The Limits of Investment Math

Genius Failed Famously, Sir Isaac Newton lost nearly his entire net worth--20,000 pounds, equivalent to about $4 million in today's U.S. dollars--investing in one of the earliest stocks available. The South Sea Company was granted a monopoly by the British Crown in trade with Spanish South America in exchange for assuming the country's war debt. Newton profited initially but kept buying on the way up, as the stock appreciated sharply, which cost him dearly when the shares collapsed to their original price.

Newton’s response, “I can calculate the motions of heavenly bodies, but not the madness of men,” tells half the story. Yes, investor irrationality does not lend itself to mathematics. Newton could not measure the temporary sanity of those who bought South Seas shares. But his math challenge went deeper than that. He also had no tools with which to gauge South Sea’s business prospects. The calculus solves many problems--but not that of estimating how much trade will be generated with the colonies of an opposing superpower.

Thus, he could just as well have said, “I can calculate the motions of heavenly bodies, but not the profits of emerging ventures.” (Just as well that he didn’t, because nobody would have remembered such a dull quote.) In other words, Newton would have been no better than the rest of us at understanding how Apple will fare under Tim Cook.

Where Math Matters To be sure, being very good at math is required for several investment fields.

One is arbitrage--judging if a cheaper alternative can be substituted for an existing investment. Because the latter is a precisely known quantity, in the sense that its price is perfectly understood (whether that price is ultimately reasonable is beside the point; all that matters is how the security is currently valued), it is a matter of calculation to determine if the substitute is a better bargain. The computations can get complex indeed for derivatives, which is why Nobel Prizes were awarded to those who solved the code for options pricing and why the big banks hire bushels of quantitative Ph.D.s each year, but math it is.

Another field is trading. This subject, admittedly, I know very little about, as the mutual funds and exchange-traded funds that comprise my field hire few such experts. But I have met those who work at specialized trading firms that buy and sell securities for their own accounts, and the first thing those companies do when hiring, before even an interview, is test their prospective traders on a series of mathematical puzzles. The math is not of a high level, but getting correct answers requires an agile mind. Those who are not unusually adept with numeric patterns are rejected.

Finally, there is the growing field of data mining--or, as those practitioners would have it, evidence-based research. As each year passes, investment databases and computational powers grow larger, which permits deeper, more-complex searches through the historical records, seeking investment "factors" that appear to have been successful. This is the hunting ground of finance and economics Ph.D.s. The math required to sift through these reams of data is not novel, but it is a specialized skill. Ordinary mortals need not apply.

And Where It Doesn't (Much) But none of these endeavors would seem to matter to us, the long-term investor. We neither arbitrage nor day-trade, and while we might very well purchase the outputs of the evidence-based researchers, in the form of "strategic beta" ETFs (or even as aspects of traditional, actively managed mutual funds), we don't create those funds ourselves. Math does little good in judging the claims of ETF providers. The critical item is judgment--understanding when the reputed investment factors might be economically grounded and thus sustainable, as opposed to when they were accidental and do not figure to repeat.

For us, too much math can be a drawback. It can mislead.

Consider, for example, the (true) case of the emerging-markets stock fund manager who approached Morningstar, hoping to be selected for the company’s 401(k) plan. That manager presented to the committee a grand, quantitative plan for how the fund allocated its assets among the different countries. Unfortunately, the process was highly sensitive, in an unpredictable way, to small changes in investment inputs. The system was a giant “black box,” as the nomenclature goes. Morningstar took a pass, its analysts having seen the havoc wrought on other funds by black boxes. A few years later, that fund was shut down.

Then there was the case of the quantitative researcher who found a better way to “optimize” a basket of stocks, by using a new technique to “smooth” the problems that occur from mathematical routines that assume 100% data precision but use estimates of future market occurrences that are anything but guaranteed. The new process found that the ideal large-cap stock portfolio would have 8% of its assets in AOL, as opposed to 13% under the previous method. The actual best weighting was nothing at all, this being 1999 and AOL being the modern version of South Sea shares.

Or, more recently, there are the “efficient frontier” portfolios built and sold by one of the nation’s largest brokerage firms. Among the funds used in those portfolios is a short-term bond fund that is coded as being more volatile than all but the riskiest of stock funds--an error term of 40-fold. Such “garbage in, garbage out” results are common when the focus becomes the (alleged) sophistication of the portfolio-creation schemes, rather than the basics of finding the best possible building blocks and acknowledging that combining those blocks is far from an exact science. Or, perhaps, a science at all.

Sir Isaac Newton’s South Seas debacle is typically told as a parable of the dangers of market manias, which can consume even the brightest of investors. That is true. However, Newton’s South Seas adventure also illustrates another, less commonly acknowledged point: Many critical investment questions cannot be solved by math. And devoting too much attention to matters quantitative, while giving insufficient attention to issues such as judgment and data quality, can be outright harmful to portfolio results.

John Rekenthaler has been researching the fund industry since 1988. He is now a columnist for Morningstar.com and a member of Morningstar's investment research department. John is quick to point out that while Morningstar typically agrees with the views of the Rekenthaler Report, his views are his own.