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:

- By selecting stocks that score well on multiple factors simultaneously, stocks that do extremely well on a single factor, but not well on others, will be left out. This leads to a pool of securities that are
*jacks of all trades, but masters of none*: a pool that already has diluted factor scores. - Factors premiums have different maturity lengths (or, put another way, factor portfolios turnover at different rates). How frequently an integrated portfolio is rebalanced will dictate which factors have the largest impact on portfolio construction. As we’ve written about before, we believe this is the fundamental argument behind the Cliff Asness / Rob Arnott debate on factor timing.

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.

*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:

Factor | Source | Description |

Market – RFR | Fama/French | Total U.S. stock market return, minus t-bills |

HML Devil | AQR | Value premium |

SMB | Fama/French | Small-cap premium |

UMD | AQR | Momentum premium |

QMJ | AQR | Quality premium |

BAB | AQR | Anti-beta premium |

LV-HB | Newfound | Low-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 1/5^{th} to 1/4^{th} of those found on the integrated approaches.

The results:

*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:

*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.

*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.

## Capital Efficiency in Multi-factor Portfolios

By Corey Hoffstein

On October 17, 2016

In Portfolio Construction, Risk & Style Premia, Weekly Commentary

This blog post is available as a PDF here.Summarycapital efficientthan mixed portfolios in realized return data for several multi-factor ETFs.in theory. We find that for some broad assumptions, they definitively are.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.