The Matrix Book: A DFA Tradition

Friday, May 6, 2016 28,350 views

"Data! Data! Data!" he cried impatiently, "I cannot make bricks without clay!"

— The Adventures of Sherlock Holmes, The Adventure of the Copper Beeches - Sir Arthur Conan Doyle, 1892

Call us data wonks, but at Index Fund Advisors, one of the things we look forward to every spring is the release of the DFA Matrix Book. For those who are not familiar with it, the DFA Matrix Book is a compendium of returns data going back as far as 1926 for forty-four asset classes and six portfolios (DFA’s Balanced Strategies) from which the IFA portfolios were originally derived. Starting from 2,572 calendar year returns, triangular matrices containing a total of 92,364 values are constructed.

These matrices enable us to quickly find the historical annualized average rate of return. For example, in less time than it took me to type out this sentence, I was able to determine that the S&P 500 Index had an annualized average return of 5.6% from 1930 to 1950. One may ask why, in this age of ubiquitous computers, would we need a book of returns calculations? The answer is simply that the book allows us to see the returns from a holistic point of view that we just can’t get from a computer screen, especially not from a smartphone screen. For example, I was able to quickly determine that for the S&P 500, no matter how bad a start an investor had, she never had to wait more than 15 years to break even (before inflation), and most of the time it was much less than 15 years.

The Matrix Book was started in 1982, a year after DFA’s launch, by one of the two founders of DFA, David Booth. The recently published 2016 book is the 35th edition. Besides the treasure trove of data, each matrix book has a unique cover picture and introduction. Some of the cover pictures are shown below. Click the cover of each edition to see details.

The introduction for the 2016 book is an interview between Dimensional Founder and Co-CEO, David Booth, and Nobel Laureate, professor, and Dimensional Board Member, Robert Merton, where they discuss Professor Meton's career, the science of finance, and what they believe the future holds for their industry. 

As an expression of our respect for the concept of the returns matrix, IFA has created its own version for twenty portfolios and fifteen indexes. In this example for IFA Index Portfolio 50, you can view either the annualized return or the growth of a dollar for a time period of 35, 50, or 85 years. The highlighted diagonal line of 8-year returns shows the annualized returns (or growth of $1) for the recommended minimum holding period for Portfolio 50 at all the different starting years. As you can see, 8-year holders of Portfolio 50 had a return that ranged from a low of 3.66% (starting on 1/1/2008) to a high of 16.60% (starting on 1/1/1975) over the last 50 years.

The returns matrix is one of those enduring concepts in finance that should never become obsolete. IFA is looking forward to at least another 35 years of the DFA Matrix Book, but by then we will probably need a good magnifying glass to see the numbers.

To see the IFA Matrix, visit here. And to learn more about the Dimensional Fund Advisors' Matrix, click here.

 To better understand the origins of Dimensional Fund Advisors, watch this video:

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