variations.  No surprise: diversification has neutralized timing luck.

Source: CSI Analytics.  Calculations by Newfound Research.  Results are 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.  Past performance is not an indicator of future results.  

Source: CSI Analytics.  Calculations by Newfound Research.  Results are 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.  Past performance is not an indicator of future results.  

But besides being “average by design,” how can we measure the benefits of diversification?

As with most ensemble approaches, we see a reduction in realized risk metrics.  For example, below we plot the maximum realized drawdown for annual variations, semi-annual variations, quarterly variations, and the monthly variation.  While the dispersion is limited to just a few hundred basis points, we can see that the diversification embedded in the monthly variation is able to reduce the bad luck of choosing an unfortunate rebalance date.

Source: CSI Analytics.  Calculations by Newfound Research.  Results are 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.  Past performance is not an indicator of future results.  

Just Rebalance more Frequently?

One of the major levers in the timing luck equation is how frequently the portfolio is rebalanced.  However, we firmly believe that while rebalancing frequency impacts timing luck, timing luck should not be a driving factor in our choice of rebalance frequency.

Rather, rebalance frequency choices should be a function of the speed at which our signal decays (e.g. fast-changing signals such as momentum versus slow-changing signals like value) versus implementation costs (e.g. explicit trading costs, market impact, and taxes).  Only after this choice is made should we seek to limit timing luck.

Nevertheless, we can ask the question, “how does rebalancing more frequently impact timing luck in this case?”

To answer this question, we will evaluate quarterly-rebalanced portfolios.  The distinction here from the quarterly overlapping portfolios above is that the entire portfolio is rebalanced each quarter rather than only a quarter of the portfolio.  Below, we plot the equity curves for the three possible variations.

Source: CSI Analytics.  Calculations by Newfound Research.  Results are 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.  Past performance is not an indicator of future results.  

The best performing variation returns 11.7% annualized while the worst returns 9.7% annualized, for a spread of 200 basis points.  This is actually larger than the spread we saw with the three quarterly overlapping portfolio variations, and likely due to the fact that turnover within the portfolios increased meaningfully.

While we can see that increasing the frequency of rebalancing can help, in our opinion the choice of rebalance frequency should be distinct from the choice of managing timing luck.

Conclusion

In our opinion, there are at least two meaningful conclusions here:

The first is for product manufacturers (e.g. index issuers) and is rather simple: if you’re going to have a fixed rebalance schedule, please implement overlapping portfolios.  It isn’t hard.  It is literally just averaging.  We’re all better off for it.

The second is for product users: realize that performance dispersion between similarly-described systematic strategies can be heavily influenced by when they rebalance. The excess return may really just be a phantom of luck, not skill.

The solution to this problem, in our opinion, is to either: (1) pick an approach and just stick to it regardless of perceived dispersion, accepting the impact of timing luck; (2) hold multiple approaches that rebalance on different days; or (3) implement an approach that accounts for timing luck.

We believe the first approach is easier said than done.  And without a framework for distinguishing between timing luck and alpha, we’re largely making arbitrary choices.

The second approach is certainly feasible but has the potential downside of requiring more holdings as well as potentially forcing an investor to purchase an approach they are less comfortable with.   For example, blending IWD (Russell 1000 Value), RPV (S&P  500 Pure Value), VLUE (MSCI U.S. Enhanced Value), and QVAL (Alpha Architect U.S. Quantitative Value) may create a portfolio that rebalances on many different dates (annual in May; annual in December; semi-annual in May and November; and quarterly, respectively), it also introduces significant process differences.  Though research suggests that investors may benefit from further manager/process diversification.

For investors with conviction in a single strategy implementation, the last approach is certainly the best.  Unfortunately, as far as we are aware, there are only a few firms who actively implement overlapping portfolios (including Newfound Research, O’Shaughnessy Asset Management, AQR, and Research Affiliates). Until more firms adopt this approach, timing luck will continue to loom large.

 

 

Ensemble Multi-Asset Momentum

By

On July 22, 2019

In Craftsmanship, Momentum, Popular, Risk & Style Premia, Risk Management, Weekly Commentary

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.

Min

Max

2008*

-9.91%

0.85%

2009

2.36%

4.59%

2010

6.46%

9.65%

2011

3.31%

10.15%

2012

6.76%

10.83%

2013

3.42%

6.13%

2014

5.98%

10.60%

2015

-5.93%

-2.51%

2016

4.18%

8.45%

2017

9.60%

11.62%

2018

-6.00%

-2.53%

2019 YTD

5.93%

10.01%

* 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.

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