Revenge of the Matrix
Ross M. Miller
Miller Risk Advisors
November 13, 2006
[This commentary appears in the
of Financial Engineering News.
This is the raw, unedited version of that commentary.]
The Marty McFlys among the FENews readership
might imagine that if they hopped into their De Loreans, set the dial back
30 years to 1976, and rocketed to Harvard Business School (HBS) that
everyone would be buzzing about option pricing theory and all that it
might do to change the world. Well, I was there, at least when was I not
hanging around the economics department and law school, so if options were
among the things of which the news had come to Harvard, very few people
talked about them. Management consulting attracted all the buzz and it was
the chosen career path of most Baker Scholars, including future CEOs
Michael Carpenter (Kidder, Peabody) and Jeffrey Skilled (Enron).
Finance never goes entirely out of fashion, but it was
the skinny tie of the late 1970s. Financial deregulation, stagflation, and
a moribund stock market restricted the flow of new blood into Wall Street,
so the world would have to wait almost ten years for the seeds of the
financial revolution planted in the early 1970s to bear fruit. Calculus
was over the heads of many business school students and faculty, and so
the stochastic variety was out of the question. Matrices, however, were
hot stuff. But any old matrix would not do.
Bruce Henderson, who nearly graduated from HBS (like
Bill Gates over at Harvard College, he was distracted by business
opportunities and never felt the desire to complete his degree), got the
matrix ball rolling. I met him when he came by to give one of his regular
guest lectures and to distribute literature on his matrix and the company
that he founded to spread the word about it, Boston Consulting Group (BCG).
Henderson's matrix, commonly known as the growth-share
matrix, is would not be at home in most linear algebra courses. For one
thing, it doubles as a home for domesticated animals. Like the many
competing management matrices inspired by it, this matrix is nothing more
than a hunk of two-dimensional space upon which circles of various sizes
representing a company's businesses or products reside. Exactly where a
product sits in the matrix depends on its market share (the horizontal
axis) and its growth rate (the vertical axis). To add to its esoteric
nature, the horizontal axis runs from high to low as one goes from left to
Both market share and growth rates are intrinsically
fuzzy concepts unsuited to deterministic quantification. Market share
critically depends on how one chooses to define a product's market. Many
an antitrust suit has hinged on just such a definition and an entire
segment of the management consulting industry grew up around the idea that
businesses should know what market they were really in. (You're not in the
publishing business. You are in the information business. My invoice for
$2 million is in the mail.) As for a product's growth rate, especially one
that pretends to look forward, feel free to pick a number, any number.
Considering the numerous judgment call requires to construct a
growth-share matrix, one can see why a team of consultants with the proper
training and pedigrees is highly recommended.
It was obvious during the days of disco that the best
product to have in your business portfolio was one with both high market
share and high growth potential. These products were called
"stars." In the best of all possible worlds, all your products
would be stars. Of course, such a business would feel no need for strategy
consultants. Through the marvels of synergy, however, one could get
something almost as good as a star by combining a low-growth,
high-market-share product that throws off lots of cash (the cash cow) with
a high-growth, low-market-share product with the potential to become
tomorrow's star (the question mark). What remains, then, are the products
with little in way of either market share or growth potential. Such sad
products were originally known as "dogs," but radical
revisionists have reportedly renamed them "pets."
If all of this seems vaguely familiar, it is because
this analysis is a form of modern portfolio theory that has been seriously
lost in the translation to strategic analysis. Dashes of Harry Markowitz
can be seen with appropriate magnification, but traces of the late
professors Franco Modigliani and Merton Miller do not even appear at the
quantum level. For one who lives in a world with anything resembling
well-functioning capital markets, keeping a herd of cash cows is
unnecessary and generally inefficient. Of course, if the capital markets
of the 1970s had functioned well, many of the business school students who
went into consulting might have chosen to become investment bankers
instead, which is exactly what they did once the 1980s were in full swing.
Indeed, many stars of the management-consulting world, such as the two
examples mentioned above, would depart consulting as soon as the window to
the financial world opened.
Healthy financial markets, replete with junk bonds and
venture capital, had the effect of collapsing Henderson's matrix to the
single dimension of market share. Jack Welch, who had been one of BCG's
biggest clients, would come to champion the belief that size was all that
mattered. Market dominance, however defined, leads to pricing power, and
outsized profits (as well as the occasional anti-trust suit) would
The matrix itself did not die, but was repurposed as
Morningstar's "style box." In an attempt to disguise its
origins, it has been both transposed and flipped. Market share is now
market capitalization and low-growth has been euphemized as value. This
neomatrix still applies to a portfolio, which now consists of securities,
not products or businesses. What has not changed is that the matrix is
still imbued with a healthy dose of arbitrariness.
The nice things about financial concepts like beta,
volatility, and duration is while they are abstractions, real-world
versions of them can be derived directly from market-based price
information. Moreover, they do not require that one trust either a
corporation or its accountants to produce a value for them.
Market capitalization seems straightforward—just take
a stock's price and multiply it by the number of shares outstanding and
there you are. The only problem, and admittedly it is rarely a big one, is
determining what does or should count as equity.
Growth vs. value, however, is more problematic. The
standard procedure is to combine the price/earnings and price/book value
ratios for a company into a single measure of value. Unfortunately, even
under Sarbox, both a company's earnings and its book value are subject to
The irony of the Morningstar matrix is that, as
documented by Eugene Fama and Kenneth French and confirmed by recent
history, the sector of the matrix formerly known as dogs is now home to
what have become some of the hottest investments, small-cap stocks.
Whatever misspecification may lurk in the Fama-French model and its many
relatives, something along the lines of size and value appear to be
important factors for determining the returns of equity investments,
particularly at the portfolio level.
Harvard Business School did leave a lasting mark on
finance in the late 1970s involving a matrix of sorts, one dreamt up by
HBS student Dan Bricklin and became VisiCalc. That spreadsheet program
first ran on the Apple II computer, the hot toy at HBS in 1977. That
computer, its inventor, and its intimate connection to option valuation
are the focus of the next Capital Notions.
Copyright 2006 by Miller Risk Advisors and Financial