Old World Map

The Matrix Book: A Dimensional Tradition

Old World Map

"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 geeks. At Index Fund Advisors, one of the things we look forward to every year is the release of the DFA Matrix Book.

For those who are not familiar with it, this compendium of returns data goes back as far as 1926 and covers more than 60 different indexes and asset classes. Also included are allocation breakdowns among the different benchmarks used in a dozen of DFA's index wealth model allocations. Like the IFA Index Portfolios, these models track more than 13,000 stocks across 40-plus countries. 

Starting from an index's initial full-calendar year worth of returns, the book is organized into triangular matrices, which enable us to quickly find the historical annualized average rate of return.

For example, we can determine that the S&P 500 Index had an annualized return of 10.6% from 1970 through 2019 by simply looking along the triangle's top row marking the first year, then going down that column to the end date.

With such a clever layout, we find the Matrix Book even easier to track returns over longer periods than working off a standard returns spreadsheet generated by Excel or some other financial program. 

Still, one may ask: "Why in this age of ubiquitous computers, would we need a book of returns calculations?"

Good question. The answer is simply that this book allows us to see the returns from a holistic point of view -- i.e., one we just can't get from a computer screen, especially not from a smartphone screen. For instance, it's possible to quickly determine that no matter how bad of a slump took place in the S&P 500, an investor's perception of such a period's aftereffects on a portfolio were probably worse than the real results. 

Using the book's grid, we can immediately find 1929's S&P 500 negative return marked in red. By glancing down at the string of red returns, which goes unbroken until 1936, it quickly becomes apparent that the Great Depression lingered through 1942. That's because of the book's color coding, easily letting us identify that while short strings of positive returns (marked in black) took place from 1936 through 1942, negative returns (on an inflation-adjusted basis) still cropped up. 

Another neat feature is that if you just want to look at a few years, you can cross-reference returns using each chart's bottom axis, then go up to the corresponding vertical axis to find a particular year's returns. Also, charts for every index on the upper right-hand side graphically display the growth of $1 from the first year considered through the last calendar period compared. 

The Matrix Book was first published in 1982, which was a year after Dimensional's launch. Its guiding vision came from one of the fund company's two original founders, David Booth. Besides a treasure trove of data, each matrix book has its own cover picture and introduction. Some of these cover pictures are shown below. For more details of each of these editions, see IFA's Book Library.

What makes it even more interesting to us is that each year, the Matrix Book features a different in-depth piece to provide greater insights into global markets. To start 2020's book, for instance, Dimensional's researchers analyze major developments in fixed-income over the past four decades. This includes a review of how dealers report over-the-counter secondary market transactions and advances in how Dimensional analyzes variable credit spreads to identify bonds with higher expected returns.  

The introduction for the 2016 book is an interview between Booth and Robert Merton, a Nobel laureate and Dimensional board member. The discussion involved a look at the professor's decorated career, the science of finance and their thoughts on what the future might hold for the asset-management industry over the longer-term.  

IFA has used the Matrix Book as a basis to build an even wider range of data for our benchmarks and Index Portfolios. In this example for IFA Index Portfolio 70, among other things, you can view monthly rolling risk-and-return data back to 1928. We've also built charts to measure different Simulated Passive Investor Experiences (SPIEs), including the ability for investors to customize periods studied. 

In our view, these latest computer-based tools don't take away from the enduring value of The Matrix Book. Such an 'old-school' presentation of returns data is an enduring concept in finance that will never become obsolete. IFA is looking forward to many more years of reading such a work and utilizing it to help our clients to reach their overarching wealth-building goals.

To better understand the intellectual and academic origins that's made Dimensional our preferred funds provider, we've compiled a number of video interviews between Booth and IFA Founder and President Mark Hebner. You can view this series by clicking here


This is not to be construed as an offer, solicitation, recommendation, or endorsement of any particular security, product or service. There is no guarantee investment strategies will be successful.  Investing involves risks, including possible loss of principal. Performance may contain both live and back-tested data. Data is provided for illustrative purposes only, it does not represent actual performance of any client portfolio or account and it should not be interpreted as an indication of such performance. IFA Index Portfolios are recommended based on time horizon and risk tolerance. Take the IFA Risk Capacity Survey (www.ifa.com/survey) to determine which portfolio captures the right mix of stock and bond funds best suited to you.  For more information about Index Fund Advisors, Inc, please review our brochure at https://www.adviserinfo.sec.gov/ or visit www.ifa.com.