Flirting with Models

The Research Library of Newfound Research

Author: Corey Hoffstein Page 5 of 18

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.

Factor Orphans

By

On October 28, 2019

In Risk & Style Premia, Weekly Commentary

This post is available as a PDF download here.

Summary­

  • To generate returns that are different than the market, we must adopt a positioning that is different than the market.
  • With the increasing adoption of systematic factor portfolios, we explore whether an anti-factor stance can generate contrarian-based profits.
  • Specifically, we explore the idea of factor orphans: stocks that are not included in any factor portfolio at a given time.
  • To identify these stocks, we replicate four popular factor indices: the S&P 500 Enhanced Value index, the S&P 500 Momentum index, the S&P 500 Low Volatility index, and the S&P 500 Quality index.
  • On average, there are over 200 stocks in the S&P 500 that are orphaned at any given time.
  • Generating an equal-weight portfolio of these stocks does not exhibit meaningfully different performance than a naïve equal-weight S&P 500 portfolio.

Contrarian investing is nothing new.  Holding a variant perception to the market is often cited as a critical component to generating differentiated performance.  The question in the details is, however, “contrarian to what?”

In the last decade, we’ve witnessed a dramatic rise in the popularity of systematically managed active strategies.  These so-called “smart beta” portfolios seek to harvest documented risk premia and market anomalies and implement them with ruthless discipline.

But when massively adopted, do these strategies become the commonly-held view and therefore more efficiently priced into the market?  Would this mean that the variant perception would actually be buying those securities totally ignored by these strategies?

This is by no means a new idea.  Morningstar has long maintained its Unloved strategy that purchases the three equity categories that have witnessed the largest outflows at the end of the year.  A few years ago, Vincent Deluard constructed a “DUMB” beta portfolio that included all the stocks shunned by popular factor ETFs.  In the short out-of-sample period the performance of the strategy was tested, it largely kept pace with an equal-factor portfolio.  More recently, a Bank of America research note claimed that a basket of most-hated securities – as defined by companies neglected by mutual funds and shorted by hedge funds hedge funds – had tripled the S&P 500’s return over the past year.

The approach certainly has an appealing narrative: as the crowd zigs to adopt smart beta, we zag.  But has it worked?

To test this concept, we wanted to identify what we call “factor orphans”: those securities not held by any factor portfolio.  Once identified, we can build a portfolio holding these stocks and track its performance over time.

As a quant, this idea strikes us as a little crazy.  A stock not held in a value, momentum, low volatility, or quality index is likely one that is expensive, highly volatile, with poor fundamentals and declining performance.  Precisely the type of stock factor investing would tell us not to own.

But perhaps the fact that these securities are orphaned means that there are no more sellers: the major cross-section of market strategies have already abandoned the stock.  Thus, stepping in to buy them may allow us to offload them later when they are picked back up by these systematic approaches.

Perhaps this idea is crazy enough it just might work…

To test this idea, we first sought to replicate four common factor benchmarks: the S&P 500 Enhanced Value index, the S&P 500 Momentum index, the S&P 500 Low Volatility index and the S&P 500 Quality index.  Once replicated, we can use the underlying baskets as being representative of the holdings for factor portfolios is general.

Results of our replication efforts are plotted below.  We can see that our models fit the shape of most of the indices closely, with very close fits for the Momentum and Low Volatility portfolios.

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 Quality replication represents the largest deviation from the underlying index, but still approximates the shape of the total return profile rather closely.  This gives us confidence that the portfolio we constructed is a quality portfolio (which should come as no surprise, as securities were selected based upon common quality metrics), but the failure to more closely replicate this index may represent a thorn in our ability to identify truly orphaned stocks.

At the end of each month, we identify the set of all securities held by any of the four portfolios.  The securities in the S&P 500 (at that point in time) but not in the factor basket are the orphaned stocks.  Somewhat surprisingly, we find that approximately 200 names are orphaned at any given time, with the number reaching as high as 300 during periods when underlying factors converge.

Also interesting is that the actual overlap in holdings in the factor portfolios is quite low, rarely exceeding 30%.  This is likely due to the rather concentrated nature of the indices selected, which hold only 100 stocks at a given time.

Source: Sharadar.  Calculations by Newfound Research.

Once our orphaned stocks are identified, we construct a portfolio that holds them in equal weight.  We rebalance our portfolio monthly to sell those stocks that have been acquired by a factor portfolio and roll into those securities that have been abandoned.

We plot the results of our exercise below as well as an equally weighted S&P 500 benchmark.

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. 

While the total return is modestly less (but certainly not statistically significantly so), what is most striking is how little deviation there is in the orphaned stock portfolio versus the equal-weight benchmark.

However, as we have demonstrated in the past, the construction choices in a portfolio can have a significant impact upon the realized results.  As we look at the factor portfolios themselves, we must acknowledge that they represent relative tilts to the benchmark, and that the absence of one security might actually represent a significantly smaller relative underweight to the benchmark than the absence of another.  Or the absence of one security may actually represent a smaller relative underweight than another that is actually included.

Therefore, as an alternative test we construct an equal-weight factor portfolio and subtract the S&P 500 market-capitalization weights.  The result is the implied over- and under-weights of the combined factor portfolios.  We then rank securities to select the 100 most under-weight securities each month and hold them in equal weight.

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. 

Of course, we didn’t actually have to perform this exercise had we stepped back to think for a moment.  We generally know that these (backtested) factors have out-performed the benchmark.  Therefore, selecting stocks that they are underweight means we’re taking the opposite side of the factor trade, which we know has not worked.

Which does draw an important distinction between most underweight and orphaned.  It would appear that factor orphans do not necessarily create the strong anti-factor tilt the way that the most underweight portfolio does.

For the sake of completion, we can also evaluate the portfolios containing securities held in just one of the factor portfolios, two of the factor portfolios, three of the factor portfolios, or all of the factor portfolios at a given time.

Below we plot the count of securities in such portfolios over time.  We can see that it is very uncommon to identify securities that are simultaneously held by all the factors, or even three of the factors, at once.

Source: Sharadar.  Calculations by Newfound Research.

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 can see that the portfolio built from stocks held in just one factor (“In One”) closely mimics the portfolio built from stocks held in no factor (“In Zero”), which in turn mimics the S&P 500 Equal Weight portfolio.  This is likely because the portfolios include so many securities that they effectively bring you back to the index.

On the other end of the spectrum, we see the considerable risks of concentration manifest in the portfolios built from stocks held in three or four of the factors.  The portfolio comprised of stocks held in all four factors simultaneously (“In Four”) not only goes long stretches of holding nothing at all, but is also subject to large bouts of volatility due to the extreme concentration.

We also see this for the portfolio that holds stocks held by three of the factors simultaneously (“In Three”).  While this portfolio has modestly more diversification – and even appears to out-perform the equal-weight benchmark – the concentration risk finally materializes in 2018-2019, causing a dramatic drawdown.

The portfolio holding stocks held in just two of the factors (“In Two”), though, appears to offer some out-performance opportunity.  Perhaps by forcing just two factors to agree, we strike a balance between confirmation among signals and portfolio diversification.

Unfortunately, our enthusiasm quickly wanes when we realize that this portfolio closely matches the results achieved just by naively equally-weighting exposure among the four factor portfolios themselves, which is far more easily implemented.

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

To achieve differentiated results, we must take a differentiated stance from the market.  As systematic factor portfolios are more broadly adopted, we should consider asking ourselves if taking an anti-factor stance might lead to contrarian-based profits.

In this study, we explore the idea of factor orphans: stocks not held by any factor portfolio at a given time.  Our hypothesis is that these orphaned securities may be systematically over-sold, leading to an opportunity for future out-performance if they are re-acquired by the factor portfolios at a later date.

We begin by replicating four factor indices: the S&P 500 Enhanced Value index, the S&P 500 Momentum index, the S&P 500 Low Volatility index, and the S&P 500 Quality index.  Replicating these processes allows us to identify historical portfolio holdings, which in turn allows us to identify stocks not held by the factors.

We are able to closely replicate the S&P 500 Momentum and Low Volatility portfolios, create meaningful overlap with the S&P 500 Enhanced Value method, and generally capture the S&P 500 Quality index.  The failure to more closely replicate the S&P 500 Quality index may have a meaningful impact on the results herein, though we believe our methodology still captures the generic return of a quality strategy.

We find that, on average, there are over 200 factor orphans at a given time.  Constructing an equal-weight portfolio of these orphans, however, only seems to lead us back to an S&P 500 Equal Weight benchmark.  While there does not appear to be an edge in this strategy, it is interesting that there does not appear to be a negative edge either.

Recognizing that long-only factor portfolios represent active bets expressed as over- and underweights relative to the S&P 500, we also construct a portfolio of the most underweight stocks.  Not surprisingly, as this portfolio actively captures a negative factor tilt, the strategy meaningfully underperforms the S&P 500 Equal Weight benchmark.  Though the relative underperformance meaningfully dissipates in recent years.

Finally, we develop portfolios to capture stocks held in just one, two, three, or all four of the factors simultaneously.  We find the portfolios comprised stocks held in either three or four of the factors at once exhibit significant concentration risk.  As with the orphan portfolio, the portfolio of stocks held by just one of the factors closely tracks the S&P 500 Equal Weight benchmark, suggesting that it might be over-diversified.

The portfolio holding stocks held by just two factors at a time appears to be the Goldilocks portfolio, with enough concentration to be differentiated from the benchmark but not so much as to create significant concentration risk.

Unfortunately, this portfolio also almost perfectly replicates a naïve equal-weight portfolio among the four factors, suggesting that the approach is likely a wasted effort.

In conclusion, we find no evidence that factor orphans have historically offered a meaningful excess return opportunity.  Nor, however, do they appear to have been a drag on portfolio returns either.  We should acknowledge, however, that the adoption of factor portfolios accelerated rapidly after the Great Financial Crisis, and that backtests may not capture current market dynamics.  More recent event studies of orphaned stocks being added to factor portfolios may provide more insight into the current environment.

Risk-Adjusted Momentum: A Momentum and Low-Volatility Barbell?

By

On October 21, 2019

In Defensive, Momentum, Weekly Commentary

This post is available as a PDF download here.

Summary

  • After the Great Financial Crisis, the Momentum factor has exhibited positive returns, but those returns have been largely driven by the short side of the portfolio.
  • One research note suggests that this is driven by increased risk aversion among investors, using the correlation of high volatility and low momentum baskets as evidence.
  • In contradiction to this point, the iShares Momentum ETF (MTUM) has generated positive excess annualized returns against its benchmark since inception. The same note suggests that this is due to the use of risk-adjusted momentum measures.
  • We explore whether risk-adjusting momentum scores introduces a meaningful and structural tilt towards low-volatility equities.
  • For the examples tested, we find that it does not, and risk-adjusted momentum portfolios behave very similarly to momentum portfolios.

A research note recently crossed my desk that aimed to undress the post-Global Financial Crisis (GFC) performance of the momentum factor in U.S. equities.  Not only have we witnessed a significant reduction in the factor’s return, but the majority of the return has been generated by the short side of the strategy, which can be more difficult for long-only investors to access.

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 Long (Alpha) strategy is a monthly rebalanced portfolio that goes long, in equal weight, the top 50 securities in the S&P 500 ranked on 12-1 month momentum and shorts an equal-weight S&P 500 portfolio.  The Short (Alpha) strategy is a monthly rebalanced portfolio that goes long an equal-weight S&P 500 portfolio and shorts, in equal weight, the bottom 50 securities in the S&P 500 ranked on 12-1 month momentum.

The note makes the narratively-appealing argument that the back-to-back recessions of the dot-com bubble and the Great Financial Crisis amplified investor risk aversion to downside losses.  The proposed evidence of this fact is the correlation of the cumulative alpha generated from shorting low momentum stocks and the cumulative alpha generated from shorting high volatility stocks.

While correlation does not imply causation, one argument might be that in a heightened period of risk aversion, investors may consistently punish higher risk stocks, causing them to become persistent losers.  Or, conversely, losers may be rapidly sold, creating both persistence and high levels of volatility.  We can arguably see this in the convergence of holdings in low momentum and high volatility stocks during “risk off” regimes.

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 HI VOL (Alpha) strategy is a monthly rebalanced portfolio that goes long an equal-weight S&P 500 portfolio and shorts, in equal weight, the bottom 50 securities in the S&P 500 ranked on trailing 252-day realized volatility.  The LO MOM (Alpha) strategy is a monthly rebalanced portfolio that goes long an equal-weight S&P 500 portfolio and shorts, in equal weight, the bottom 50 securities in the S&P 500 ranked on 12-1 month momentum.

Given these facts, we would expect long-only momentum investors to have harvested little out-performance in recent years.  Yet we find that the popular iShares Momentum ETF (MTUM) has out-performed the S&P 500 by 290 basis points per year since its inception in 2013.

The answer to this conundrum, as proposed by the research note, is that MTUM’s use of risk-adjusted momentum is the key.

If we think of risk-adjusted momentum as simply momentum divided by volatility (which is how MTUM defines it), we might interpret it as an integrated signal of both the momentum and low-volatility factors.  Therefore, risk-adjusting creates a multi-factor portfolio that tilts away from high volatility stocks.

And hence the out-performance.

Except if we actually create a risk-adjusted momentum portfolio, that does not appear to really be the case at all.

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 alpha of the risk-adjusted momentum strategy is defined as the return of a monthly rebalanced portfolio that goes long, in equal weight, the top 50 securities in the S&P 500 ranked on risk-adjusted momentum (12-1 month momentum divided by 252-day realized volatility) and shorts an equal-weight S&P 500 portfolio.

To be fair, MTUM’s construction methodology differs quite a bit from that employed herein.  We are simply equally-weighting the top 50 stocks in the S&P 500 when ranked by risk-adjusted momentum, whereas MTUM uses a blend of 6- and 12-month risk-adjusted momentum scores and then tilts market-capitalization weights based upon those scores.

Nevertheless, if we look at actual holdings overlap over time of our Risk-Adjusted Momentum portfolio versus Momentum and Low Volatility portfolios, not only do we see persistently higher overlap with the Momentum portfolio, but we see fairly low average overlap with the Low Volatility portfolio.

For the latter point, it is worth first anchoring ourselves to the standard overlap between Momentum and Low Volatility (green line below).  While we can see that the Risk-Adjusted Momentum portfolio does indeed have a higher average overlap with Low Volatility than does the Momentum portfolio, the excess tilt to Low Volatility due to the use of risk-adjusted momentum (i.e. the orange line minus the green line) appears rather small.  In fact, on average, it is just 10%.

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 risk-adjusted momentum strategy is a monthly rebalanced portfolio that goes long, in equal weight, the top 50 securities in the S&P 500 ranked on risk-adjusted momentum (12-1 month momentum divided by 252-day realized volatility).  The momentum strategy is a monthly rebalanced portfolio that goes long, in equal weight, the top 50 securities in the S&P 500 ranked on 12-1 month momentum.  The low volatility strategy is a monthly rebalanced portfolio that goes long, in equal weight, the top 50 securities in the S&P 500 ranked on trailing 252-day realized volatility.

This is further evident by looking at the actual returns of the strategies themselves:

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 risk-adjusted momentum strategy is a monthly rebalanced portfolio that goes long, in equal weight, the top 50 securities in the S&P 500 ranked on risk-adjusted momentum (12-1 month momentum divided by 252-day realized volatility).  The momentum strategy is a monthly rebalanced portfolio that goes long, in equal weight, the top 50 securities in the S&P 500 ranked on 12-1 month momentum.  The low volatility strategy is a monthly rebalanced portfolio that goes long, in equal weight, the top 50 securities in the S&P 500 ranked on trailing 252-day realized volatility.

The Risk-Adjusted Momentum portfolio performance tracks that of the Momentum portfolio very closely.

As it turns out, the step of adjusting for risk creates far less of a low volatility factor tilt in our top-decile portfolio than one might initially suspect.  (Or, at least, I’ll speak for myself: it created far less of a tilt than I expected.)

To understand this point, we will first re-write our risk-adjusted momentum signal as:

While trivial algebra, re-writing risk-adjusted momentum as the product of momentum and inverse volatility is informative to understanding why risk-adjusted momentum appears to load much more heavily on momentum than low volatility.

At a given point in time, it would appear as if Momentum and Low Volatility should have an equal influence on the rank of a given security.  However, we need to dig a level deeper and consider how changes in these variables impact change in risk-adjusted momentum.

Fortunately, the product makes this a trivial exercise: holding INVVOL constant, changes in MOM are scaled by INVVOL and vice versa.  This scaling effect can cause large changes in risk-adjusted momentum – and therefore ordinal ranking – particularly as MOM crosses the zero level.

Consider a trivial example where INVVOL is a very large number (e.g. 20) due to a security having a very low volatility profile (e.g. 5%).  This would appear, at first glance, to give a security a structural advantage and hence create a low volatility tilt in the portfolio.  However, a move from positive prior returns to negative prior returns would shift the security from ranking among the best to ranking among the worst in risk-adjusted momentum.1

A first order estimate of change in risk-adjusted momentum is:

So which term ultimately has more influence on the change in scores over time?

To get a sense of relative scale, we plot the cross-sectional mean absolute difference between the two terms over time.  This should, at least partially, capture interaction effects between the two terms.

Source: Sharadar.  Calculations by Newfound Research.

We can see that the term including the change in MOM has a much more significant influence on changes in risk-adjusted momentum than changes in INVVOL do.  Thus, we might expect a portfolio driven entirely by changes in momentum to share more in common with our risk-adjusted momentum portfolio than one driven entirely by changes in volatility.

This is somewhat evident when we plot the return of MTUM versus our top 50 style portfolios.  The correlation of daily returns between MTUM and our Momentum, Low Volatility, and Risk-Adjusted Momentum portfolios is 0.93, 0.72, and 0.93 respectively, further suggesting that MTUM is driven more by momentum than volatility.

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 risk-adjusted momentum strategy is a monthly rebalanced portfolio that goes long, in equal weight, the top 50 securities in the S&P 500 ranked on risk-adjusted momentum (12-1 month momentum divided by 252-day realized volatility).  The momentum strategy is a monthly rebalanced portfolio that goes long, in equal weight, the top 50 securities in the S&P 500 ranked on 12-1 month momentum.  The low volatility strategy is a monthly rebalanced portfolio that goes long, in equal weight, the top 50 securities in the S&P 500 ranked on trailing 252-day realized volatility.

This is only one part of the equation, however, as it is possible that changes to the risk-adjusted momentum score are so small – despite being largely driven by momentum – that relative rankings never actually change.  Or, because we have constructed our portfolios by choosing only the top 50 ranked securities, that momentum does drive the majority of change across the entire universe, but the top 50 are always structurally advantaged by the non-linear scaling of low volatility.

To create a more accurate picture, we can rank-weight the entire S&P 500 and evaluate the holdings overlap over time.

Source: Sharadar.  Calculations by Newfound Research.

Note that by now including all securities, and not just selecting the top 50, the overlap with both the Momentum and Low Volatility portfolios naturally appears higher on average.  Nonetheless, we can see that the overlap with the Momentum portfolio is consistently higher than that of the Low Volatility portfolio, again suggesting that momentum has a larger influence on the overall portfolio composition than volatility does.

Conclusion

Without much deep thought, it would be easy to assume that a risk-adjusted momentum measure – i.e. prior returns divided by realized volatility – would tilt a portfolio towards both prior winners and low-volatility securities, resulting in a momentum / low-volatility barbell.

Upon deeper consideration, however, the picture complicates quickly.  For example, momentum can be both positive and negative; dividing by volatility creates a non-linear impact; and momentum tends to change more rapidly than volatility.

We do not attempt to derive a precise, analytical equation that determines which of the two variables ultimately drives portfolio composition, but we do construct long-only example portfolios for empirical study.  We find that a high-concentration risk-adjusted momentum portfolio has significantly more overlap in holdings with a traditional momentum portfolio than a low-volatility portfolio, resulting in a more highly correlated return stream.

The most important takeaway from this note is that intuition can be deceiving: it is important to empirically test our assumptions to ensure we truly understand the impact of our strategy construction choices.

 

 

Yield Curve Trades with Trend and Momentum

By

On October 14, 2019

In Momentum, Term, Weekly Commentary

This post is available as a PDF download here.

Summary­

  • Yield curve changes over time can be decomposed into Level, Slope, and Curvature changes, and these changes can be used to construct portfolios.
  • Market shocks, monetary policy, and preferences of different segments of investors (e,g. pensions) may create trends within these portfolios that can be exploited with absolute and relative momentum.
  • In this commentary, we investigate these two factors in long/short and long/flat implementations and find evidence of success with some structural caveats.
  • Despite this, we believe the results have potential applications as either a portable beta overlay or for investors who are simply trying to figure out how to position their duration exposure.
  • Translating these quantitative signals into a forecast about yield-curve behavior may allow investors to better position their fixed income portfolios.

It has been well established in fixed income literature that changes to the U.S. Treasury yield curve can be broken down into three primary components: a level shift, a slope change, and a curvature twist.

A level change occurs when rates increase or decrease across the entire curve at once.  A slope change occurs when short-term rates decrease (increase) while long-term rates increase (decrease).  Curvature defines convexity and concavity changes to the yield curve, capturing the bowing that occurs towards the belly of the curve.

Obviously these three components do not capture 100% of changes in the yield curve, but they do capture a significant portion of them. From 1962-2019 they explain 99.5% of the variance in daily yield curve changes.

We can even decompose longer-term changes in the yield curve into these three components.  For example, consider how the yield curve has changed in the three years from 6/30/2016 to 6/30/2019.

Source: Federal Reserve of St. Louis.

We can see that there was generally a positive increase across the entire curve (i.e. a positive level shift), the front end of the curve increased more rapidly (i.e. a flattening slope change) and the curve flipped from concave to convex (i.e. an inverted bowing of the curve).

Using the historical yield curve changes, we can mathematically estimate these stylized changes using principal component analysis.  We plot the loadings of the first three components below for this three-year change.

Source: Federal Reserve of St. Louis.  Calculations by Newfound Research.

We can see that –PC1– has generally positive loadings across the entire curve, and therefore captures our level shift component.  –PC2– exhibits negative loadings on the front end of the curve and positive loadings on the back, capturing our slope change.  Finally, –PC3– has positive loadings from the 1-to-5-year part of the curve, capturing the curvature change of the yield curve itself.

Using a quick bit of linear algebra, we can find the combination of these three factors that closely matches the change in the curve from 6/30/2016 to 6/30/2019.  Comparing our model versus the actual change, we see a reasonably strong fit.

Source: Federal Reserve of St. Louis.  Calculations by Newfound Research.

So why might this be useful information?

First of all, we can interpret our principal components as if they are portfolios.  For example, our first principal component is saying, “buy a portfolio that is long interest rates across the entire curve.”  The second component, on the other hand, is better expressed as, “go short rates on the front end of the curve and go long rates on the back end.”

Therefore, insofar as we believe changes to the yield curve may exhibit absolute or relative momentum, we may be able to exploit this momentum by constructing a portfolio that profits from it.

As a more concrete example, if we believe that the yield curve will generally steepen over the next several years, we might buy 2-year U.S. Treasury futures and short 10-year U.S. Treasury futures.  The biggest wrinkle we need to deal with is the fact that 2-year U.S. Treasury futures will exhibit very different sensitivity to rate changes than 10-year U.S. Treasury futures, and therefore we must take care to duration-adjust our positions.

Why might such changes exhibit trends or relative momentum?

  • During periods where arbitrage capital is low, trends may emerge. We might expect this during periods of extreme market shock (e.g. recessions) where we might also see the simultaneous influence of monetary policy.
  • Effects from monetary policy may exhibit autocorrelation. If investors exhibit any anchoring to prior beliefs, they might discount future policy changes.
  • Segmented market theory suggests that different investors tend to access different parts of the curve (e.g. pensions may prefer the far end of the curve for liability hedging purposes). Information flow may therefore be segmented, or even impacted by structural buyers/sellers, creating autocorrelation in curve dynamics.

In related literature, Fan et al (2019) find that the net hedging or speculative position has strong cross-sectional explanatory power for agricultural and currency futures returns, but not in fixed income markets.  To quote,

“In sharp contrast, we find no evidence of a significant speculative pressure premium in the interest rate and fixed income futures markets. Thus, albeit from the lens of different research questions, our paper reaffirms Bessembinder (1992) and Moskowitz et al. (2012) in establishing that fixed income futures markets behave differently from other futures markets as regards the information content of the net positions of hedgers or speculators.  A hedgers-to-speculators risk transfer in fixed income futures markets would be obscured if agents choose to hedge their interest rate risk with other strategies (i.e. immunization, temporary change in modified duration).”

Interestingly, Markowitz et al. (2012) suggest that speculators may be profiting from time-series momentum at the expense of hedgers, suggesting that they earn a premium for providing liquidity.  Such does not appear to be the case for fixed income futures, however.

As far as we are aware, it has not yet been tested in the literature whether the net speculator versus hedger position has been tested for yield curve trades, and it may be possible that a risk transfer does not exist at the individual maturity basis, but rather exists for speculators willing to bear level, slope, or curvature risk.

Stylized Component Trades

While we know the exact loadings of our principal components (i.e. which maturities make up the principal portfolios), to avoid the risk of overfitting our study we will capture level, slope, and curvature changes with three different stylized portfolios.

To implement our portfolios, we will buy a basket of 2-, 5-, and 10-year U.S. Treasury futures contracts (“UST futures”).  We will assume that the 5-year contract has 2.5x the duration of the 2-year contract and the 10-year contract has 5x the duration of the 2-year contract.

To capture a level shift in the curve, we will go long across all the contracts.  Specifically, for every dollar of 2-year UST futures exposure we purchase, we will buy $0.4 of 5-year UST futures and $0.20 of 10-year UST futures.  This creates equal duration exposure across the entire curve.

To capture slope change, we will go short 2-year UST futures and long the 10-year UST futures, holding zero position in the 5-year UST futures.  As before, we will duration-adjust our positions such that for each $1 short of the 2-year UST futures position, we are $0.20 long the 10-year UST futures.

Finally, to capture curvature change we will construct a butterfly trade where we short the 2- and 10-year UST futures and go long the 5-year UST futures.  For each $1 long in the 5-year UST futures, we will short $1.25 of 2-year UST futures and $0.25 of 10-year UST futures.

Note that the slope and curvature portfolios are implemented such that they are duration neutral (based upon our duration assumptions) so a level shift in the curve will generate no profit or loss.

An immediate problem with our approach arises when we actually construct these portfolios.  Unless adjusted, the volatility exhibited across these trades will be meaningfully different.  Therefore, we target a constant 10% volatility for all three portfolios by adjusting the notional exposure of each portfolio based upon an exponentially-weighted estimate of prior 3-month realized volatility.

Source: Stevens Futures.  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.

It appears, at least to the naked eye, that changes in the yield curve – and therefore the returns of these portfolios – may indeed exhibit positive autocorrelation.  For example, –Slope– appears to exhibit significant trends from 2000-2004, 2004-to 2007, and 2007-2012.

Whether those trends can be identified and exploited is another matter entirely.  Thus, with our stylized portfolios in hand, we can begin testing.

Trend Signals

We begin our analysis by exploring the application of time-series momentum signals across all three of the portfolios.  We evaluate lookback horizons ranging from 21-to-294 trading days (or, approximately 1-to-14 months).  Portfolios assume a 21-trading-day holding period and are implemented using 21 overlapping portfolios to control for timing luck.

Source: Stevens Futures.  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.

Some observations:

  • Time-series momentum appears to generate positive returns for the Level portfolio. Over the period tested, longer-term measures (e.g. 8-to-14-month horizons) offer more favorable results.
  • Time-series momentum on the Level portfolio does, however, underperform naïve buy-and-hold. The returns of the strategy also do not offer a materially improved Sharpe ratio or drawdown profile.
  • Time-series momentum also appears to capture trends in the Slope portfolio. Interestingly, both short- and long-term lookbacks are less favorable over the testing period than intermediate-term (e.g. 4-to-8 month) ones.
  • Finally, time-series momentum appeared to offer no edge in timing curvature trades.

Here we should pause to acknowledge that we are blindly throwing strategies at data without much forethought.  If we consider, however, that we might reasonably expect duration to be a positively compensated risk premium, as well as the fact that we would expect the futures to capture a generally positive roll premium (due to a generally upward sloping yield curve), then explicitly shorting duration risk may not be a keen idea.

In other words, it may make more sense to implement our level trade as a long/flat rather than a long/short.  When implemented in this fashion, we see that the annualized return versus buy-and-hold is much more closely maintained while volatility and maximum drawdown are significantly reduced.

Source: Stevens Futures.  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.

Taken together, it would appear that time-series momentum may be effective for trading the persistence in Level and Slope changes, though not in Curvature.

Momentum Signals

If we treat each stylized portfolio as a separate asset, we can also consider the returns of a cross-sectional momentum portfolio.  For example, each month we can rank the portfolios based upon their prior returns.  The top-ranking portfolio is held long; the 2nd ranked portfolio is held flat; and the 3rd ranked portfolio is held short.

As before, we will evaluate lookback horizons ranging from 21-to-294 trading days (approximately 1-to-14 months) and assuming a 21-trading-day holding period, implemented with 21 overlapping portfolios.

Results – as well as example allocations from the 7-month lookback portfolio – are plotted below.

Source: Stevens Futures.  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.

Here we see very strong performance results except in the 1- and 2-month lookback periods.  The allocation graph appears to suggest that results are not merely the byproduct of consistently being long or short a particular portfolio and the total return level appears to suggest that the portfolio is able to simultaneously profit from both legs.

If we return back to the graph of the stylized portfolios, we can see a significant negative correlation between the Level and Slope portfolios from 1999 to 2011.  The negative correlation appears to disappear after this point, almost precisely coinciding with a 6+ year drawdown in the cross-sectional momentum strategy.

This is due to a mixture of construction and the economic environment.

From a construction perspective, consider that the Level portfolio is long the 2-, the 5-, and the 10-year UST futures while the Slope portfolio is short 2-year and long the 10-year UST futures.  Since the positions are held in a manner that targets equivalent duration exposure, when the 2-year rate moves more than the 10-year rate, we end up in a scenario where the two trades have negative correlation, since one strategy is short and the other is long the 2-year position.  Conversely, if the 10-year rate moves more than the 2-year rate, we end up in a scenario of positive correlation, since both strategies are long the 10-year.

Now consider the 1999-2011 environment.  We had an easing cycle during the dot-com bust, a tightening cycle during the subsequent economic expansion, and another easing cycle during the 2008 crisis.  This caused significantly more directional movement in the 2-year rate than the 10-year rate.  Hence, negative correlation.

After 2008, however, the front end of the curve became pinned to zero.  This meant that there was significantly more movement in the 10-year than the 2-year, leading to positive correlation in the two strategies.  With positive correlation there is less differentiation among the two strategies and so we see a considerable increase in strategy turnover – and effectiveness – as momentum signals become less differentiated.

With that in mind, had we designed our Slope portfolio to be long 2-year UST futures and short 10-year UST futures (i.e. simply inverted the sign of our allocations), we would have seen positive correlation between Level and Slope from 1999 to 2011, resulting in a very different set of allocations and returns.  In actually testing this step, we find that the 1999-2011 period is no longer dominated by Level versus Slope trades, but rather Slope versus Curvature.  Performance of the strategy is still largely positive, but the spread among specifications widens dramatically.

Taken all together, it is difficult to conclude that the success of this strategy was not, in essence, driven almost entirely by autocorrelation in easing and tightening cycles with a relatively stable back end of the curve.1   Given that there have only been a handful of full rate cycles in the last 20 years, we’d be reluctant to rely too heavily on the equity curve of this strategy as evidence of a robust strategy.

Conclusion

In this research note, we explored the idea of generating stylized portfolios designed to isolate and profit from changes to the form of the yield curve.  Specifically, using 2-, 5-, and 10-year UST futures we design portfolios that aim to profit from level, slope, and curvature changes to the US Treasury yield curve.

With these portfolios in hand, we test whether we can time exposure to these changes using time-series momentum.

We find that while time-series momentum generates positive performance for the Level portfolio, it fails to keep up with buy & hold.  Acknowledging that level exposure may offer a positive long-term risk premium, we adjust the strategy from long/short to long/flat and are able to generate a substantially improved risk-adjusted return profile.

Time-series momentum also appears effective for the Slope portfolio, generating meaningful excess returns above the buy-and-hold portfolio.

Applying time-series momentum to the Curvature portfolio does not appear to offer any value.

We also tested whether the portfolios can be traded employing cross-sectional momentum.  We find significant success in the approach but believe that the results are an artifact of (1) the construction of the portfolios and (2) a market regime heavily influenced by monetary policy.  Without further testing, it is difficult to determine if this approach has merit.

Finally, even though our study focused on portfolios constructed using U.S. Treasury futures, we believe the results have potential application for investors who are simply trying to figure out how to position their duration exposure.  For example, a signal to be short (or flat) the Level portfolio and long the Slope portfolio may imply a view of rising rates with a flattening curve.  Translating these quantitative signals into a forecast about yield-curve behavior may allow investors to better position their fixed income portfolios.

Since this study utilized U.S. Treasury futures, these results translate well to implementing a portable beta strategy. For example, if you were an investor with a desired risk profile on par with 100% equities, you could add bond exposure on top of the higher risk portfolio. This would add a (generally) diversifying return source with only a minor cash drag to the extent that margin requirements dictate.

 

 

Trend Following Active Returns

By

On September 23, 2019

In Risk & Style Premia, Trend

This post is available as a PDF download here.

Summary­

  • Recent research suggests that equity factors exhibit positive autocorrelation, providing fertile ground for the application of trend-following strategies.
  • In this research note, we ask whether the same techniques can be applied to the active returns of long-only style portfolios.
  • We construct trend-following strategies on the active returns of popular MSCI style indices, including Value, Size, Momentum, Minimum Volatility, and Quality.
  • A naïve, equal-weight portfolio of style trend-following strategies generates an information ratio of 0.57.
  • The interpretation of this result is largely dependent upon an investor’s pre-conceived views of style investing, as the diversified trend-following approach generally under-performs a naïve, equal-weight portfolio of factors except during periods of significant and prolonged factor dislocation.

There have been a number of papers published in the last several years suggesting that positive autocorrelation in factor returns may be exploitable through time-series momentum / trend following.  For example,

  • Ehsani and Linnainmaa (2017; revised 2019) document that “most factors exhibit positive autocorrelation with the average factor earning a monthly return of 2 basis points following a year of losses but 52 basis points following a positive year.”
  • Renz (2018) demonstrates that “risk premiums are significantly larger (lower) following recent uptrends (downtrends) in the underlying risk factor.”
  • Gupta and Kelly (2018; revised 2019) find that, “in general, individual factors can be reliably timed based on their own recent performance.”
  • Babu, Levin, Ooi, Pedersen, and Stamelos (2019) find “strong evidence of time-series momentum” across the 16 long/short equity factors they study.

While this research focuses mostly only long/short equity factors, it suggests that there may be opportunity for long-only style investors to improve their realized results as well.  After all, long-only “smart beta” products can be thought of as simply a market-cap benchmark plus a dollar-neutral long/short portfolio of active bets.

Therefore, calculating the returns due to the active bets taken by the style is a rather trivial exercise: we can simply take the monthly returns of the long-only style index and subtract the returns of the long-only market-capitalization-weighted benchmark.  The difference in returns will necessarily be due to the active bets.1

Below we plot the cumulative active returns for five popular equity styles: Value (MSCI USA Enhanced Value), Size (MSCI USA SMID), Momentum (MSCI USA Momentum), Minimum Volatility (MSCI USA Minimum Volatility), and Quality (MSCI USA Quality).

The active returns of these indices certainly rhyme with, but do not perfectly replicate, their corresponding long/short factor implementations.  For example, while Momentum certainly exhibits strong, negative active returns from 6/2008 to 12/2009, the drawdown is nowhere near as severe as the “crash” that occurred in the pure long/short factor.

This is due to two facts:

  1. The implied short side of the active bets is constrained by how far it can take certain holdings to zero. Therefore, long-only implementations tend to over-allocate towards top-quintile exposures rather than provide a balanced long/short allocation to top- and bottom-quintile exposures.
  2. While the active bets form a long/short portfolio, the notional size of that portfolio is often substantially lower than the academic factor definitions (which, with the exception of betting-against-beta, more mostly assumed to have a notional exposure of 100% per leg). The active bets, on the other hand, have a notional size corresponding to the portfolio’s active share, which frequently hovers between 30-70% for most long-only style portfolios.
  3. The implementation details of the long-only style portfolios and the long/short factor definitions may not perfectly match one another. As we have demonstrated a number of times in past research commentaries, these specification details can often swamp style returns in the short run, leading to meaningful cross-sectional dispersion in same-style performance.

Source: MSCI.  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.  You cannot invest in an index.

Source: MSCI; AQR.  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.  You cannot invest in an index.

 

Nevertheless, “rhymes but does not replicate” may be sufficient for long-only investors to still benefit from trend-following techniques.

In our test, we will go long the style / short the benchmark (i.e. long active returns) when prior N-month returns are positive and short the style / long the benchmark (i.e. short active returns) when prior N-month returns are negative. Portfolios are formed monthly at the end of each month.  Performance results are reported in the table below for 1, 3, 6, 9, and 12-month lookback periods.

 

Annualized ReturnAnnualized VolatilityInformation RatioMaximum DrawdownSample Size (Months)
1Value1.7%6.1%0.28-15.1%261
Size-0.8%8.2%-0.10-44.4%303
Momentum-0.2%7.5%-0.03-21.3%302
Minimum Volatility-0.1%5.7%-0.01-25.0%375
Quality1.3%3.8%0.35-8.9%302
3Value3.3%6.0%0.55-15.5%261
Size1.1%8.2%0.13-34.5%303
Momentum-0.8%7.5%-0.11-38.0%302
Minimum Volatility0.7%5.7%0.13-19.4%375
Quality0.9%3.8%0.24-10.1%302
6Value2.9%6.0%0.48-21.0%261
Size1.7%8.2%0.20-20.8%303
Momentum0.7%7.5%0.09-28.8%302
Minimum Volatility0.5%5.7%0.09-27.8%375
Quality0.6%3.9%0.16-14.6%302
9Value3.4%6.0%0.57-14.8%261
Size2.0%8.2%0.24-27.1%303
Momentum1.2%7.5%0.16-23.4%302
Minimum Volatility0.9%5.7%0.15-20.8%375
Quality0.3%3.9%0.07-14.7%302
12Value3.2%6.0%0.54-11.2%261
Size1.8%8.2%0.22-29.9%303
Momentum1.9%7.5%0.25-20.0%302
Minimum Volatility1.4%5.7%0.24-17.3%375
Quality1.3%3.8%0.34-11.0%302

Source: MSCI.  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.  You cannot invest in an index.

Below we plot the equity curves of the 12-month time-series momentum strategy. We also plot a portfolio that takes a naïve equal-weight position across all five trend-following strategies.  The naïve blend has an annualized return of 2.3%, an annualized volatility of 4.0%, and an information ratio of 0.57.

Source: MSCI.  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.  You cannot invest in an index.

This analysis at least appears to provide a glimmer of hope for this idea.  Of course, the analysis comes with several caveats:

  1. We assume that investors can simultaneously generate signals and trade at month end, which may not be feasible for most.
  2. We are analyzing index data, which may be different than the realized results of index-tracking ETFs.
  3. We do not factor in trading costs such as impact, slippage, or commissions.

It is also important to point out that the per-style results vary dramatically.  For example, trend-following on the size style has been in a material drawdown since 2006.  Therefore, attempting to apply time-series momentum onto of a single style to manage style risk may only invite further strategy risk; this approach may be best applied with an ensemble of factors (and, likely, trend signals).

What this commentary has conveniently ignored, however, is that the appropriate benchmark for this approach is not zero.  Rather, a more appropriate benchmark would be the long-only active returns of the styles themselves, as our default starting point is simply holding the styles long-only.

The results, when adjusted for our default of buy-and-hold, is much less convincing.

Source: MSCI.  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.  You cannot invest in an index.

What is clear is that the strategy can now only out-perform when the style is under­-performing the benchmark.  When the portfolio invests in the style, our relative return versus the style is flat.

When a diversified trend-following portfolio is compared against a diversified long-only factor portfolio, we see the general hallmarks of a trend-following approach: value-add during periods of sustained drawdowns with decay thereafter.   Trend-following on styles, then, may be more appropriate as a hedge against prolonged style under-performance; but we should expect a cost to that hedge.

Source: MSCI.  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.  You cannot invest in an index.

For some styles, like Minimum Volatility, this appears to have helped relative performance drawdowns in periods like the dot-com bubble without too much subsequent give-up.  Size, on the other hand, also benefited during the dot-com era, but subsequently suffered from significant trend-following whipsaw.

Conclusion

Recent research has suggested that equity style premia exhibit positive autocorrelation that can be exploited by trend followers.  In this piece, we sought to explore whether this empirical evidence could be exploited by long-only investors by isolating the active returns of long-only style indices.

We found that a naïve 12-month time-series momentum strategy proved moderately effective at generating a timing strategy for switching between factor and benchmark exposure.  Per-style results were fairly dramatic, and trend-following added substantial style risk of its own.  However, diversification proved effective and an equal-weight portfolio of style trend-following strategies offered an information ratio of 0.57.

However, if we are already style proponents, a more relevant benchmark may be a long-only style portfolio.  When our trend-following returns are taken in excess of this benchmark, results deflate dramatically, as the trend-following strategy can now only exploit periods when the style under-performs a market-capitalization-weighted index.  Thus, for investors who already implement long-only styles in their portfolio, a trend-following overlay may serve to hedge periods of prolonged style drawdowns but will likely come with whipsaw cost which may drag down realized factor results.

 

 

Es-CAPE Velocity: Value-Driven Sector Rotation

By

On August 26, 2019

In Portfolio Construction, Risk & Style Premia, Value, Weekly Commentary

This post is available as a PDF download here.

Summary­

  • Systematic value strategies have struggled in the post-2008 environment, so one that has performed well catches our eye.
  • The Barclays Shiller CAPE sector rotation strategy – a value-based sector rotation strategy – has out-performed the S&P 500 by 267 basis points annualized since it launched in 2012.
  • The strategy applies a unique Relative CAPE metric to account for structural differences in sector valuations as well as a momentum filter that seeks to avoid “value traps.”
  • In an effort to derive the source of out-performance, we explore various other valuation metrics and model specifications.
  • We find that what has actually driven performance in the past may have little to do with value at all.

It is no secret that systematic value investing of all sorts has struggled as of late.  With the curious exception, that is, of the Barclays Shiller CAPE sector rotation strategy, a strategy explored by Bunn, Staal, Zhuang, Lazanas, Ural and Shiller in their 2014 paper Es-cape-ing from Overvalued Sectors: Sector Selection Based on the Cyclically Adjusted Price-Earnings (CAPE) Ratio.  Initial performance suggests that the idea has performed quite well out-of-sample, which stands out among many “smart-beta” strategies which have failed to live up to their backtests.

Source: CSI Data.  Calculations by Newfound Research.  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.  

Why is this strategy finding success where other value strategies have not?  That is what we aim to explore in this commentary.

On a monthly basis, the Shiller CAPE sector rotation portfolio is rebalanced into an equal-weight allocation across four of the ten primary GICS sectors.  The four are selected first by ranking the 10 primary sectors based upon their Relative CAPE ratios and choosing the cheapest five sectors.  Of those cheapest five sectors, the sector with the worst trailing 12-month return (“momentum”) is removed.

The CAPE ratio – standing for Cyclically-Adjusted Price-to-Earnings ratio – is the current price divided by the 10-year moving average of inflation-adjusted earnings.  The purpose of this smoothing is to reduce the impact of business cycle fluctuations.

The potential problem with using the raw CAPE value for each sector is that certain sectors have structurally higher and lower CAPE ratios than their peers.  High growth sectors – e.g. Technology – tend to have higher CAPE ratios because they reinvest a substantial portion of their earnings while more stable sectors – e.g. Utilities – tend to have much lower CAPE ratios.  Were we to simply sort sectors based upon their current CAPE ratio, we would tend to create structural over- and under-weights towards certain sectors.

To adjust for this structural difference, the strategy uses the idea of a Relative CAPE ratio, which is calculated by taking the current CAPE ratio and dividing it by a rolling 20-year average CAPE ratio1 for that sector.  The thesis behind this step is that dividing by a long-term mean normalizes the sectors and allows for better comparison.  Relative CAPE values above 1 mean that the sector is more expensive than it has historically been, while values less than 1 mean it is cheaper.

It is important to note here that the actual selection is still performed on a cross-sector basis.  It is entirely possible that all the sectors appear cheap or expensive on a historical basis at the same time.  The portfolio will simply pick the cheapest sectors available.

Poking and Prodding the Parameters

With an understanding of the rules, our first step is to poke and prod a bit to figure out what is really driving the strategy.

We begin by first exploring the impact of using the Relative CAPE ratio versus just the CAPE ratio.

For each of these ratios, we’ll plot two strategies.  The first is a naïve Value strategy, which will equally-weight the four cheapest sectors.  The second is the Shiller strategy, which chooses the top five cheapest sectors and drops the one with the worst momentum.  This should provide a baseline for comparing the impact of the momentum filter.

Strategy returns are plotted relative to the S&P 500.

Source: Siblis Research; Morningstar; CS Data.  Calculations by Newfound Research.  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.  

For the Relative CAPE ratio, we also vary the lookback period for calculating the rolling average CAPE from 5- to 20-years.

Source: Siblis Research; Morningstar; CSI Data.  Calculations by Newfound Research.  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 few things immediately stand out:

  • Interestingly, standard CAPE actually appears to perform better than Relative CAPE for both the traditional value and Shiller implementations.
  • The Relative CAPE approach fared much more poorly from 2004-2007 than the simple CAPE approach.
  • There is little difference in performance for the Value and Shiller strategy for standard CAPE, but a meaningful difference for Relative CAPE.
  • While standard CAPE value has stagnant relative performance since 2007, Relative CAPE appears to continue to work for the Shiller approach.
  • A naïve value implementation seems to perform quite poorly for Relative CAPE, while the Shiller strategy appears to perform rather well.
  • There is meaningful performance dispersion based upon the lookback period, with longer-dated lookbacks (darker shades) appearing to perform better than shorter-period lookbacks (lighter shades) for the Relative CAPE variation.

The second-to-last point is particularly curious, as it implies that using momentum to “avoid the value trap” creates significant value (no pun intended; okay, pun intended) for the strategy.

Varying the Value Metric (in Vain)

To gain more insight, we next test the impact of the choice of the CAPE ratio. Below we plot the relative returns of different Shiller-based strategies (again varying lookbacks from 5- to 20-years), but use price-to-book, trailing 12-month price-to-earnings, and trailing 12-month EV/EBITDA as our value metrics.

A few things stand out:

  • Value-based sector rotation seems to have “worked” from 2000 to 2009, regardless of our metric of choice.
  • Almost all value-based strategies appear to exhibit significant relative out-performance during the dot-com and 2008 recessions.
  • After 2009, most value strategies appear to exhibit random relative performance versus the S&P 500.
  • All three approaches appear to suffer since 2016.

Source: Siblis Research; Morningstar; CSI Data.  Calculations by Newfound Research.  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.  

At this point, we have to ask: is there something special about the Relative CAPE that makes it inherently superior to other metrics?

A Big Bubble-Based Bet?

If we take a step back for a moment, it is worth asking ourselves a simple question: what would it take for a sector rotation strategy to out-perform the S&P 500 over the last decade?

With the benefit of hindsight, we know Consumer Discretionary and Technology have led the pack, while traditionally stodgy sectors like Consumer Staples and Utilities have lagged behind (though not nearly as poorly as Energy).

As we mentioned earlier, a naïve rank on the CAPE ratio would almost certainly prefer Utilities and Staples over Technology and Discretionary.  Thus, for us to outperform the market, we must somehow construct a value metric that identifies the two most chronically expensive sectors (ignoring back-dated valuations for the new Communication Services sector) as being among the cheapest.

This is where dividing by the rolling 20-year average comes into play.  In spirit, it makes a certain degree of sense. In practice, however, this plays out perfectly for Technology, which went through such an enormous bubble in the late 1990s that the 20-year average was meaningfully skewed upward by an outlier event.  Thus, for almost the entire 20-year period after the dot-com bubble, Technology appears to be relatively cheap by comparison.  After all, you can buy for 30x earnings today what you used to be able to buy for 180x!

The result is a significant – and near-permanent tilt – towards Technology since the beginning of 2012, which can be seen in the graph of strategy weights below.

One way to explore the impact of this choice is calculate the weight differences between a top-4 CAPE strategy and a top-4 Relative CAPE strategy, which we also plot below.  We can see that after early 2012, the Relative CAPE strategy is structurally overweight Technology and underweight Financials and Utilities.  Prior to 2008, we can see that it is structurally underweight Energy and overweight Consumer Staples.

If we take these weights and use them to construct a return stream, we can isolate the return impact the choice of using Relative CAPE versus CAPE has.  Interestingly, the long Technology / short Financials & Utilities trade did not appear to generate meaningful out-performance in the post-2012 era, suggesting that something else is responsible for post-2012 performance.

Source: Siblis Research; Morningstar; CSI Data.  Calculations by Newfound Research.  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 Miraculous Mojo of Momentum

This is where the 12-month momentum filter plays a crucial role.  Narratively, it is to avoid value traps.  Practically, it helps the strategy deftly dodge Financials in 2008, avoiding a significant melt-down in one of the S&P 500’s largest sectors.

Now, you might think that valuations alone should have allowed the strategy to avoid Technology in the dot-com fallout.  As it turns out, the Technology CAPE fell so precipitously that in using the Relative CAPE metric the Technology sector was still ranked as one of the top five cheapest sectors from 3/2001 to 11/2002.  The only way the strategy was able to avoid it?  The momentum filter.

Removing this filter makes the relative results a lot less attractive.  Below we re-plot the relative performance of a simple “top 4” Relative CAPE strategy.

Source: Siblis Research; Morningstar; CSI Data.  Calculations by Newfound Research.  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 how much impact does the momentum filter have?  We can isolate the effect by taking the weights of the Shiller strategy and subtracting the weights of the Value strategy to construct a long/short index that isolates the effect.  Below we plot the returns of this index.

It should be noted that the legs of the long/short portfolio only have a notional exposure of 25%, as that is the most the Value and Shiller strategies can deviate by.  Nevertheless, even with this relatively small weight, when isolated the filter generates an annualized return of 1.8% per year with an annualized volatility of 4.8% and a maximum drawdown of 11.6%.

Scaled to a long/short with 100% notional per leg, annualized returns jump to 6.0%. Though volatility and maximum drawdown both climb to 20.4% and 52.6% respectively.

Source: Siblis Research; Morningstar; CSI Data.  Calculations by Newfound Research.  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.  

Conclusion

Few, if any, systematic value strategies have performed well as of late.  When one does – as with the Shiller CAPE sector rotation strategy – it is worth further review.

As a brief summary of our findings:

  • Despite potential structural flaws in measuring cross-sectional sector value, CAPE outperformed Relative CAPE for a naïve rank-based value strategy.
  • There is significant dispersion in results using the Relative CAPE metric depending upon which lookback parameterization is selected.Initial tests suggest that the longer lookbacks appear to have been more effective.
  • Using valuation metrics other than CAPE – e.g. P/B, P/E (TTM), and EV/EBITDA (TTM) – do not appear as effective in recent years.
  • Longer lookbacks allow the Relative CAPE methodology to create a structural overweight to the Technology sector over the last 15 years.
  • The momentum filter plays a crucial role in avoiding the Technology sector in 2001-2002 and the Financial sector in 2008.

 

Taken all together, it is hard to not question whether these results are unintentionally datamined.  Unfortunately, we just do not have enough data to extend the tests further back in time for truly out-of-sample analysis.

What we can say, however, is that the backtested and live performance hinges almost entirely a few key trades:

  • Avoiding Technology in 2001-2002 due to the momentum filter.
  • Avoiding Financials in 2008 due to the momentum filter.
  • Avoiding a Technology underweight in recent years due to an inflated “average” historical CAPE due to the dot-com bubble.
  • Avoiding Energy in 2014-2016 due to the momentum filter.

 

Three of these four trades are driven by the momentum filter.  When we further consider that the Shiller strategy is in effect the returns of the pure value implementation – which suffered in the dot-com run-up and was a mostly random walk thereafter – and the returns of the isolated momentum filter, it becomes rather difficult to call this a value strategy at all.

As of the date of this document, neither Newfound Research nor Corey Hoffstein holds a position in the securities discussed in this article and do not have any plans to trade in such securities.  Newfound Research and Corey Hoffstein do not take a position as to whether this security should be recommended for any particular investor.  

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