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The Matrix Book: A DFA Tradition

Call us data wonks, but at Index Funds Advisors, one of the things we look forward to every spring is the release of the DFA Matrix Book.
The Matrix Book: A DFA TraditionCall us data wonks, but at Index Funds Advisors, one of the things we look forward to every spring is the release of the DFA Matrix Book.


"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 Funds 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 thirty-five asset classes and six portfolios (DFA’s Balanced Strategies) from which the IFA portfolios were originally derived. Starting from 2,511 calendar year returns, triangular matrices containing a total of 82,984 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 2013 book is the 32nd 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.

DFA Matrix Books

The introduction for the 2013 book was written by David Booth himself and provides an evolutionary history of Dimensional, discussing how decades of academic research have been consistently incorporated into the DFA funds.

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 3.98% (starting on 1/1/2001) to a high of 17.23% (starting on 1/1/1982) 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 32 years of the DFA Matrix Book, but by then we will probably need a good magnifying glass to see the numbers.

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