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The Limits of Investment Math

For long-term investors, knowing higher math isn’t necessarily an advantage.

John Rekenthaler, 01/31/2017

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.

is vice president of research for Morningstar.

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