“‘Bomb patterns?’ General Peckem repeated,
twinkling with self-satisfied good humor. ‘A bomb pattern is a term I dreamed
up just several years ago. It means nothing, but you’d be surprised at how
rapidly it’s caught on. Why, I’ve got all sorts of people convinced I think
it’s important for the bombs to explode close together and make a neat aerial
photograph. There’s one colonel in Pianosa who’s hardly concerned any more with
whether he hits the target or not.’” Catch-22, Joseph Heller
Like the top officers in Catch-22, the leading thinkers in the financial industry
have long used the elegance of statistics – specifically, standard deviation as
a measure of volatility – to frame the definition of risk. It worked so cleanly
on the blackboards of academia that it just had to be used in the
boardrooms of America.
There was only one problem.
The theory was wrong.
To paraphrase our friendly physicist Richard Feynman, “a guess
that is wrong is wrong, no matter how elegant, no matter who made it.”
And
that’s a problem for 401k plan sponsors who rely on the investment industry to design menu options and advise
participants. More importantly, if the old paradigm is dead, what new paradigm
has replaced it? To begin to answer this question, we need to get a better idea
of how this problem started in the first place. It begins with a familiar
phrase, one that launched the advent of Modern Portfolio Theory (MPT) in the
1950s: “Risk and Return are related.” This is the relationship Harry Markowitz
famously wrote of in his groundbreaking treatise “Portfolio Selection” (Journal of Finance,
1952) even before Bill Haley and the Comets took their turn rocking around the
clock.
Oh,
those were happier days back then, the greatest generation having just won
World War Two, the same “good war” Heller would reference a generation later.
The big theme of the Allies’ success in the second World War revolved around
such words as “logistics” and “operations.” Everything was reduced to numbers,
and, with the world about to be thrust into the Sputnik Era, it didn’t take
much to transfer portfolio management from a droll accounting exercise to a
formula-laden scientific enterprise.
As we all know, formulas (or “formulae,” for those who have been
blessed with an education in the Latin language) contain, in addition to
various mathematical operands, loads of numbers and variables (variables being
merely numbers in disguise as letters). Everyone could easily pick out the
number we needed to use for “return,” but folks had a devil of a time
identifying the right number to use for “risk.” Finally, Markowitz discovered
the solution.
But computers back then weren’t powerful enough
for him to use it, so he had to settle on standard deviation. (William Sharpe,
who along with Markowitz would late win a Nobel Prize for their work on MPT, in
his own seminal paper, admits (albeit in an obscure footnote hidden deep in the
article) “Under certain circumstances, the mean-variance approach can be shown
to lead to unsatisfactory predictions of behavior. Markowitz suggests that a
model based on the semi-variance would be preferable; in light of the
formidable computational problems, however, he bases his analysis on the
variance and standard deviation.” (Sharpe, W.F., Capital Asset Prices: A Theory
of Market Equilibrium under Considerations of Risk, The Journal of Finance, Volume 19, Issue 3,
September 1964, 425-42))
There you have it. From the beginning we understood the lower
partial moment (i.e., that part of the standard deviation below the mean) was a
better measure for risk than standard deviation. Standard deviation equates
missing the goal at the same level of risk as surpassing the goal. Using the
full standard deviation didn’t make sense to Markowitz at the time (and
presumably still doesn’t), but, computers being what they were back then, was all
he could settle for.
Soon thereafter, standard deviation became the universal
measure of “risk.” Eventually, it found its way in portfolio optimization
programs. You know these, don’t you? These are the programs they use to
determine a recommended asset allocation. Are you starting to connect the dots
here? Do you begin to see why so much we see in the financial industry is
defective? It’s because academia and industry have constructed the main
apparati (happy, Latin lovers?) based on a flawed theory.
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