Genuine Math for the Investment Industry
Objective Data Plus Defined Purpose
On January 26, 2026, Advisor Perspectives – an online newsletter for registered financial advisors, published an article by Michael Edesess titled Sham Mathematics in the Investment Industry. These subject hits home. Not only do we use quantitative evidence to make investment and cash flow strategy decisions, but we also reject the industry methods that are not objectively proven.
The purpose of this brief essay is to identify the claims of the author that are relevant to The Moneyball Method. Identify the claims that are relevant to the traditional practices of the investment advice industry. And identify the claims that support or contradict the philosophy and process of Objective Investing.
The first five paragraphs do not help much. They address the intellectualism of the author: “I have a PhD in pure mathematics. My doctoral dissertation was in stochastic processes, on Brownian motion.” And they introduce a fascinating book idea to support the article’s theme, Lecturing Birds on Flying: Can Mathematical Theories Destroy the Financial Markets? by Pablo Triana. And with paragraph six, we finally get somewhere, starting with Modern Portfolio Theory (MPT):
Markowitz’s algorithmic solution to the quadratic programming problem, which arose from his need to maximize expected return for a given level of variance, is probably the best piece of mathematics in the history of the industry. But don’t get too excited about it: Despite its elegance, other algorithms that solved the same problem were already available.
So far, we have concurrence with The Moneyball Method and a tacit endorsement of the elegance of markets - which happens to be the title of Chapter Three. The next two investment industry standards in Edesess’ article are two methods for calculating expected rates of return and options contract pricing based on assumed risk, the Capital Asset Pricing Model (CAPM) and the Black-Scholes-Merton formula (BSM):
Sharpe’s 1964 CAPM paper, for which he was awarded the Nobel Prize, uses no mathematics at all, unless you consider its reliance on a two-dimensional graph for its argument mathematics. The Black-Scholes formula depended on the solution to the heat equation, a partial differential equation that was solved by Joseph Fourier more than 200 years ago.
In other words, there is no “sham mathematics” in the Markowitz, Sharpe, or Merton standards, only posturing by Edesess: “None of these would have survived a peer-review process if submitted to a mathematics journal, with the possible exception of Markowitz.” As the Meatloaf classic satirizes, Two Out of Three Ain’t Bad, so where’s the beef?
This is where the article becomes interesting and useful: the conflict surrounds abnormal distributions of investment returns, the impossibility of predicting future volatility, and the impact of extreme market events. Not only does Edesess challenge the premise of normal distributions in Pablo Triana’s book, but he also drags Nassim Taleb into the mix because Taleb was a source and endorser for Triana’s book:
These errors highlight the fact that much of Taleb’s and Triana’s critiques of financial mathematics are criticisms of the fact that it doesn’t account for “fat tails” — the more-frequent-than-expected outliers that are neglected by the normal distribution, which Taleb dubbed Black Swans. It’s true that this is an important omission in much financial theory, but it doesn’t apply to Markowitz or Sharpe.
Apparently, it is not the mathematics with which Edesess has a problem, but the subjective bias of the users of the software that processes the algorithms:
Markowitz’s mean-variance analysis has no meaningful practical application, except for snowjob purposes. It suffers, most importantly, from a fatal garbage-in-garbage-out problem. This is now widely known. For example, it has been highlighted by William Bernstein in articles and books, among many others.
Readers of The Moneyball Method may recall several important references to Taleb, but the link above to Bernstein’s article is a strong echo of my warning about the widespread misuse of modeling software to predict economic outcomes, financial markets and climate change:
In the case of MVO, because the algorithm’s outputs are exquisitely sensitive to its inputs, changing an asset’s estimated or historical return by a percent this way or that leads either to its dominating the portfolio or disappearing entirely from it.
“Changing an asset’s estimated or historical return” is precisely what every investment firm and software firm does with their capital market assumptions. In my book, I categorize these as forward-looking projections, conservative assumptions, recent history, and regime-based predictions that are useful to no one. And Bernstein and Edesess take their critique to include Value at Risk methods:
Similarly, the inadequacies of VaR’s underlying historical database rendered it worse than useless during an honest to God meltdown.
A reliable “underlying historical database” is precisely what every asset allocator using small and alternative categories is lacking – and The Moneyball Method eliminates those potential assumption errors. What we have with the Sham Mathematics article has little to do with mathematics, but everything to do with the subjective inputs and limited historical databases. In addition, the author makes what I believe to be the prize observation about the futility of predicting the future:
In order to price an option, you have to input to the formula a sigma, that is, the expected future volatility of the underlying asset. This might be OK if there were a reliable estimate of that number.
The future volatility of a stock is not knowable, just like the actual return of that or any other stock is not knowable. Innovation and competition are a function of free will and ingenuity and human potential defies mathematical modeling. And regarding MPT, expected return and standard deviation are two of the three attributes that define entire asset classes.
In summary, the only reliable assumptions are those from broad-market asset classes with the most long-term price histories. Yet Edesess blames MPT, CAPM and BSM for financial market meltdowns, not the fallacy of using them to predict the future:
The “portfolio insurance” crash on Black Monday, October 19, 1987, was the result of the belief by creators of portfolio insurance that markets would move continuously, as was assumed by the BSM model. When they moved in jumps on that day, creating a cascade of sales, a crash occurred.
Yes, “portfolio insurance” drove the program trading volume that contributed to a historic market meltdown of almost 23%. I was there – a rookie financial advisor with a major Wall Street brokerage office, the tape was more than two hours behind, and no one knew where the Dow Jones was priced, except one guy. The broker who specialized in futures trading.
But money isn’t stupid, markets are efficient, and there were other reasons for the sell-off including failed currency manipulation schemes amid rising interest rates that metastasized over the weekend. On top of that, the House Ways and Means Committee had introduced a bill that reduced the tax benefits of leveraged buyouts - further restricting the free flow of capital. I asked my congressman about that the next week during a local Chamber of Commerce meeting, but he was totally unaware.
I was also there for the Dotcom crash of 2000-02, but it wasn’t until the Great Recession of 2007-09 that I began to understand the nature of markets and the most reliable ways for individual investors to live and enjoy the confidence of true wealth management.
This essay concerns many technical aspects of financial markets and investing, but they are of secondary importance. First, we must gain respect for money, prices, markets and profits - and then focus on what we can control - the goal and aspirations that require money and make life worth living. That is what it means to be an objective investor.