*This post is available as PDF download here.*

# Summary

- New research from Axioma suggests that tilting less – through lower target tracking error – can actually create more academically pure factor implementation in long-only portfolios.
- This research highlights an important question: how should long-only investors think about factor exposure in their portfolios?Is measuring against an academically-constructed long/short portfolio really appropriate?
- We return to the question of style versus specification, plotting year-to-date excess returns for long-only factor ETFs.While the general style serves as an anchor, we find significant specification-driven performance dispersion.
- We believe that the “right answer” to this dispersion problem largely depends upon the investor.

When quants speak about factor and style returns, we often do so with some sweeping generalizations. Typically, we’re talking about some long/short specification, but precisely how that portfolio is formed can vary.

For example, one firm might look at deciles while another looks at quartiles. One shop might equal-weight the holdings while another value-weights them. Some might include mid- and small-caps, while others may work on a more realistic liquidity-screened universe.

More often than not, the precision does not matter a great deal (with the exception of liquidity-screening) because the general conclusion is the same.

But for investors who are actually realizing these returns, the precision matters quite a bit. This is particularly true for long-only investors, who have adopted smart-beta ETFs to tap into the factor research.

As we have discussed in the past, any active portfolio can be decomposed into its benchmark plus a dollar-neutral long/short portfolio that encapsulates the active bets. The active bets, then, can actually approach the true long/short implementation.

To a point, at least. The “shorts” will ultimately be constrained by the amount the portfolio can under-weight a given security.

For long-only portfolios, increasing active share often means having to lean more heavily into the highest quintile or decile holdings. This is not a problem in an idealized world where factor scores have a monotonically increasing relationship with excess returns. In this perfect world, increasing our allocation to high-ranking stocks creates just as much excess return as shorting low-ranking stocks does.

Unfortunately, we do not live in a perfect world and for some factors the premium found in long/short portfolios is mostly found on the short side.^{1} For example, consider the Profitability Factor. The annualized spread between the top- and bottom-quintile portfolios is 410 basis points. The difference between the top quintile portfolio and the market, though, is just 154 basis points. Nothing to scoff at, but when appropriately discounted for data-mining risk, transaction costs, and management costs, there is not necessarily a whole lot left over.

Which leads to some interesting results for portfolio construction, at least according to a recent study by Axioma.^{2} For factors where the majority of the premium arises from the short side, tilting *less *might mean achieving more.

For example, Axioma found that a portfolio optimized maximize exposure to the profitability factor while targeting a tracking error to the market of just 10 basis points had a meaningfully higher correlation than the excess returns of a long-only portfolio that simply bought the top quintile. In fact, the excess returns of the top quintile portfolio had *zero correlation *to the long/short factor returns. Let’s repeat that: the active returns of the top quintile portfolio had zero correlation to the returns of the profitability factor. Makes us sort of wonder what we’re actually buying…

*Source: Kenneth French Data Library; Calculations by Newfound Research.*

* *

**Cumulative Active Returns of Long-Only Portfolios**

So, what does it actually mean for long-only investors when we plot long/short equity factor returns? When we see that the Betting-Against-Beta (“BAB”) factor is up 3% on the year, what does that imply for our low-volatility factor ETF? Momentum (“UMD”) was down nearly 10% earlier this year; were long-only momentum ETFs really under-performing by that much?

And what does this all mean for the results in those fancy factor decomposition reports the nice consultants from the big asset management firms have been running for me over the last couple of years?

*Source: AQR. Calculations by Newfound Research.*

We find ourselves back to a theme we’ve circled many times over the last few years: *style versus specification*. Choices such as how characteristics are measured, portfolio concentration, the existence or absence of position- and industry/sector-level constraints, weighting methodology, and rebalance frequency (and even date!) can have a profound impact on realized results. The little details compound to matter quite a bit.

To highlight this disparity, below we have plotted the excess return of an equally-weighted portfolio of long-only style ETFs versus the S&P 500 as well as a standard deviation cone for individual style ETF performance.

While most of the ETFs are ultimately anchored to their style, we can see that short-term performance can meaningfully deviate.

*Source: CSI Analytics. Calculations by Newfound Research. Results are hypothetical. Results assume the reinvestment of all distributions. Results are gross of all fees, including, but not limited to, manager fees, transaction costs, and taxes, with the exception of underlying ETF expense ratios. Past performance is not an indicator of future results. Year-to-Date returns are computed by assuming an equal-weight allocation to representative long-only ETFs for each style. Returns are net of underlying ETF expense ratios. Returns are calculated in excess of the SPDR&P 500 ETF (“SPY”). The ETFs used for each style are (in alphabetical order): Value: FVAL, IWD, JVAL, OVLU, QVAL, RPV, VLU, VLUE; Size: IJR, IWM, OSIZ; Momentum: FDMO, JMOM, MMTM, MTUM, OMOM, QMOM, SPMO; Low Volatility: FDLO, JMIN, LGLV, OVOL, SPLV, SPMV, USLB, USMV; Quality; FQAL, JQUA, OQAL, QUAL, SPHQ; Yield: DVY, FDVV, JDIV, OYLD, SYLD, VYM; Growth: CACG, IWF, QGRO, RPG, SCHG, SPGP, SPYG; Trend: BEMO, FVC, LFEQ, PTLC. Newfound may hold positions in any of the above securities.*

**Conclusion**

In our opinion, the research and data outlined in this commentary suggests a few potential courses of action for investors.

- For certain styles, we might consider embracing smaller tilts for purer factor exposure.
- To avoid specification risk, we might embrace the potential benefits of multi-manager diversification.
- Or, if there is a particular approach we prefer, simply acknowledge that it may not behave anything like the academic long/short definition – or even other long-only implementations – in the short-term.

Academically, we might be able to argue for one approach over another. Practically, the appropriate solution is whatever is most suitable for the investor and the approach that they will be able to stick with.

If a client measures their active returns with respect to academic factors, then understanding how portfolio construction choices deviate from the factor definitions will be critical.

An advisor trying to access a style but not wanting to risk choosing the wrong ETF might consider asking themselves, “why choose?” Buying a basket of a few ETFs will do wonders to reduce specification risk.

On the other hand, if an investor is simply trying to maximize their compound annualized return and nothing else, then a concentrated approach may very well be warranted.

Whatever the approach taken, it is important to remember that results between two strategies that claim to implement the same style can and will deviate significantly, especially in the short run.

## Re-specifying the Fama French 3-Factor Model

By Nathan Faber

On December 16, 2019

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

This post is available as a PDF download here.## Summary

In their 1992 paper,

The Cross-Section of Expected Stock Returns, Eugene Fama and Kenneth French outlined their three-factor model to explain stock returns.While the Capital Asset Pricing Model (CAPM) only describes asset returns in relation to their exposure to the market’s excess return through the stock’s beta and identifies any return beyond that as alpha, Fama and French’s three-factor model reattributed some of that supposed alpha to exposures to a value factor (High-minus-low or HML) based on returns stratified by price-to-book ratios and a size factor (small-minus-big or SMB) based on returns stratified by market capitalization.

This gave investors a tool to judge investment strategies based on the loadings to these risk factors. A manager with a seemingly high alpha may have simply been investing in value and small-cap stocks historically.

The notion of compensated risk premia has also opened the floodgate of many additional factors from other researchers (such as momentum, quality, low beta, etc.) and even two more factors from Fama and French (investment and profitability).

A richer factor universe opens up a wide realm of possibilities for analysis and attribution. However, setting further developments aside and going back to the original three-factor model, we would be remiss if we didn’t dive a bit further into its specification.

At the highest level, we agree with treating “value” and “size” as risk factors, but there is more than one way to skin a factor.

What is “value”?

Fama and French define it using the price-to-book ratio of a stock. This seems legitimate for a broad swath of stocks, especially those that are very capital intensive – such as energy, manufacturing, and financial firms – but what about industries that have structurally lower book values and may have other potential price drivers? For example, a technology company might have significant intangible intellectual property and some utility companies might employ leverage, which decreases their book value substantially.

To determine value in these sectors, we might utilize ratios that account for sales, dividends, or earnings. But then if we analyzed these strategies using the Fama French three-factor model as it is specified, we might misjudge the loading on the value factor.

“Size” seems more straightforward. Companies with low market capitalizations are small. However, when we consider how the size factor is defined based on the value factor, there might even be some differences in SMB using different value metrics.

In this commentary, we will explore what happens when we alter the definition of value for the value factor (and hence the size factor) and see how this affects factor regressions of a sample of value ETFs along with our Systematic Value strategy.

HML Factor DefinitionsIn the standard version of the Fama French 3-factor model, HML is constructed as a self-financing long/short portfolio using a 2×3 sort on size and value. The investment universe is split in half based on market capitalization and in three parts (30%/40%/30%) based on valuation, in this base case, price-to-book ratio.

Using additional data from the Kenneth French Data Library and the same methodology, we will construct HML factors using sorts based on size and:

The common inception date for all the factors is June 1951.

The chart below shows the growth of each of the four value factor portfolios.

Source: Kenneth French Data Library. 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.Over the entire time period – and for many shorter time horizons – the standard HML factor using price-to-book does not even have the most attractive returns. Price-to-earnings and price-to-cash flow often beat it out.

On the other hand, the HML factor formed using dividend yields doesn’t look so hot.

One of the reasons behind this is that the small, low dividend yield companies performed much better than the small companies that were ranked poorly by the other value factors. We can see this effect borne out in the SMB chart for each factor, as the SMB factor for dividend yield performed the best.

(Recall that we mentioned previously how the Fama French way of defining the size factor is dependent on which value metric we use.)

Source: Kenneth French Data Library. 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.Looking at the statistical significance of each factor through its t-statistic, we can see that Price-to-Earnings and Price-to-Cash Flow yielded higher significance for the HML factor than Price-to-Book. And those two along with Dividend Yield all eclipsed the Price-to-Book construction of the SMB factor.

T-Statistics for HML and SMB Using Various Value MetricsPrice-to-BookDividend YieldPrice-to-EarningsPrice-to-Cash FlowHMLSMBAssuming that we do consider all metrics to be appropriate ways to assess the value of companies, even if possibly under different circumstances, how do different variants of the Fama French three-factor model change for each scenario with regression analysis?

The Impact on Factor RegressionsUsing a sample of U.S. value ETFs and our Systematic Value strategy, we plot the loadings for the different versions of HML. The regressions are carried out using the trailing three years of monthly data ending on October 2019.

Source: Tiingo, Kenneth French Data Library. Calculations by Newfound Research.Past performance is not an indicator of future results. Returns represent live strategy results. Returns for the Newfound Systematic Value strategy are gross of all management fees and taxes, but net of execution fees. Returns for ETFs included in study are gross of any management fees, but net of underlying ETF expense ratios. Returns assume the reinvestment of all distributions.For each different specification of HML, the differences in the loading between investments is generally directionally consistent. For instance, DVP has higher loadings than FTA for all forms of HML.

However, sometimes this is not the case.

VLUE looks more attractive than VTV based on price-to-cash flow but not dividend yield. FTA is roughly equivalent to QVAL in terms of loading when price-to-book is used for HML, but it varies wildly when other metrics are used.

The tightest range for the four models for any of the investments is 0.09 (PWV) and the widest is 0.52 (QVAL). When we factor in that these estimates each have their own uncertainty, distinguishing which investment has the better value characteristic is tough. Decisions are commonly made on much smaller differences.

We see similar dispersion in the SMB loadings for the various constructions.

Source: Tiingo, Kenneth French Data Library. Calculations by Newfound Research.Past performance is not an indicator of future results. Returns represent live strategy results. Returns for the Newfound Systematic Value strategy are gross of all management fees and taxes, but net of execution fees. Returns for ETFs included in study are gross of any management fees, but net of underlying ETF expense ratios. Returns assume the reinvestment of all distributions.Many of these values are not statistically significant from zero, so someone who has a thorough understanding of uncertainty in regression would likely not draw a strict comparison between most of these investments.

However, one implication of this is that if a metric is chosen that does ascribe significant size exposure to one of these investments, an investor may make a decision based on not wanting to bear that risk in what they desire to be a large-cap investment.

Can We Blend Our Way Out?One way we often mitigate model specification risk is by blending a number of models together into one.

By averaging all of our HML and SMB factors, respectively, we arrive at blended factors for the three-factor model.

Source: Tiingo, Kenneth French Data Library. Calculations by Newfound Research.Past performance is not an indicator of future results. Returns represent live strategy results. Returns for the Newfound Systematic Value strategy are gross of all management fees and taxes, but net of execution fees. Returns for ETFs included in study are gross of any management fees, but net of underlying ETF expense ratios. Returns assume the reinvestment of all distributions.All of the investments now have HML loadings in the top of their range of the individual model loadings, and many (FTA, PWV, RPV, SPVU, VTV, and the Systematic Value strategy) have loadings to the blended HML factor that exceed the loadings for all of the individual models.

The opposite is the case for the blended SMB factor: the loadings are in the low-end of the range of the individual model loadings.

Source: Tiingo, Kenneth French Data Library. Calculations by Newfound Research.So which is the correct method?

That’s a good question.

For some investments, it is situation-specific. If a strategy only uses price-to-earnings as its value metric, then putting it up against a three-factor model using the P/E ratio to construct the factors is appropriate for judging the efficacy of harvesting that factor.

However, if we are concerned more generally about the abstract concept of “value”, then the blended model may be the best way to go.

ConclusionIn this study, we have explored the impact of model specification for the value and size factor in the Fama French three-factor model.

We empirically tested this impact by designing a variety of HML and SMB factors based on three additional value metrics (price-to-earnings, price-to-cash flow, and dividend yield). These factors were constructed using the same rules as for the standard method using price-to-book ratios.

Each factor, with the possible exceptions of the dividend yield-based HML, has performance that could make it a legitimate specification for the three-factor model over the time that common data is available.

Running factor regressions using these alternate specifications on a suite of value ETFs and Newfound’s Systematic Value strategy, led to a wide array of results, both numerically and directionally.

While many investors consider the uncertainty of the parameter estimates from the regression using the three-factor model, most do not consider the uncertainty that comes from the assumption of how you construct the equity factors in the first place.

Understanding the additional uncertainty is crucial for decision-making. Managers and investors alike must consider what risks they are trying to measure and control by using tools like factor regression and make sure their assumptions align with their goals.

“Value” is in the eye of the beholder, and blind applications of two different value factors may lead to seeing double conclusions.