Cloning DFA

January 28, 2015

RiskBudgetIndexesWhen the craving is strong, it’s not uncommon for regular folks to want to figure out how to make the Colonel’s original, finger-licking Kentucky Fried Chicken at home. The trick is figuring out the Colonel’s secret recipe. The term for the copycat process is “deformulation” or “reverse engineering”; and—from a chemistry standpoint—it can be very difficult to do. Fortunately, regular investors have a much easier task if they want to home-brew DFA or their favorite “smart beta” ETF.

The original in the “alternative index” or “superior passive” space was Dimensional Fund Advisors, which was co-founded by Rex Sinquefield, whose pioneering work on long-term performance statistics roughly 40 years ago—when matched with Eugene Fama’s development of the efficient markets hypothesis—helped establish the bedrock of passive investing. In fact, the epic shift out of bonds and into stocks that financial analysts associate with best-selling and influential books like Jeremy Siegel’s, “Stocks for the Long Run: The Definitive Guide to Financial Market Returns and Long-Term Investment Strategies” can trace its roots to Sinquefield’s original research with Roger Ibbotson in the early 1970s on the long-term risk premiums: “Stocks, Bonds, Bills, and Inflation.”

Why DFA?
DFA was founded to apply academic research on capital market behavior to the practical world of managing investment portfolios, and its success has been epic. According to Morningstar, 75 percent of its funds have beaten their respective category benchmarks for the past 15 years. Today trillions of dollars worldwide are invested in passive portfolios, and DFA—with its uniquely close ties to academic financial research—is an index-fund icon, even though the funds don’t actually track indexes. The booming 600-person firm manages more than $378 billion in equity, fixed income and other strategies, and is partially owned by a blue-ribbon board of directors that has included Nobel laureates Myron Scholes and the late Merton Miller, as well as distinguished academic theorists Eugene Fama, Donald Keim, Kenneth French and Roger Ibbotson. The firm serves more than 200 corporate, government, college endowment, charitable and Taft-Hartley clients, and has drawn such a passionate following that enthusiastic clients have been known to sing a DFA fight song at company events, leading some wags to refer to it as a religion or, more dismissively, a cult.

That’s the good news; the bad news is that the firm’s mutual funds are not offered directly to the public. One of the dimensional focuses of DFA—hence the name “Dimensional Funds”—is to deliver low-cost exposure to the market, but DFA funds are only available through approved fee-only registered investment advisors who often have minimums of $200,000 or more, and generally levy additional “wrap fees” of up to 1 percent on top of DFA’s underlying management expense ratios. This quirky, difficult-to-buy distribution feature means DFA is a different kind of passive vehicle; DFA investors have made the decision to take advantage of indexing’s low-fee structure, but they potentially—and paradoxically—give away a significant portion of indexing’s cost advantage when the additional fees required to gain access to the funds are tacked on.

Investment advice is a big business, and the big money is in advising people how to invest, not actually investing. Your garden-variety index fund charges a management fee that commonly ranges between 0.04 percent and 0.17 percent; DFA’s funds, however, array between 0.38 and 0.70 percent, and average about 35 basis points, which is higher than most of the biggest index funds, but far lower than most actively managed mutual funds. DFA’s charges are very competitive, but not so low that some observers haven’t commented on the inconsistency between preaching the merits of passive investing and then charging quasi-active fees somewhere between a true index fund and an active management fee. The genius here is selling index funds with near-active management fees, which explains how co-founder and co-CEO David Booth annually makes the Forbes list of the richest Americans with a personal net worth that is reportedly in excess of $5 billion—a not-so-subtle reminder that low-cost money management can pay off big-time.

Something both strikingly obvious and often ignored is the fact that DFA’s headline-worthy performance and the thought engine behind it are well-established both in academia and the real world. Because DFA’s approach is quantitatively driven by computer models, there are no star managers. All DFA funds operate on the same principles; it’s all math, and Rex Sinquefield, Eugene Fama and the rest literally “wrote the book” on investing. All self-investors interested in these academically inspired approaches need to do is read the book(s).

It also used to be said that DFA took additional actions to slightly enhance returns and serve as the market maker of last resort, but that’s no longer the case: 95 percent of their trades today are black pool versus block trades. Nowadays trades are brought to the market in smaller pieces; DFA uses an automated direct-market-access trading model to place nearly all of its trades. The trading component is no longer there; it’s not part of the value added, so we may be paying for a brand of indexing when we probably shouldn’t be. Today they’re not costing you anything on trading, but they’re not gaining you anything either. More than ever before, if the style attributes are mirrored in a Fama-French context, investors can expect to capture the largest return drivers of DFA.



Increased concern about portfolio building fees and retainers is creating pressure for institutional and individual investors alike to re-evaluate managers, costs, risks and opportunities. In a perfect world, we’d like access to DFA mutual funds at Vanguard prices and—in this era of do-it-yourself portfolios—to put academic theory into practice on our own. It’s a pretty standard strategy: The Fama-French three-factor model is the root of Dimensional’s strategy, so it’s only natural to wonder if it’s possible to:

  1. Avoid the additional 1 percent or so charged by DFA-approved registered investment advisors
  2. Use broadly similar strategies to track the same asset classes at a reduced expense level

Furthermore, a portion of DFA’s previous outperformance may reflect its “indexation” of parts of the market that were previously unindexed and difficult to access. Under Sinquefield and Booth, DFA boomed by enabling investors to invest in the very smallest stocks and in “deep value” stocks that trade at the largest discount to book value. It was hard to find funds that had very high loadings on “small minus big” (SmB), say, above 0.7, so to a certain subset of passive investors, DFA funds used to be the only way to get “proper” exposure to small- and microcap stocks. DFA established its first fund in 1981, and at that time, Vanguard had no value or small value funds, so if you were going to slice and dice a portfolio, DFA was the best and cheapest carving knife.

However, low-cost funds, especially ETFs, now occupy every asset category offered by DFA. As new indexes have come to market, investors can get the unloved and unwanted part of the market for a lot less. Today DFA offerings are very close to what other major market benchmark providers deliver; the DFA U.S. Small Cap Value, for example, is not dissimilar from the iShares SmallCap 600 Value Index Fund (IJS|A-87). Where there’s not a perfect substitute, it’s rather easy to combine two less expensive funds and create an effective clone.

The Vanguard Alternative
DFA portfolios employ semi-passive strategies designed to capture the return behavior of an entire asset class, so as a core holding for replicating DFA, John Bogle’s behemoth Valley Forge, Pennsylvania-based Vanguard Group is a logical choice to start. It isn’t a requirement to use Vanguard as the base, but passive is a scale game, and Vanguard has always kept its expenses very, very low. As Andrew Tobias puts it, “In the investment race, that gives your horse the lightest jockey.”

There are some important differences between the two firms. A mistake that many make is to assume the Vanguard Small Cap Value is equivalent to DFA Small Cap value. That is not true. DFA has a twist: Compared with Vanguard, the firm is a much stronger advocate of the wisdom of using small-cap and value tilts within different equity asset classes. One needs a higher percentage of small-cap to get the numbers in the nine-box style grid to where they might mimic the DFA Small Cap Value portfolio (Figure 1).




While both Vanguard and DFA offer passively managed funds, each follows a distinctive approach, and they are both “best in class” at what they do. Vanguard is happy to settle for market performance, so it slavishly replicates widely accepted indexes. DFA aims for more, so it tries to “improve” the performance by spicing the stew. We’ll use Vanguard as a base for off-the-shelf commercially available indexes, then kick it up a bit like celebrity chef Emeril Lagasse. Despite the marketing, there really is no index smack-down—just broad-based multifactor exposure to the same return drivers at varying prices.

It’s not a debate so much as a choice. DFA focuses only on market dimensions where research documents a reward for risk taken; their faith in small-cap and value is a cornerstone of its business. It’s all based on historical data. Meanwhile, Vanguard is dirt cheap. We’re not settling the question of whether Vanguard or DFA is best; we’re taking the two leading providers of passively managed funds and showing that we can transform one into the other.

Getting Started
Dimensional’s equity strategy is based on the work of esteemed finance professors Eugene Fama and Kenneth French, which basically says stocks are riskier than bonds, so stocks should reward investors with higher returns over the long term. This is called the “market factor.” The model also notes that value stocks (those with low price-to-book ratios) and small-cap stocks are riskier than the broad market and, therefore, have higher long-term return as well. In a nutshell, DFA incorporates Ibbotson’s decades-old research showing that small and value stocks outperform the rest of the market over the long haul. From this perspective, equity investing therefore largely consists of deciding the extent to which your portfolio will participate in each of the equity market dimensions: small/large and value/growth.

In this paper, we explore the feasibility of taking ETFs and index funds available in most retirement plans and ginning up a return stream identical to DFA, essentially cobbling together a mix that captures the inherent value and size tilts—“the DFA-ness”—that is baked in at DFA. The deep small-cap and value orientation of DFA funds cannot be replicated with Vanguard funds off-the-shelf, but it certainly might be reverse-engineered if we mix and match using the broad range of offerings available today. The benchmark defines the strategy of an index fund; in this case, DFA is the reference portfolio, so we will target its funds’ systematic risk factors with precision.

Fama and French’s work informs the construction of DFA funds, so the way to replicate DFA’s style in a “comparison portfolio” is to construct a portfolio of ETFs with the same Fama-French coefficients as the targeted DFA fund. The question to be answered is whether we can invest in a manner aligned with these ideas by mimicking the loadings of less expensive, widely available funds. An ancillary issue is how much more, if anything, an investor can expect to earn with a DFA fund than with a basket of inexpensive index funds that have the same Fama-French loadings. Using factor-based analysis to synthetically replicate the performance has the potential to save public and private pension plans millions of dollars in fees.

The really good news is that size and book-to-equity are two easily measured variables, so it’s a relatively easy-to-implement approach. Fama-French replication is pretty simple, mathematically, but very few individual investors use the three-factor model in allocation decisions—or at least not to this extent. However, it might be worth their while. The first step is to calculate the same Fama-French size, SmB, and book-to-market (“high minus low,” or HmL) factors that DFA uses to build its funds, compare those with Vanguard’s Fama-French factors and then adjust accordingly to build a portfolio of index funds that achieve comparable Fama-French factor loadings.

A good matching of risk factors is essential, and with Internet access to formerly exclusive databases, the do-it-yourself investors now have some very powerful tools at their disposal. We can find the historical “market” (Rm-Rf), “small-cap” (SmB) and “value” (HmL) factors needed to home-brew DFA in the Ken French Data Library, which goes back to 1926, and is available for free from the Dartmouth College Tuck School of Business.1



We originally replicated DFA with generic capitalization-weighted indexes rather than ETFs because we could go back even further in time, i.e., pre-ETF. This assured a long history of returns to work with and served as a proof of concept. Next we explored the implementation via retail ETFs or institutional funds that offer less return history than the pure indexes themselves but that are directly investable. The return of a DFA fund can be described as the return of a basket of indexes plus an error term, and our characteristic-adjusted replica had a very low error term using data back to the year 2000 (Figure 2).


The Methodology
Our methodology of mapping DFA products to ETFs and creating a tracker structure was as follows:

  1. Obtain return streams for a sample of DFA funds.
  2. Select traditional capitalization-weighted indexes that intuitively would be a good starting point for replication. To manufacture DFA Small Cap Value, for example, start with Vanguard Small Cap Value and expect to add Russell Micro Cap or other funds to increase the SmB factor.
  3. Run a multiple-factor regression to calculate coefficients for DFA using the Carhart-Fama-French four-factor return streams (more on this later).
  4. Equate the clone’s exposure to the targeted DFA fund by controlling the exposure to the risk factors that drive portfolio return. In other words, compose a blended mix of traditional indexes by matching the Fama-French factors.2

Start by going to the website and downloading the (monthly) world-famous Fama-French factors. Next, subtract the monthly risk-free rate from the targeted DFA fund’s monthly returns (Figure 3).




From there, calculate the Fama-French factors in the usual way—ordinary least squares (OLS) regressions. The DFA returns are the dependent variable; the “market return,” “small cap” (SmB), “value” (HmL) and “momentum” premiums are the independent variables (Figure 4).


We added a factor for “momentum” because DFA started using momentum around 2005. When we add momentum, the model technically is referred to as the Carhart four-factor model. The R-squared in Figure 4 tells us that the model can explain 99 percent of DFA’s return variability. That’s an impressive number that tells us that the factors for market beta, small-cap effect (SmB) and value effect (HmL) are each very strong when explaining DFA’s returns. The betas may look small, because numbers like 0.44 and 0.93 are tiny, but don’t let that fool you. The t-stat is the true measure of how statistically significant the beta coefficients are and the relative strength of a prediction; it’s technically more reliable than the regression coefficient because it takes error into account.

As you may recall from sophomore statistics, the greater the t-stat, the greater the relative influence of the independent variable on the dependent variable. A t-stat over 1.96 is considered strong, so the t-stats we see in Figure 4 of 45, 20 and 10 are huge. Simply put, it means the generalizability of the findings beyond the sample is safe. In our case, the “market,” “small-cap” and “value” factors are absolutely, unequivocally driving DFA’s returns. The intercept is what industry practitioners would refer to as “alpha.” but the coefficient is small (0.00) and the t-stat insignificant. This implies that DFA does not supply any additional value after taking into account the “small-cap” and “value” factor loads.

Next, you have to address how you want to replicate the Fama-French factors. It doesn’t make sense to try and match all the betas at once. From a data perspective, we have to take into account statistical significance as well as relevance. The “market” beta has the largest t-stat—over 45, which is enormous, so it’s the most significant factor. A few points off on that beta are far more important than a few points off on “size,” “value” or “momentum.” The “small-cap” effect (SmB) is the next most important, and then “value” (HmL). Only factors that are statistically significant need to be targeted; theoretically, you’d like to keep the betas in balance proportional to each factor’s t-stat and p-value.

We require that the differential error in SmB betas be smaller than the differential error in HmL betas because SmB is more statistically significant, but we have to be cognizant that a numerical difference in betas is more meaningful when the numbers themselves are smaller. We have to scale the differences in the size of the coefficient betas as well as take into account the volatility of the coefficient. If a factor has a large expected return associated with a very small beta, then we need to make sure the clone doesn’t stray too far from that low, but powerful, beta.



We match what we need to match and leave out what we don’t. If the target fund doesn’t have a statistically significant “value” coefficient, then there’s no need to bother matching the HmL factor. Balance is the key. The clone will always work best when we have the statistically significant betas as closely matched as possible. Exactly matching one variable is generally a good solution, but not the best; try to align them all simultaneously. Even with an optimizer, it’s not possible to literally match each and every one of them exactly. With optimization, you can exactly match one thing (the objective function) and then subject that objective function to several constraints.

Capturing the market-beating advantage of “small” and “value” stocks is easy; the key is to measure it exactly if you want to match DFA exactly.3 There are three time periods of interest—the in-sample period, the out-of-sample period and the entire period—so we measure the factor loads and returns over each. Data is split into estimation and evaluation periods: The in-sample period is the portion of the data that is backtested. The out-of-sample period evaluates a model’s forward performance and provides confirmation of a model’s effectiveness. Out-of-sample tests help guard against data mining, so many researchers regard out-of-sample performance as the “ultimate test of a forecasting model.”

DFA’s Small Cap Value fund is a bit more “value-y” and more “small” than Vanguard, so we salt in a little microcap to increase the “small-cap” weighting (SmB) (Figure 5). Our DFA clone was built from Vanguard’s plain-Jane version of a small-cap value index (85 percent) and iShares’ Russell Microcap Index (15 percent).




The small-cap value clone tracks DFA quite well during the test period (Figure 6). More importantly, the returns during the out-of-sample period are in line (Figure 7). And the growth-of-a-dollar chart is spot-on for all practical purposes, indicating that a well-designed mix of inexpensive ETFs is an effective clone both out-of-sample and in-sample (Figure 8).






Sometimes only a quarter of the returns come from a particular tilt, and there is variability in that tilt because Fama-French factors are not stationary over time. The important thing to note is that DFA and the indexes that we use as building blocks experience factor drift in the same direction from period to period (Figure 9).


The coefficient drift isn’t coming from DFA putting less weight on “value” or more weight on “small cap”; it’s coming from the market. DFA’s emphasis on the factors is relatively constant, so the clone and DFA will rise and fall with the tide together. The factor control is illustrated in Figure 10.


The Successful Clone
We have to address what it means to successfully clone something. A successful “clone” will “act the same,” i.e., have a pattern of returns that mimics the DFA portfolio as closely as possible. Statistically, this can mean many things: beta and correlation both close to 1, a minimum of tracking error, etc. However, each rule—on a stand-alone basis—suffers from some weakness.



Small differences in monthly returns could potentially add up to a meaningful shortfall over a long time period; similarly, two funds can have an identical cumulative return but vary quite a bit between start and endpoints. The correlation between two funds can be equal but not capture the exaggerated movements of one fund relative to another, because it’s only a measure of the sympathetic movement between two series. Correlation measures pattern similarity and direction, basically the average frequency with which the two returns move together; it doesn’t take into account the magnitude of how asset returns move together.

There is no one-size-fits-all calculation to assess the comparability between our proxy-DFA and the authentic DFA that it is designed to imitate. The challenge is to create an alternative return stream that has the same first moment (mean return) and is equal in return distribution to the DFA fund it replaces.

Looking at the results, our Frankenstein blend tracks DFA’s Small Cap Value offering very well for the eight years that all of these funds have been available. DFA and the clone return 47.6 percent and 45.7 percent, respectively, in the out-of-sample period. Annualized over the entire period, DFA returns 0.61 percent, while the clone returns 0.60 percent. Correlation in the out-of-sample period is 0.97; beta is 0.85 and the tracking error is 0.95 percent (Figure 11). Typical tracking error for an active equity mandate is usually 5-7 percent, while anything under 2 percent is considered good for a passive index, so we consider the clone to be a good one.




DFA reconstitutes its portfolios on a daily basis, but the Fama-French factors don’t move meaningfully day to day. As a result, mindful of trading costs, we rebalanced monthly. The differences between DFA Small Value and our artificial blend are de minimus, implying that investors can use a combination of ETFs from a variety of providers—within a relatively broad range of asset mixes—to mimic the exposure of the DFA fund. The clone isn’t all that sensitive to the percentages. Any ratio of VBR and IWC between 85 percent and 15 percent and 75 percent and 25 percent works pretty well and is certain to save on fees (Figure 12).


Lagging DFA by a squeak is no cause for concern. The inequality in SmB and HmL betas is the source of our remaining mismatch in returns. Our clone still has lower SmB and HmL loadings than DFA. If we reduce the shortfalls, we’ll reduce the bandwidth around the clone. Coefficients equal to DFA will lead to equal returns; if investors want to “win” and have their clone outperform, then they can make sure their clone factor coefficients are greater than their DFA target. We used Vanguard and iShares funds because they had long histories but were an imperfect fit; today there are more offerings with even higher “small-cap” and “value” factor loads, so we could make an even better clone.

Benchmarking Benchmarks: The Investment Landscape Viewed Through A Factor Lens
To obtain the desired target values of SmB and HmL, etc., we’re building portfolios of index funds, which is simple enough, but how do investors know what building blocks to use? There is a wide range of SmB and HmL loadings within the small-cap value space that allows investors to accurately target the dimensions of higher expected returns (Figure 13). Any low-cost fund is a suitable building block. Vanguard isn’t on no-transaction fee platforms, other than its own, because it won’t pay distribution fees; but that’s not a problem. Mutual funds—and ETFs, by extension—are generally priced as if they are highly differentiated products, when in reality it is very much a commodity business.




It’s important to recognize that every index has factor exposures at some level. The scatter charts in Figures 13 and 14 plot well-known ETFs as well as Vanguard’s old and new indexes since they recently switched. The three-factor model on average explains about 96 percent of the variation of equity, and viewed as such, Vanguard’s change from MSCI to CRSP is little more than a slight factor weight change.4 Some small-cap value strategies tend to hold somewhat larger-cap stocks, on average.


In Figure 13, note the location of the iShares Microcap ETF that has more SmB, and the Vanguard Small Cap Value that has less SmB in comparison to the target DFA fund, which lies somewhere in between the other two. These funds have a long history, which is helpful for this type of cloning analysis, but clearly, the iShares S&P SmallCap 600 (SPSV), which has been around since 2009, would be a superlative building block, as its SmB loading and that of the DFA fund are directly on top of each other.5 There are a plethora of ETF offerings with SmBs of approximately 0.80 that investors can mix and match.

The premiums exist independently of strategy construction. An investor doesn’t need to match the holdings, only the size, value and momentum factors that are the backbone of these funds. You can be quite agnostic with respect to getting exposure—iShares, SPDR, Schwab—SmB is SmB wherever you get it. DFA knows this as well, as it is indifferent regarding stock A or stock B when trading. DFA focuses on the overall characteristics of a portfolio and treats stocks that have similar characteristics as close substitutes for one another. The premiums driving the returns are the same. You can have the same “loadings”—the degree of exposure to the factor—as a fund but own different mutual funds and different stocks. In fact, you don’t have to have midcap in a portfolio to get a midcap return.

The Vanguard Small Cap Value ETF isn’t as small as DFA’s Small Cap Value offering, so we needed to pair it with something smaller than DFA. Several small-cap indexes are available: The most actively traded U.S. small-cap ETF is the iShares Russell 2000 Index (IWM | A-85), while Bridgeway’s Ultra Small Cap strategy—a mutual fund—is focused on the “smallest of the small,”—the CRSP 10 decile. The natural building blocks to load up on SmB would be the iShares Micro-Cap ETF (IWC | B-87), the PowerShares Zacks Micro Cap Fund (PZI | C-79) and the Wilshire MicroCap (WMCR | D-92).

Clones are linear combinations of the factor loadings of their building blocks. One fund can be a little low on a coefficient because you can make up for the shortfall by grabbing another fund that has more than the target. With the two building blocks that we chose, it’s possible to match the SmB, but DFA is still more “value-y” than the components the clone is made out of. We built the clone out of two funds that simply don’t have the ability to get the HmL to the exact level of the DFA fund. Adding a third fund with more HmL is an option, and there are newer funds that have entered the ETF scene that would make better inputs, like the iShares Morningstar Small-Cap Value ETF (JKL | A-87), which comes closer to the DFA Small Cap Value HmL loading than does the Vanguard Small Cap Value ETF (VBR | A-100) (Figure 14).

If you look closely, the PowerShares Zacks Micro Cap ETF would be a better source of SmB without giving up as much HmL. The iShares Morningstar Small-Cap Value offering has both more HmL and SmB than the Vanguard ETF that we used as an input. We’re combining premiums in a linear way so the end HmL and SmB coefficient of the clone will be a weighted average somewhere along a line between the two building block funds. There are multiple ways to get to the same place.

It used be hard to get the same factor weights as DFA but, today, investors can find funds—ETFs and standard mutual funds—that have even larger factor weights. Guggenheim, Bridgeway and Vericimetry are among a slew of players in the ultra-small-cap/deep-value space that factor-based investors should become familiar with. Each offers exposure to the most value-y and extremely small companies. The database can help investors find ETFs that fit the bill, such as the iShares Morningstar Small Value Index (JKL), the SPDR S&P 600 Small Cap Value (SLYV | A-87), the Guggenheim S&P SmallCap 600 Pure Value (RZV | B-49), the First Trust Small Cap Value AlphaDEX (FYT | B-65) and Vanguard’s S&P Small-Cap 600 Value ETF (VIOV | B-83).



Some of these new products provide components, while others provide total solutions. Graphing SmB and HmL simultaneously shows that newer ETFs like the Guggenheim S&P SmallCap 600 Pure Value are sitting right on top of DFA. In fact, it appears to be a squeak smaller and more value-y (Figure 15).


With nearly 10 percent of all U.S.-listed ETF assets deployed across factor-based funds, investors would certainly benefit from an understanding of the finer points of factor investing. The most important thing to know is that higher betas contribute to higher returns, with market beta providing the most octane. Next in importance is to be aware that straight/pure small-cap strategies generally have a much higher market beta than a blend of small and value. Value stocks tend to be larger than growth stocks, so the value filter prevents a “small cap+ value” fund from being as “small” as it could otherwise be if it were only “small cap.” When you combine value and small-cap, the value tilt makes the universe “less small” than the stand-alone small-cap space.

All in all, we find DFA’s performance historically replicable. At the end of the day, you get the same return, but time series properties and sector weightings are equally important, so we reran the analysis to determine if the two investments were similar when analyzed with a state-of-the-art sophisticated risk engine like Cognity’s FinAnalytica. Further analysis showed that both DFA and copycat DFA share similar sector and style exposures; risk management metrics—beta exposures, expected tail loss, value-at-risk, expected tail return—are also similar (Figures 16-18).








A Few Nitty-Gritty Facts
DFA excludes certain asset classes, such as real estate investment trusts and highly regulated utilities that enjoy large value coefficients, so investors who replicate DFA using traditional index funds will appear to have the same HML as DFA, but they really don’t, because utilities and REITs are pretty sluggish sectors. Since DFA attains high factor loadings and deeper value exposure without these sectors, the clone should compensate by having slightly higher “value” (HmL) beta coefficients than the DFA target fund. By including these sectors (REITs and utilities), clones made from cap-weighted indexes include more securities and, therefore, have a more diversified portfolio. Broad, diversified exposure is to be desired because research has shown that the size and value premiums are not driven by all the securities moving together but by a few star stocks performing extremely well.

The traditional value-index approach excludes the half of the market that is nonvalue, and then weights the value half by market capitalization. Adding back missing sectors makes the clone DFA more inclusive; indexes like the Research Affiliates Fundamental indexes (RAFI) or the MSCI factor indexes take in the whole universe so all stocks are represented. The iShares MSCI USA Value Factor ETF (VLUE | B-84), for example, is positioned as a factor fund rather than a value fund because it tilts toward “value” by weighting all of the securities in a universe rather than by selection, which would entirely exclude some of them. Factor indexes, particularly risk efficiency strategies, also tend to rebalance more frequently and have higher turnover than market-cap-weighted indexes.

Investors can map other DFA funds as well. DFA Emerging Markets Value can be mapped with emerging markets, emerging markets value and emerging markets small-cap indexes from various providers. Figure 19 shows a possible DFA emerging market value clone that is 40 percent the SPDR S&P Emerging Markets Small Cap ETF (EWX | D-82) and 60 percent the Vanguard Emerging Markets ETF (VWO | C-84).


Historically, without the availability of something like EWX, investors could not keep pace with DFA but, today we have the ability to acquire this niche-beta. Vanguard is “deep and cheap,” but in areas like emerging market small-caps where they have no offering, there are other ETFs, such as the SPDR Emerging Markets Small Cap (EWX | D-82) that can fill the breach. A portfolio that is 40 percent VWO and 60 percent EWX looks strikingly similar to DFA’s emerging markets product. iShares has an Emerging Markets Value ETF (EVAL | C-92) that works as well. The profusion of ETFs has eliminated whatever moat DFA used to enjoy.

DFA augments returns with securities lending, while Vanguard doesn’t. However, we believe the potential savings in fees more than washes out any difference in performance. Exact implementation savings will vary in proportion to the size of the assets being invested and the market accessed. However, in the appendix to this article, available in the online version at, we rank a selection of funds by their exposure to the relevant factors per unit of cost.



Domestically, institutional investors of scale don’t need to pay 45 basis points—they can go to indexing giants like Northern Trust or State Street and pay 1-5 basis points; for retail investors, Vanguard comes in a variety of share classes, i.e., Investor, Admiral, Institutional, ETF (Figure 20).


Overlapping Dimensions
We don’t pretend to have access to the exact methodology, liquidity premia, market making, securities lending, “patient trading” and other aspects of DFA’s proprietary investment model—nor was it our intention. DFA’s commitment to the academic approach means it makes refinements to reflect the latest research, such as that relating to the so-called fourth factor—momentum. DFA funds have historically had a higher negative momentum load than common index funds, and only started incorporating momentum screens in its funds in 2005. Since 2006, DFA Large Value and Small Value have had some negative momentum exposure, but it is less than half (coefficient of 0.05) of what it was compared to the 1993-2005 period, when it had a coefficient of more than 0.15. DFA incorporates momentum by delaying purchase of a stock that is falling until that negative momentum has dissipated, and by delaying the sale of securities that have been rising recently.

Momentum is one of the strongest and most puzzling anomalies. It’s large and persistent; in fact, Eugene Fama and Kenneth French have noted its place as “the center stage anomaly of recent years … the premier anomaly” but large weightings to the “momentum” (WmL) factor of Carhart (1997) had simply been unavailable to investors. Now that the absence of a passive investment vehicle that provides investors exposure has been addressed, investors who could formerly only get limited exposure to WmL can now access direct, efficient, low-cost access to momentum.6

We computed momentum in our analysis, but didn’t explicitly incorporate it in our clone; however, a slew of new commercial products from ETF providers have given investors a whole new set of tools for constructing precise portfolios tailored to deliver desired factor exposures. The database shows five ETFs that incorporate momentum: the iShares MSCI USA Momentum Factor, the First Trust Dorsey Wright Focus Five, the SPDR S&P 1500 Momentum TILT and the Elements Spectrum Large Cap US Sector Momentum Index.

The challenge in replicating DFA is to monitor variability in factor trends and modifications to DFA’s core model. Over time, DFA has changed the way it runs its value strategies. DFA incorporated the profitability factor across all its equity strategies over the past year, but the impact isn’t as big as the research would suggest. Robert Novy-Marx’s research showed that profitable firms increase expected returns despite higher valuation ratios, but DFA investors will never capture it. Remember, long-only strategies are hamstrung by the fact that—at best—they can underweight or exclude some unprofitable companies and expand the universe of acceptable value stocks. They’re not going long and short the most profitable and unprofitable companies like Novy-Marx did in his research. They can’t get the 4 percent shown in long/short analysis because these funds don’t load 100 percent on the premium. For that matter, most ETFs can’t go long and short like Ken French either. The most they can deliver is the spread in returns between high profitability and low profitability.

DFA investors shouldn’t expect to outperform the market by the difference between the high and the low indexes used to illustrate the premium, because they’re only excluding a small subset of securities that have high relative prices and low profitability. They’re excluding less than 10 percent of small-caps in most markets, whereas the true, full-blown Novy-Marx filter would exclude approximately 70 percent of the aggregate market cap of small stocks. These are definitely improving the portfolio return, but it is likely to be in the range of approximately 30 bps a year, and many of the indexes used to replicate DFA capture profitability as well.

The real questions are: “To what degree does ‘profitability’ increase returns when the existing model already incorporates price-to-book or an existing measure of value?” To what degree do these factors work independently? What is the correlation of the ‘profitability’ factor to ‘value’?” In Figure 21, we’ve plotted HML and PCF coefficients on the same scatter chart to illustrate the degree to which they capture the same thing. In many cases, the “value” (HmL) dots are right on top of “profitability” (PCF) stars, indicating that the benefits of adding profitability after incorporating other measures of value are of a diminishing nature. These aren’t entirely unique risk factors but rather different empirical proxies that represent the same type of economic risk.




There is overlap between premiums, as seen in Figure 21. When you look at the co-variation of the profitability premium with the value premium, there’s a lot of common ground, and the rest of the impact is a bit of a growth tilt that will offset your pure value bets. Low beta is negatively correlated with value and positively correlated with quality. Most investors don’t realize that if you want to exploit all the factors, they are not going to be additive, because the premiums are not independent of each other. You can’t get full “market” premium plus the full “small cap” premium plus the full “value” premium—that would sum to more than 25 percent per year (Figure 22)!


DFA’s unusual distribution strategy can keep its funds out of reach for investors with assets too low to pique the interest of most advisors. Similarly, there have always been advisors who want to work with DFA, but there was no shortcut to the advisor-approval process. DFA also has never worked with full-service brokerages, nor has it been available to 401(k) platforms.

Although the firm’s record is referred to by some as “the most impressive track record in investing,” systematic risk factor approaches—value, small-cap, momentum—are comparatively straightforward for investors to understand and access. DFA funds are built using only a four-factor model, and really, the only tool required is a spreadsheet. 7

Carhart, M. M. (1997). “On Persistence in Mutual Fund Performance.” The Journal of Finance 52: 57–82.

2 The sum of the weights must equal 100% and, to keep things simple, we require all weights to be positive which means conceptually that no index funds are sold short.
3 We used Excel’s slope function to point the HmL from the Tuck Library to the HmL return stream of DFA and then to the HmL of a mix of funds.
4 At the time of Vanguard’s change announcement, the No. 3 U.S. ETF provider went to great lengths to downplay any differences in returns between the MSCI indexes and the new enlisted ones. The new CRSP indexes, created by a research center of the University of Chicago’s Booth School of Business, were designed to be replicated by an ETF or index fund with great effort to minimize trading and front-running.
5 Vanguard and BlackRock offer identical Small-Cap 600 Value ETFs. Vanguard is cheaper (0.2 percent versus 0.3 percent) but BlackRock has more assets ($3.2 billion versus $.076 billion). BlackRock’s ETF is arguably more liquid and cheaper to trade, which is important, since small-caps are—as a group—expensive to trade, but it’s unclear which is “better.”
6 Momentum is a factor affecting returns that was informally added by DFA in 2004, but it’s technically not considered a “dimension” of equity returns by the company, because there’s no real explanation for why returns should be higher.
7 The authors are working with Silicon Cloud Technologies, LLC which will offer software at that computes these factors automatically.


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