If you explore the library of a major university you’ll find dozens, or even hundreds, of books on financial engineering, replete with arcane mathematics. You’ll see the same if you browse academic finance journals.
Most people think those books describe what goes on in the world of investment finance: highly sophisticated, excruciatingly technical results of great import, Einsteinian in their brilliance, accessible only to industry insiders.
And most people would assume that being able to access and employ those treasures leads those insiders to inspired, mathematically driven investment methodologies and vast wealth.
They’d be wrong.
Most professionally managed investment funds — of late, upward of 90 % — do not outperform a simple stock market average, easily investible via an index fund. And because outperformance seems to occur randomly, it is impossible to predict which ones will occasionally outperform.
Yet these professional funds are managed by the same people who read, write, and converse in the language of those journals. And some of the language used in those books and papers — terms like “excess return” and “return bonus” — seems to imply that by applying these theories, you’ll get a substantial boost in your investment returns.
How is this possible?
Virtually all of this mathematical theory rests on the bedrock assumption of efficient markets. Fundamental to that assumption is that you can’t beat the market except by random chance. Therefore, the math can only tell you the odds of getting one return or another — not how to beat those odds.
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This is similar to the theory of gambling. Other than in very rare cases — like a game of blackjack when the decks haven’t been shuffled enough — there’s no way to beat the laws of chance over time. But you can still develop plenty of mathematical theory about it.
That’s the way the laws of probability were first derived in the 17th century by great mathematicians like Blaise Pascal and Pierre de Fermat: They began with gambling problems, working until they could derive probabilities for such events as throwing 10 sevens in 20 tosses of a pair of dice, or of drawing a full house in a five-card poker draw.
None of that can tell you how to beat the house in a long-run game of craps.
Similarly, none of the complicated mathematics in the finance books and journals tells you how to beat the market — even if the articles and books have a bad habit of implying, in their English language passages, results that aren’t actually in the math. (That’s how you get terminology like “excess return” and “return bonus.”)
You don’t have to look far to see where the motivation for this language lies. Many of the authors and readers of these arcane publications are either employed by or retained by richly paid investment management and consulting firms.
The habit — indeed the requirement — in those firms is to use language that gives clients the impression that they can greatly improve their investment results. This is called “marketing language,” but it unfortunately sometimes trickles into the technical books and journals.
In most cases, the math in those books and journals is not good math. While real math is painfully precise, Ph.D.s in financial engineering too often don’t state what they are trying to prove precisely enough, taking liberties when they give their English language version of it.
In other words, while they use terms that suggest they’ve proved mathematically that there’s a way to beat the market, they haven’t. Their “genius” lies in using what looks and feels like hard math, but facilitating its interpretation in misleading ways.
Let’s take an example. Researchers at a major university’s business school performed a study in which they “randomly” generated investment portfolios, finding that all of their random portfolios beat the market. The result, predictably, attracted media attention, but it was absurd.
The researchers, whose study was funded by a company that earns large consulting fees by trafficking in the arcana of academic finance, didn’t take random samples of actual portfolios which, if combined, would equal the total market. Instead, they took random samples of individual stocks, combining them into portfolios in which the stocks were — arbitrarily — weighted equally.
All together, their portfolios represented only a minuscule fraction of the whole market, one far more volatile than the market itself. Therefore, in some time periods they will far underperform the market, and in others they will far outperform it.
The researchers never made clear that “random” is a mathematical term that can be defined in many ways, nor did they explain why they chose the definition they did. This is typical of failures in academic finance. No one in the field seems to notice, because they are mesmerized by the superficial complexity of the math — and well-paid by others who are.
Investors, however, shouldn’t be mesmerized, and they should be wary of advisers and investment managers who are — and who believe they should be, too. It is for another column to explain why this is true: but if you avoid them and their fees, you will have 80 % more retirement income than if you do.
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Economist and mathematician Michael Edesess is chief investment strategist of mobile financial planning software company Plynty and a research associate of the Edhec-Risk Institute. E-mail him at [email protected] Follow him on Twitter at @MichaelEdesess.