As advocates for passive investing, it is a common question amongst clients and prospects about why our 100 IFA Index Portfolios utilize strategies from Dimensional Fund Advisors versus better-known passive fund companies such as Vanguard or iShares.

**The answer is quite simple: performance!**

For example, if we were to compare the performance of 20 IFA Index Portfolios utilizing strategies from Dimensional versus that of Vanguard over the 18 years ending 12/31/2016, we see a consistent trend of outperformance across almost all risk levels. We have written before about why Dimensional is our preferred fund partner here.

Click to see the full interactive chart on ifa.com

Today we are going to take a deep dive into why and how Dimensional was able to provide superior returns.

First, let's review the Fama/French 3 Factor Model, which was introduced in 1992 in their groundbreaking research paper, "The Cross Section of Expected Returns."

Examining U.S. equity returns from 1962 to 1989, they found three key factors that explained much of the variation in historical stock returns. They were the market, size, and relative-price (value) factors. Their findings led to a revolution in the index fund industry as new index funds built around small cap stocks emerged, which up to that time was dominated by funds tracking the S&P 500.

From an investment advisory standpoint, guiding investors to build globally diversified portfolios of index funds structured around these factors has yielded better results over the long term. For the 24-year period since the original publication of the Fama/French research paper (1993 to 2016), the return of IFA Index Portfolio 100 has yielded a 0.87% per year premium, net of advisory fee, over the S&P 500 (10.08% vs. 9.21%). In terms of the growth of wealth, $100,000 invested in IFA Index Portfolio 100 ended up with $174,000 more than just simply investing in the S&P 500.

When we examine which types of funds we would like to include in our portfolios, we want to be able to gain a general understanding of how much exposure each fund has towards these three factors. We are able to do this through the use of multiple regression analysis.

A multiple regression measures correlations between a dependent variable and multiple independent variables. The question we are asking is, "how well do the independent variables explain the variation of the dependent variable?" To give a practical example, if we were looking at the Vanguard Value Index Fund, we want to know how much of the variation of the fund is explained by the market, size, and relative-price factors, *independently.* The diagram below illustrates a multiple regression using the Fama/French 5 Factor Model.

If we can gain an understanding of how much a fund is exposed to these various factors, then we can start to make statements about future performance. For example, let's compare the performance of the Vanguard Value Index Fund (MUTF:VIVAX) versus the DFA U.S. Large Value Strategy (MUTF:DFLVX) from 10/1/1999 to 12/31/2016 (the longest period where performance for both is available).

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Source: Dimensional Fund Advisors. See disclosures below.*

As you can see, DFLVX outperformed VIVAX by 2.18% **per year .** Aren't they both indexing value stocks? Yes they are, but not all indexes are created equal and the ability for a fund management company to capture premiums in the market is no easy task. In other words, there is very little argument about whether or not these premiums exist. How a fund company goes about capturing them is a completely different story. You will also see that Dimensional outperforms Vanguard across the U.S. Small Cap and U.S. Small Cap Value asset classes as well.

But we already know that the driving factor behind DFLVX's outperformance must be coming from their ability to have an exposure that is more sensitive to the market, size, and relative price premiums. This can be seen in the individual regressions for DFLVX and VIVAX.

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Source: Dimensional Fund Advisors. See disclosures below.*

Let's first explain the variables.

- Alpha (α): the excess return of the fund compared to its risk-adjusted (β) benchmark
- MKT-B: measures the fund's sensitivity to the market factor. A numerical value greater than 1 indicates the fund is more volatile than the overall market and vice versa
- SmB: measures the fund's sensitivity to the size factor. A positive number indicates an overall exposure that tilts towards small cap stocks while a negative number indicates a tilt towards large cap stocks
- HmL: measures the fund's sensitivity to the relative-price (value) factor. A positive number indicates an overall exposure that tilts towards value stocks while a negative number indicates a tilt towards growth stocks.
- Adj R2: measures how well the overall model explains the variation of the fund, adjusting for the amount of independent variables. You can read the number as a percent
- T-Stat: indicates the level of statistical significance of the estimate in the model. A level of 2 or greater indicates a high level (95%) of statistical significance, making the estimates highly reliable.

First thing you should notice is that neither fund has a statistically significant alpha, which is what we would expect in a properly functioning market. Second thing to notice is the adjusted R-squared for each is over 90%, meaning that the overall model explains the vast majority of the historical performance of each fund, which indicates that the model can be seen as highly reliable.

Lastly, if we look at the individual risk factors, we see that DFLVX has a greater exposure to the market, size, and relative-price factors, meaning that the overall portfolio is slightly smaller in terms of market capitalization and has a greater tilt towards value stocks compared to that of VIVAX. All of these estimates are highly reliable (t-stat>2). Since we know a greater exposure to these factors is likely to yield greater performance, we can now understand why DFA has provided superior returns.

We can use the same analysis when comparing DFA and Vanguard in the U.S. Small Cap and U.S. Small Cap Value segments of the market.

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Source: Dimensional Fund Advisors. See disclosures below.*

It is important to note that this outperformance is not free. As we would expect in a properly functioning capital market, a higher return must be associated with higher risk. If we plot each strategy in terms of standard deviation, we can see that there are higher levels associated with the strategies from DFA. What this means for investors is that we should expect to see more variability in the returns of the DFA strategies, emphasizing the importance of taking a disciplined approach to investing when you are pursuing risk premiums. We believe the help of an independent wealth advisor assists in maintaining that discipline and capturing the overall benefits the capital markets provide the long-term investor.

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Source: Dimensional Fund Advisors. See disclosures below.*

So now lets look at the year by year Factor Gaps (different exposures to the dimensions of returns) of Dimensional passive funds recommended by IFA versus the closest Vanguard alternative passive fund, which we refer to as the "BENCHMARK" in the following charts. The green bars illustrate years when Dimensional's factor tilts and implementation strategies had higher returns than the Vanguard alternative and the red bars illustrate when Vanguard Funds had higher returns with standard indexes. Generally speaking, Vanguard indexes have lower tilts to small and value factors. A t-stat of 2 or greater indicates statistical significance of the factor gap difference. All comparisons, except a 0.04% difference on the S&P 500 fund in favor of Vanguard (see this article), showed higher average returns in Dimensional Funds and 4 of the 10 showed statistical significance. For the calculation of t-stats and very long term factor premium charts, see this article.

As a fiduciary it is our responsibility to provide guidance rooted in doing right by our clients and backed up by empirical research. Although Vanguard is better known in the passive investment community, we understand that Dimensional has better captured the premiums that have been shown to reward investors over the long-term. We have structured our portfolios around these premiums in a diversified manner so that they can get the most that the capital markets provide.

*Disclosure from DFA*

Performance data shown represents past performance. Past performance is no guarantee of future results and current performance may be higher or lower than the performance shown. The investment return and principal value of an investment will fluctuate so that an investor's shares, when redeemed, may be worth more or less than their original cost. Average annual total returns include reinvestment of dividends and capital gains. To obtain performance data current to the most recent month-end access our website at us.dimensional.com. See Standardized Performance Data and Disclosures. Performance for periods greater than one year are annualized unless specified otherwise. Selection of funds, indices and time periods presented chosen by advisor. Indices are not available for direct investment and performance does not reflect expenses of an actual portfolio. This report and the information contained herein are subject to the terms of the End User License Agreement for Returns Program.

**Disclosure:** I am/we are long DFLVX, DFUSX, DFSCX, DFSVX. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it. I have no business relationship with any company whose stock is mentioned in this article.