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Tag: multi-factor

Diversification in Multi-Factor Portfolios

By

On March 20, 2017

In Craftsmanship, Portfolio Construction, Risk & Style Premia

This blog post is available as a PDF here.

Summary­­

  • The debate rages on over the application of valuation in factor-timing methods. Regardless, diversification remains a prudent recommendation.
  • How to diversify multi-factor portfolios, however, remains up for debate.
  • The ActiveBeta team at Goldman Sachs finds new evidence that composite diversification approaches can offer a higher information ratio than integrated approaches due to interaction effects at low-to-moderate factor concentration levels.
  • At high levels, they find that integrated approaches have higher information ratios due to high levels of idiosyncratic risks in composite approaches.
  • We return to old research and explore empirical evidence in FTSE Russell’s tilt-tilt approach to building an integrated multi-factor portfolio to determine if this multi-factor approach does deliver greater factor efficiency than a comparable composite approach.

The debate over factor timing between Cliff Asness and Rob Arnott rages on.  This week saw Cliff publish a blog post titled Factor Timing is Hard providing an overview of his recently co-authored work Contrarian Factor Timing is Deceptively Difficult.  Generally in academic research, you find a certain level of hedged decorum: authors rarely insult the quality of work, they just simply refute it with their own evidence.

This time, Cliff pulled no punches.

“In multiple online white papers, Arnott and co-authors present evidence in support of contrarian factor timing based on a plethora of mostly inapplicable, exaggerated, and poorly designed tests that also flout research norms.”

At the risk of degrading this weekly research commentary into a gossip column: Ouch.  Burn.

We’ll be providing a much deeper dive into this continued factor-timing debate (as well as our own thoughts) in next week’s commentary.

In the meantime, at least there is one thing we can all agree on – including Cliff and Rob – factor portfolios are better diversified than not.

Except, as an industry, we cannot even agree how to diversify them.

Diversifying Multi-Factor Portfolios: Composite vs. Integrated

When it comes to building multi-factor portfolios, there are two camps of thought.

The first camp believes in a two-step approach.  First, portfolios are built for each factor.  To do this, securities are often given a score for each factor, and when a factor sleeve is built, securities with higher scores receive an overweight position while those with lower scores receive an underweight.  After those portfolios are built, they are blended together to create a combined portfolio.  As an example, a value / momentum multi-factor portfolio would be built by first constructing value and momentum portfolios, and then blending these two portfolios together.  This approach is known as “mixed,” “composite,” or “portfolio blend.”

Source: Ghayur, Heaney, and Platt (2016)

The second camp uses a single-step approach.  Securities are still given a score for each factor, but those scores are blended into a single aggregate value representing the overall strength of that security.  A single portfolio is then built, guided by this blended value, overweighting securities with higher scores and underweighting securities with lower scores.  This approach is known as “integrated” or “signal blend.”

Source: Ghayur, Heaney, and Platt (2016)

To re-hash the general debate:

  • Portfolio blend advocates tend to prefer the simplicity, transparency, and control of the approach. Furthermore, there is a preponderance of evidence supporting single-factor portfolios, but research exploring the potential interaction effects of a signal blend approach is limited and therefore potentially introduces unknown risks.
  • Signal blend advocates argue that a portfolio blend approach introduces inefficiencies: that by constructing each sleeve independently, securities with canceling factor scores can be introduced and dilute overall factor exposure. The general argument goes along the line of, “we want the decathlon athlete, not a team full of individual sport athletes.”

Long-time readers of our commentary may, at this point, be groaning; how is this topic not dead yet?  After all, we’ve written about it numerous times in the past.

  • In Beware Bad Multi-Factor Portfolios we argued that the integrated approach was fundamentally flawed due to the different decay rates of factor alpha (which is equivalent to saying that factor portfolios turnover at different rates). By combining a slow-moving signal with a fast-moving signal, variance in the composite signal becomes dominated by the fast-moving signal.In retrospect, our choice of wording here was probably a bit too concrete.  We believe our point still stands that care must be taken in integrated approaches because of relative turnover speed differences in different factors, but it is not an insurmountable hurdle in construction.
  • In Multi-Factor: Mix or Integrate? we explored an AQR paper that advocated for an integrated approach. We found it ironic that this was published shortly after Cliff Asness had published an article discussing the turnover issues that make applying value-based timing difficult for factors like momentum – an argument similar to our past blog post.In this post, we continued to find evidence that integrated approaches ran the risk of being governed by high turnover factors.
  • In Is That Leverage in my Multi-Factor ETF? we explored an argument made by FTSE Russell that an integrated approach offered implicit leverage effects, allowing you to use the same dollar to access multiple factors simultaneously.This is probably the best argument we have heard for multi-factor portfolios to date.Unfortunately, empirical evidence suggested that existing integrated multi-factor ETF portfolios did not offer significantly more factor exposure than composite peers.

    It is worth noting, however, that the data we were able to explore was limited as multi-factor portfolios are largely new. We were not even able to evaluate, for example, a FTSE Russell product despite the fact it was FTSE Russell making the argument.

  • Feeling that our empirical test did not necessarily do justice to FTSE Russell’s argument, we wrote Capital Efficiency in Multi-Factor Portfolios. If we were to make an argument for our most underrated article of 2016, this would be it – but that is probably because it was filled with obtuse mathematics.The point of the piece was to try to reconcile FTSE Russell’s argument from a theoretical basis.  What we found, under some broad assumptions, was that under all cases, an integrated approach should provide at least as much, and generally much more, factor exposure than a mixed approach due to the implied leverage effect.

So, honestly, how much more can we say on this topic?

New Evidence of Interaction Effects in Multi-Factor Portfolios

Well the ActiveBeta Equity Strategies team at Goldman Sachs Asset Management published a paper late last year comparing the two approaches using Russell 1000 securities from January 1979 to June 2016.

Unlike our work, in which we compared composite and integrated portfolios built to match the percentage of stocks selected, Ghayur, Heaney, and Platt (2016) built portfolios to match factor exposure.  Whereas we matched an integrated approach that picked the top 25% of securities with a composite approach where each sleeve picked the top 25%,  Ghayur, Heaney, and Platt (2016) accounted for expected factor dilution by having the sleeves in the composite approach pick the top 12.5%.

Using this factor-exposure matching approach, their results are surprising.  Rather than a definitive answer as to which approach is superior, they find that the portfolio blend approach offers a higher information ratio at lower levels of factor exposure (i.e. lower levels of active risk), while the signal blend approach offers a higher information ratio at higher levels of factor exposure (i.e. higher levels of active risk).

How can this be the case?

The answer comes down to interaction effects.

When a portfolio is built expecting more diluted overall factor exposure – e.g. to have lower tracking error to the index – the percentage overlap between securities in the composite and integrated approaches is higher.  However, for more concentrated factor exposure, the overlap is lower.

Source: Ghayur, Heaney, and Platt (2016)

Advocates for an integrated approach have historically argued that securities found in Area 3 in the figure above would be a drag on portfolio performance.  These are the securities found in a composite approach but not an integrated approach.  The argument is that while high in one factor score, these securities are also very low in another, and including them in a portfolio only dilutes overall factor exposure via a canceling effect.

On the other hand, securities in Area 2, found only in the integrated approach, should increase factor exposure because you are getting securities with higher loadings on both factors simultaneously.

As it turns out, evidence suggests this is not the case.

In fact, for lower concentration factor portfolios, Ghayur, Heaney, and Platt (2016) find just the opposite.

Source: Ghayur, Heaney, and Platt (2016)

As it turns out, interaction effects give Area 3 positive active returns while Area 2 ends up delivering negative active returns.  To quote,

“The securities held in the portfolio blend and the signal blend can be mapped to the 4×4 quartile matrix (Table 5). The portfolio blend holds securities in the top row (Q4 value) and second-to-last column (Q4 momentum). All buckets provide positive contributions to active return. The mapping is more complicated for the signal blend but is roughly consistent with the diagram in Figure 1 (i.e., holdings will be anything to the right of the diagonal line drawn from the top left to the bottom right of the 4×4 matrix). Examining contributions to active return and risk (not reported), we find that the signal blend suffers from not holding enough of the high value/low momentum (Q4/Q1) stocks and low value/high momentum (Q1/Q4) stocks. The signal blend also incurs significant risk from holding Q3 value/Q3 momentum stocks, which have a negative active return (-0.4%). High momentum/high value (Q4/Q4) stocks earn the highest active return. These stocks offer a greater benefit to the portfolio blend as they are double-weighted.

In terms of active risk contributions, we note that low momentum/high value (Q1/Q4) stocks have a net positive exposure to value, while high momentum/low value (Q4/Q1) stocks have a net positive exposure to momentum. These two groups exhibit a high negative active return correlation and are diversifying (i.e., reduce active risk), while delivering positive active returns. As such, the assertion that avoiding securities with offsetting factor exposures improves portfolio performance is not entirely correct. If factor payoffs depict strong interaction effects, then holding such securities may actually be beneficial, and the portfolio blend benefits from investing in such securities. These contextual relationships are also present to varying degrees in other factor pairings.”

When factor concentration is higher, however, the increased degree of idiosyncratic risk found in Area 1 of the composite approach outweighs the interaction benefits found in Area 3.  This effect can be seen in the table below.  We see that Shared Securities under Portfolio Blend have an increased Active Return Contribution in comparison to the Signal Blend but also significantly higher Active Risk Contribution.  This is due to the fact that Shared Securities represent only 45% of the active weight in the High Factor Exposure example for the Signal Blend approach, but 72% of the weight in the Portfolio Blend.  The large portfolio concentration on just a few securities ultimately introduces too much idiosyncratic risk.

Source: Ghayur, Heaney, and Platt (2016)

Furthermore, while Area 3 (Securities Held Only in Portfolio Blend) remains a positive contributor to Active Return, it does not have the negative Active Risk contribution as it did in the prior, low factor concentration example.

The broad result that Ghayur, Heaney, and Platt (2016) propose is simple: for low-to-moderate levels of factor exposures, a portfolio blend exhibits higher information ratios and for higher levels of factor exposure, a signal blend approach works better.  That being said, we would be remiss if we didn’t point out that these types of conclusions are very dependent on the exact portfolio construction methodology used.  There are varying qualities of approaches to building both portfolio blend and signal blend multi-factor portfolios, which brings us back full circle to…

Re-Addressing FTSE Russell’s Tilt-Tilt Method

In our initial empirical analysis of FTSE Russell’s leverage argument, we were unable to actually test the theory on FTSE Russell’s multi-factor approach itself due to a lack of data.  In our analytical analysis, we used a standard integrated approach of averaging factor scores.  FTSE Russell takes the integrated method a step further by introducing a “tilt-tilt” approach, where instead of averaging factor signals to create an integrated signal, they use a multiplicative approach.

This multiplicative approach, however, is not run on normally distributed variables (i.e. factor z-scores) as was the case in our own analysis (and GSAM paper discussed above), but rather on uniformly distributed scores between [0, 1].

This makes things analytically gnarly (e.g. instead of working with normal and chi-squared distributions, we’re working with Irwin-Hall and product of uniform distributions).  Fortunately, we can employ a numerical approach to get an idea of what is going on.  Below we simulate scores for two factors (assumed to be independent; let’s call them A and B) for 500 stocks and then plot the distribution of resulting integrated and tilt-tilt scoring methods using those scores.

Source: Newfound Research.  Simulation-based methodology.

What we can see is that while the integrated approach looks somewhat normal (in fact, the Irwin-Hall distribution approaches normal as more uniform distributions are added; e.g. we incorporate more factors), the tilt-tilt distribution is single-tailed.

A standard next step in constructing an index would be to multiply these scores by benchmark weights and then normalize to come up with new, tilted weights.  We can get a sense for how weights are scaled by taking each distribution above and dividing it by the distribution average and then plotting scores against each other.

Source: Newfound Research.  Simulation-based methodology.

The grey dotted line provides guidance as to how the two methods differ.  If a point is above the line, it means the integrated approach has a larger tilt; points below the line indicate that the tilt-tilt method has a larger tilt.

What we can see is that for scores below average, tilt-tilt is more aggressive at reducing exposure; similarly for scores above average, tilt-tilt is more aggressive at increasing exposure.  In other words, the tilt-tilt approach works to aggressively increase the intensity of factor exposure.

Using index data for FTSE Russell factor indices, we can empirically test whether this approach actually captures the capital efficiency that integrated approaches should benefit from.  Specifically, we can compare the FTSE Russell Comprehensive Factor Index (the tilt-tilt integrated multi-factor approach) versus an equal-weight composite of FTSE Russell single-factor indices.  The FTSE Russell multi-factor approach includes value, size, momentum, quality, and low-volatility tilts, so our composite portfolio will be an equal-weight portfolio of long-only indices representing these factors.

To test for factor exposure, we regress both portfolios against long/short factors from AQR’s data library.  Data covers the period of 9/30/2001 through 1/31/2017.

We find that factor loadings for the tilt-tilt method exceed those for the equal-weight composite.

Source: FTSE Russell; AQR; calculations by Newfound Research.

We also find they do an admirable job at capturing a significant share of factor exposure available that would be available in long-only single-factor indices.  In other words, if instead of taking a composite approach – which we expect to be diluted – we decide to only purchase a long-only momentum portfolio, how much of that long-only momentum exposure can be re-captured by using this tilt-tilt integrated, multi-factor approach?

We find that for most factors, it is a significant proportion.

Source: FTSE Russell; AQR; calculations by Newfound Research.

(Note: The Bet-Against-Beta factor (“BAB”) is removed from this chart because the amount of the factor available in the FTSE Russell Volatility Factor Index was deemed to be insignificant, and so resulting relative proportions exceed 18x).

Conclusion

While the jury is still out on factor timing itself, diversifying across factors is broadly considered to be a prudent decision. How to implement that diversification remains in debate.

What makes the diversification concept in multi-factor investing unique, as compared to standard asset class diversification, is that through an integrated approach, implicit leverage can be accessed.  The same dollar can be used to introduce multiple factor exposures simultaneously.

While this implicit leverage should lead to portfolios that empirically have more factor exposure, evidence suggests that is not always the case.  A new paper by the ActiveBeta team at Goldman Sachs suggests that for low-to-moderate levels of factor exposure, a composite approach may be just as, if not more, effective as an integrated approach.  More surprisingly is that this effectiveness comes from beneficial interaction effects exactly in the area of the portfolio that integrated advocates have claimed there to be a drag.

At higher concentration levels of factor exposure, however, the integrated approach is more efficient, as the composite approach appears to introduce too much idiosyncratic risk.

We bring the conversation full circle in this piece by going back to some original research we detailed last fall, testing FTSE Russell’s unique tilt-tilt methodology to integrated mutli-factor investing.  In theory, the tilt-tilt method should increase the intensity of factor exposure compared to traditional integrated approaches.  While we previously found little empirical evidence supporting the capital efficiency argument for integrated multi-factor ETFs versus composite peers, a test of FTSE Russell index data finds that the tilt-tilt method may provide a significant boost to factor exposure.

Capital Efficiency in Multi-factor Portfolios

By

On October 17, 2016

In Portfolio Construction, Risk & Style Premia, Weekly Commentary

This blog post is available as a PDF here.

Summary­­

  • The debate for the best way to build a multi-factor portfolio – mixed or integrated – rages on.
  • Last week we explored whether the argument held that integrated portfolios are more capital efficient than mixed portfolios in realized return data for several multi-factor ETFs.
  • This week we explore whether integrated portfolios are more capital efficient than mixed portfolios in theory.  We find that for some broad assumptions, they definitively are.
  • We find that for specific implementations, mixed portfolios can be more efficient, but it requires a higher degree of concentration in security selection.

This commentary is highly technical, relying on both probability theory and calculus, and requires rendering a significant number of equations.  Therefore, it is only available as a PDF download.

For those less inclined to read through mathematical proofs, the important takeaway is this: for some broad assumptions, integrated multi-factor portfolios are provably more capital efficient (e.g. more factor exposure for your dollar) than mixed approaches.

Is That Leverage in My Multi-Factor ETF?

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On October 10, 2016

In Portfolio Construction, Risk & Style Premia, Weekly Commentary

This blog post is available as a PDF here.

Summary­­

  • The debate for the best way to build a multi-factor portfolio – mixed or integrated – rages on.
  • FTSE Russell published a video supporting their choice of an integrated approach, arguing that by using the same dollar to target multiple factors at once, their portfolio makes more efficient use of capital than a mixed approach.
  • We decompose the returns of several mixed and integrated multi-factor portfolios and find that integrated portfolios do not necessarily create more capital efficient allocations to factor exposures than their mixed peers.

 

A colleague sent us a video this week from FTSE Russell, titled Factor Indexing: Avoiding exposure to nothing.

In the video, FTSE Russell outlines their argument for why they prefer an integrated – or composite – multi-factor index construction methodology over a mixed one.

As a reminder, a mixed approach is one in which a portfolio is built for each factor individually, and those portfolios are combined as sleeves to create a multi-factor portfolio.  An integrated approach is one in which securities are selected that have high scores across multiple factors, simultaneously.

The primary argument held forth by integration advocates is that in a mixed approach, securities selected for one factor may have negative loadings on another, effectively diluting factor exposures.

For example, the momentum stock sleeve in a mixed approach may, unintentionally, have a negative loading on the value factor.  So, when combined with the value sleeve, it dilutes the portfolio’s overall value exposure.

This is a topic we’ve written about many, many times before, and we think the argument ignores a few key points:

FTSE Russell did, however, put forth an interesting new argument.  The argument was this: an integrated approach is more capital efficient because the same dollar can be utilized for exposure to multiple factors.

 

$1, Two Exposures

To explain what FTSE Russell means, we’ll use a very simple example.

Consider the recently launched REX Gold Hedged S&P 500 ETF (GHS) from REX Shares.  The idea behind this ETF is to provide more capital efficient exposure to gold for investors.

Previously, to include gold, most retail investors would have to explicitly carve out a slice of their portfolio and allocate to a gold fund.  So, for example, an investor who held 100% in the SPDR S&P 500 ETF (“SPY”) could carve out 5% and by the SPDR Gold Trust ETF (“GLD”).

The “problem” with this approach is that while it introduces gold, it also dilutes our equity exposure.

GHS overlays the equity exposure with gold futures, providing exposure to both.  So now instead of carving out 5% for GLD, an investor can carve out 5% for GHS.  In theory, they retain their 100% notional exposure to the S&P 500, but get an additional 5% exposure to gold (well, gold futures, at least).

So does it work?

One way to check is by trying to regress the returns of GHS onto the returns of SPY and GLD.  In effect, this tries to find the portfolio of SPY and GLD that best explains the returns of GHS.

ghs-factors

Source: Yahoo! Finance.  Calculations by Newfound Research.

 

What we see is that the portfolio that best describes the returns of GHS is 0.75 units of SPY and 0.88 units of GLD.

So not necessarily the perfect 1:1 we were hoping for, but a single dollar invested in GHS is like having a $1.63 portfolio in SPY and GLD.

Note: This is the same math that goes into currency-hedged equity portfolios, which is why we do not generally advocate using them unless you have a view on the currency.  For example, $1 invested in a currency-hedged European equity ETF is effectively the same as having $1 invested in un-hedged European equities and shorting $1 notional exposure in EURUSD.  You’re effectively layering a second, highly volatile, bet on top of your existing equity exposure.

This is the argument that FTSE Russell is making for an integrated approach.  By looking for stocks that have simultaneously strong exposure to multiple factors at once, the same dollar can tap into multiple excess return streams.  Furthermore, theoretically, the more factors included in a mixed portfolio, the less capital efficient it becomes.

Does it hold true, though?

 

The Capital Efficiency of Mixed and Integrated Multi-Factor Approaches 

Fortunately, there is a reasonably easy way to test the veracity of this claim: run the same regression we did on GHS, but on multi-factor ETFs using a variety of explanatory factor indices.

Here is a quick outline of the Factors we will utilize:

FactorSourceDescription
Market – RFRFama/FrenchTotal U.S. stock market return, minus t-bills
HML DevilAQRValue premium
SMBFama/FrenchSmall-cap premium
UMDAQRMomentum premium
QMJAQRQuality premium
BABAQRAnti-beta premium
LV-HBNewfoundLow-volatility premium

Note: Academics and practitioners have yet to settle on whether there is an anti-beta premium (where stocks with low betas outperform those with high betas) or a low-volatility premium (where stocks with low volatilities outperform those with high volatilities).   While similar, these are different factors.  However, as far as we are aware, there are no reported long-short low-volatility factors that are publicly available.  We did our best to construct one using a portfolio that is long one share of SPLV and short one share of SPHB, rebalanced monthly.

We will test a number of mixed-approach ETFs and a number of integrated-approach ETFs as well.

Of those in the mixed group, we will use Global X’s Scientific Beta U.S. ETF (“SCIU”) and Goldman Sachs’ ActiveBeta US Equity ETF (“GSLC”).

In the integrated group, we will use John Hancock’s Multifactor Large Cap ETF (“JHML”), JPMorgan’s Diversified Return US Equity ETF (“JPUS”), iShares’ Edge MSCI Multifactor USA ETF (“LRGF”), and FlexShares’ Morningstar U.S. Market Factor Tilt ETF (“TILT”).

We’ll also show the factor loadings for the SPDR S&P 500 ETF (“SPY”).

If the argument from FTSE Russell holds true, we would expect to see that the factor loadings for the mixed approach portfolios should be significantly lower than the integrated approach portfolios.  Since SCIU and GSLC both target to have four unique factors under the hood, and NFFPI has five, we would expect their loadings to be 1/5th to 1/4th of those found on the integrated approaches.

The results:

factor-loadings-multi-factor

Source: AQR, Kenneth French Data Library, and Yahoo! Finance.  Calculations by Newfound Research.

 

Before we dig into these, it is worth pointing out two things:

  • Factor loadings should be thought of both on an absolute, as well as a relative basis. For example, while GSLC has almost no loading on the size premium (SMB), the S&P 500 has a negative loading on that factor.  So compared to the large-cap benchmark, GSLC has a significantly higher
  • Not all of these loadings are statistically significant at a 95% level.

So do integrated approaches actually create more internal leverage?  Let’s look at the total notional factor exposure for each ETF:

total-notional-multi-factor

Source: AQR, Kenneth French Data Library, and Yahoo! Finance.  Calculations by Newfound Research.

 

It does, indeed, look like the integrated approaches have more absolute notional factor exposure.  Only SCIU appears to keep up – and it was the mixed ETF that had the most statistically non-significant loadings!

But, digging deeper, we see that not all factor exposure is good factor exposure.  For example, JPUS has significantly negative loadings on UMD and QMJ, which we would expect to be a performance drag.

Looking at the sum of factor exposures, we get a different picture.

total-factor-exposure

Source: AQR, Kenneth French Data Library, and Yahoo! Finance.  Calculations by Newfound Research.

 

Suddenly the picture is not so clear.  Only TILT seems to be the runaway winner, and that may be because it holds a simpler multi-factor mandate of only small-cap and value tilts.

 

Conclusion

The theory behind the FTSE Russell argument behind preferring an integrated multi-factor approach makes sense: by trying to target multiple factors with the same stock, we can theoretically create implicit leverage with our money.

Unfortunately, this theory did not hold out in the numbers.

Why?  We believe there are two potential reasons.

  • First, selecting for a factor in a mixed approach does not mean avoiding other factors. For example, while unintentional, a sleeve selecting for value could contain a small-cap bias or a quality bias.
  • In an integrated approach, preferring securities with high loadings on multiple factors simultaneously may avoid securities with extremely high factor loadings on a single factor. This may create a dilutive effect that offsets the benefit of capital efficiency.

In addition, we have concerns as to whether the integrated approach may degrade some of the very significant diversification benefits that can be harvested by combining factors.

Ultimately, while an interesting theoretical argument, we do not believe that capital efficiency is a justified reason for preferring the opaque complexity of an integrated approach over the simplicity of a mixed one.

 

Client Talking Points

  • At the cutting edge of investment research, there is often disagreement on the best way to build portfolios.
  • While a strongly grounded theoretical argument is necessary, it does not suffice: results must also be evident in empirical data.
  • To date, the argument that an integrated approach of building a multi-factor portfolio is more capital efficient than the simpler mixed approach does not prove out in the data.

Multi-Factor: Mix or Integrate?

By

On July 11, 2016

In Portfolio Construction, Risk & Style Premia, Weekly Commentary

This blog post is available as a PDF here.

Summary

  • Recently a paper was published by AQR where the authors advocate for an integrated approach to multi-factor portfolios, preferring securities that exhibit strong characteristics across all desired factors instead of a mixed approach, where securities are selected based upon extreme exposure to a single characteristic.
  • We believe the integrated approach fails to acknowledge the impact of the varying lengths over which different factors mature, ultimately leading to a portfolio more heavily influenced by higher turnover factors.

The Importance of Factor Maturity
Cliff Asness, founder of AQR, recently published a paper titled My Factor Philippic.  This paper was written in response to the recently popularized article How Can “Smart Beta” Go Horribly Wrong? which was co-authored by Robert Arnott, co-founder of Research Affiliates.

Arnott argues that many popular factors are currently historically overvalued and, furthermore, that the historical excess return offered by some recently popularized factors can be entirely explained by rising valuation trends in the last 30 years.
Caveat emptor, warns Arnott: valuations always matter.

Much to our delight (after all, who doesn’t like to see two titans of industry go at it?), Asness disagrees.

One of the primary arguments laid out by Asness is that valuation is a meaningless predictor for factors with high turnover.

The intuition behind this argument is simple: while valuations may be a decent predictor of forward annualized returns for broad markets over the next 5-to-10 years, the approach only works because the basket of securities stays mostly constant.  For example, valuations for U.S. equities may be a good predictor because we expect the vast majority of the basket of U.S. equities to stay constant over the next 5-to-10 years.

The same is not true for many factors.  For example, let’s consider a high turnover factor like momentum.

Valuations of a momentum basket today are a poor predictor of annualized returns of a momentum strategy over the next 5-to-10 years because the basket of securities held could be 100% different three months from now.

Unless the same securities are held in the basket, valuation headwinds or tailwinds will not necessarily be realized.

For the same reason, valuation is also poor as an explanatory variable of factor returns.  Asness argues that Arnott’s warning of valuation being the secret driver of factor returns is unwarranted in high turnover factors.

Multi-Factor: Mix or Integrate?
On July 2nd, Fitzgibbons, Friedman, Pomorski, and Serban (FFPS) – again from AQR – published a paper titled Long-Only Style Investing: Don’t Just Mix, Integrate.  

The paper attempts to conclude the current debate about the best way to build multi-factor portfolios.  The first approach is to mix, where a portfolio is built by combining stand-alone factor portfolios.  The second approach is to integrate, where a portfolio is built by selecting securities that have simultaneously strong exposure to multiple factors at once.

A figure from the paper does a good job of illustrating the difference.  Below, a hypothetical set of stocks is plotted based upon their current valuation and momentum characteristics.

AQR Paper Scatter Plots

In the top left, a portfolio of deep value stocks is selected.  In the top right, the mix approach is demonstrated, where the deepest value and the highest momentum stocks are selected.

In the bottom left, the integrated approach is demonstrated, where the securities simultaneously exhibiting strong valuation and momentum characteristics are selected.

Finally, in the bottom right we can see how these two approaches differ: with yellow securities being those only found in the mix portfolio and blue securities being found only in the integrated portfolio.

It is worth noting that the ETF industry has yet to make up its mind on the right approach.

GlobalX and Goldman Sachs prefer the mix approach in their ETFs (SCIU / GSLC) while JPMorgan and iShares prefer the integrate approach (JPUS / LRGF).

The argument made by those taking the integrated approach is that they are looking for securities with well-rounded exposures rather than those with extreme singular exposures.  Integrators argue that this approach helps them avoid holding securities that might cancel each other out.  If we look back towards the mix example above (top right), we can see that many securities selected due to strength in one factor are actually quite poor in the other.

Integrators claim that this inefficiency can create a drag in the mix portfolio.  Why hold something with strong momentum if it has a very poor valuation score that is only going to offset it?

We find it somewhat ironic that FFPS and Asness both publish for AQR, because we would argue that Asness’s argument points out the fundamental flaw in the theory outlined by integrators.  Namely: the horizons over which the premia mature differ.

Therefore, a strong positive loading in a factor like momentum is not necessarily offset by a strong negative loading in a factor like value.  Furthermore, by integrating we run the risk of the highest turnover factor actually dominating the integrated selection process.

Data
In the rest of this commentary, we will be using industry data from the Kenneth French data library.  For momentum scores, we calculate 12 one-month total return and calculate cross-sector z-scores[1].  For valuation scores, we calculate a normalized 5-year dividend yield score and then calculate cross-sector z-scores.[2]

Do Factor Premia Actually Mature at Different Time Periods?
In his paper, Asness referenced the turnover of a factor portfolio as an important variable.  We prefer to think of high turnover factors as factors whose premium matures more quickly.

For example, if we buy a stock because it has high relative momentum, our expectation is that we will likely hold it for longer than a day, but likely much shorter than a year.  Therefore, a strategy built off relative momentum will likely have high turnover because the premium matures quickly.

On the other hand, if we buy a value stock, our expectation is that we will have to hold it for up to several years for valuations to adequately reverse.  This means that the value premium takes longer to mature – and the strategy will likely have lower turnover.

We can see this difference in action by looking at how valuation and momentum scores change over time.

Z-Score Changes NoDur

We see similar pictures for other industries.  Yet, looks can be deceiving and the human brain is excellent at finding patterns where there are none (especially when we want to see those patterns).  Can we actually quantify this difference?

One way is to try to build a model that incorporates both the randomness of movement and how fast these scores mean-revert.  Fitting our data to this model would tell us about how quickly each premium matures.

One such model is called an Ornstein-Uhlenbeck process (“OU process”).  An OU process follows the following stochastic differential equation:

OU Process

To translate this into English using an example: the change in value z-score from one period to the next can be estimated as a “magnetism” back to fair value plus some randomness.  In the equation, theta tells us how strong this magnetism is, mu tells us what fair value is, and sigma tells us how much influence the randomness has.

For our momentum and valuation z-scores, we would expect mu to be near-zero, as over the long-run we would not expect a given sector to exhibit significantly more or less relative momentum or relative cheapness/richness than peer sectors.

Given that we also believe that the momentum premium is realized over a shorter horizon, we would also expect that theta – the strength of the magnetism, also called the speed of mean reversion – will be higher.  Since that strength of magnetism is higher, we will also need sigma – the influence of randomness – to be larger to overcome it.

So how to the numbers play out?[3]

For the momentum z-scores:

ThetaMuSigma
NoDur0.970.021.00
Durbl1.000.031.63
Manuf1.22-0.030.96
Enrgy0.980.061.69
HiTec1.040.031.49
Telcm1.15-0.071.52
Shops1.220.031.24
Hlth0.840.111.39
Utils1.48-0.091.61
Other1.18-0.091.13
Average1.100.001.36

For the valuation z-scores:

ThetaMuSigma
NoDur0.11-0.200.34
Durbl0.080.580.49
Manuf0.130.010.37
Enrgy0.070.190.40
HiTec0.090.230.33
Telcm0.070.030.38
Shops0.11-0.150.36
Hlth0.05-0.470.36
Utils0.06-0.350.40
Other0.11-0.010.37
Average0.08-0.010.38

We can see results that echo our expectations: the speed of mean-reversion is significantly lower for value than momentum.  In fact, the average theta is less than 1/10th.

The math behind an OU-process also lets us calculate the half-life of the mean-reversion, allowing us to translate the speed of mean reversion to a more interpretable measure: time.

The half-life for momentum z-scores is 0.27 years, or about 3.28 months.  The half-life for valuation z-scores is 3.76 years, or about 45 months.  These values more or less line up with our intuition about turnover in momentum versus value portfolios: we expect to hold momentum stocks for a few months but value stocks for a few years.

Another way to analyze this data is by looking at how long the relative ranking of a given industry group stays consistent in its valuation or momentum metric.  Based upon our data, we find that valuation ranks stayed constant for an average of approximately 120 trading days, while the average length of time an industry group held a consistent momentum rank was only just over 50 days.

Maturity’s Influence on Integration
The scatter plots drawn by FFPS are deceiving because they only show a single point in time.  What they fail to show is how the locations of the dots change over time.

With the expectation that momentum scores will change more rapidly than valuation scores, we would expect to see points move more rapidly up and down along the Y-axis than we would see them move left and right along the X-axis.
Given this, our hypothesis is that changes in our inclusion score are driven more significantly by changes in our momentum score.

To explore this, we create an integration score, which is simply the sum of the valuation and momentum z-scores.  Those industries in the top 30% of integration scores at any time are held by the integrated portfolio.

To distill the overall impact of momentum score changes versus valuation score changes, we need to examine the absolute value of these changes.  For example, if the momentum score change was +0.5 and the valuation score change was -0.5, the overall integration score change is 0.  Both momentum and value, in this case, contributed equally (or, contributed 50% each), to the overall score change.

So a simple formula for measuring the relative percentage contribution to score change is:

Contribution Formula

If value and momentum score changes contributed equally, we would expect the average contribution to equal 50%.

The average contribution based upon our analysis is 72.18% (with a standard error of 0.24%).  The interquartile range is 59.02% to 91.19% and the median value is 79.47%.

Put simply: momentum score changes are a much more significant contributor to integration score changes than valuation score changes are.

We find that this effect is increased when we examine only periods when an industry is added or deleted from the integrated portfolio.  In these periods, the average contribution climbs to 78.46% (with a standard error of 0.69%), with an interquartile range of 70.28% to 94.46% and a median value of 85.57%.

Changes in the momentum score contribute much more significantly than value score changes.

Integration: More Screen than Tilt?
The objective of the integrated portfolio approach is to find securities with the best blend of characteristics.

In reality, because one set of characteristics changes much more slowly, certain securities can be sidelined for prolonged periods of time.

Let’s consider a simplified example.  Every year, the 10 industry groups are assigned a random, but unique, value score between 1 and 10.

Similarly, every month, the 10 industry groups are assigned a random, but unique, momentum score between 1 and 10.

The integration score for each industry group is calculated as the sum of these two scores.  Each month, the top 3 scoring industry groups are held in the integrated portfolio.

What is the probability of an industry group being in the integrated portfolio, in any given month, if it has a value score of 1?  What about 2?  What about 10?
Numerical simulation gives us the following probabilities:

Probability of Inclusion Monthly

So if these are the probabilities of an industry group being selected in a given month given a certain value score, what is the probability of an industry group not being selected into the integrated portfolio at all during the year it has a given value score?

Probability of Inclusion Annual

If an industry group starts the year with a value score of 1, there is 99.1% probability it will never being selected into the integrated portfolio all year.

Conclusion
While we believe this topic deserves a significantly deeper dive (one which we plan to perform over the coming months), we believe the cursory analysis highlights a very important point: an integrated approach runs a significant risk of being more heavily influenced by higher turnover factors.  While FFPS believe there are first order benefits to the integrated approach, we think the jury is still out and that those first order effects may actually be simply due to an increased exposure to higher turnover factors.  Until more a more substantial understanding of the integrated approach is established, we continue to believe that a mixed approach is prudent.  After all, if we don’t understand how a portfolio is built and the source of the returns it generates, how can we expect to manage risk?

[1] Z-scoring standardizes, on a relative basis, what would otherwise be arbitrary values.
[2] We use yield versus historical as our measure for valuation as a matter of convenience.  However, there are two theoretical arguments justifying this choice.  First, the most common measure of value is book-to-market (B/M), which assumes that fair valuation of a company is its book value.  Another such model is the dividend discount model.  If we assume a constant growth rate of dividends and a constant cost of capital for the company, then book value should be proportional to total dividends, or, equivalently, book-to-market proportional to dividend yield.  Similarly, if you assume a constant long-term payout ratio, dividends per share are proportional to earnings per share, which makes yield inversely proportional to price-to-earnings, a popular valuation ratio.
[3] We used maximum likelihood estimation to calculate these figures.

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