Cloning DFA

January 28, 2015


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


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