The Mistress of Investment Management
Until a few years ago, applied mathematics had a very limited role in the financial profession. Standard applications involved pricing of derivative products and convex portfolio optimization. But with the advent of High-Frequency Trading and Big Data, Mathematics is now pervasive. Today, virtually every investment decision requires the analysis of massive amounts of unstructured data. Algorithms must be developed to order, filter, process, store, visualize that data. And that is before we are ready to model it! Networks must be designed to handle flows of information from multiple sources of varying quality. Optimization methods are needed to find solutions in real-time.
It would seem as if these were great days for being a Financial Mathematician. Unfortunately, that is far from being the case. As Mathematical knowledge makes its way through Wall Street, so does its misuse and abuse. C.F. Gauss (1777–1855) once famously said that Mathematics is “the Queen of the Sciences.” Profiteers would rather make her the “Mistress of Investment Management.”
Last October, Sir Andrew Wiles alerted the Mathematical profession that Financial greed “threatens the good name of Mathematics”. Customers and investors are marketed financial products as scientifically sound or mathematically proven, a situation we have highlighted through our group, Mathematicians Against Fraudulent Financial and Investment Advice (MAFFIA). Many savers, retirees and investors trust these outrageous financial claims because, they believe, if they weren’t true, Mathematicians would have challenged them.
Mathematical Fraud
One prominent example of this abuse is found in the practice of “backtest overfitting.” A backtest is the historical simulation of an investment strategy’s performance. That performance is contingent on a variety of parameters, such as when to buy or sell securities. These parameters can be optimized to maximize the backtest’s performance. The problem is, the more we associate the behavior of the strategy to past performance, the less able it becomes to capture future investment opportunities. This situation is analogous, however different, to overfitting in regression analysis.
As we have explained in this paper, backtested results are meaningless unless financial analysts disclose the number of trials involved in identifying the investment opportunity. If someone flips a coin enough number of times, at some point he will get ten straight tails. If that coin-flipper hides the fact that it took him over a thousand trials to achieve this result, he may try to mislead us into believing that the coin is unfair. In Finance, backtest overfitting is the analogue to hiding trials in Pharmaceutical Research: Only outstanding results are presented to investors.
Our responsibility
We Mathematicians tend to be naive about the implications of our work. G.H. Hardy (1877-1947) took comfort in the belief that he had not discovered anything of practical application:
“No discovery of mine has made, or is likely to make, directly or indirectly, for good or ill, the least difference to the amenity of the world.” [G.H. Hardy, A Mathematicians Apology, 1941]
He was proven wrong shortly after, when much of his work unexpectedly found applications in many branches of science. What Mathematicians do has the greatest of impacts in the world. If we do not make an effort to communicate our ideas clearly, others will misuse them and take advantage of our good name, as Sir Andrew has pointed out. If we do not speak out, we risk losing the next generation of Mathematicians.
What can we do?
The good news is, we are not alone. In fact, many people in Finance want to do the right thing, putting back some honesty in numbers. The International Association for Quantitative Finance and the Thalesians are two leading Quantitative think-tanks. The former counts with 7 Nobel prize laureates in Economics among its fellows, and the latter coordinates a growing and active community of applied mathematicians working in Finance. Last Monday, January 13 2014, both organizations held a joint seminar to discuss what may be the most common form of Mathematical fraud: Backtest overfitting.
A record number of attendees showed up to this event, held at New York University’s Kimmel Center. Questions were incredibly profound and technical, evidencing that people had made an important effort in understanding the above cited papers. What was scheduled as a one hour presentation lasted for over two hours. Many of the attendees stood up for the entire length of the presentation. It was a very encouraging experience. While there may be no silver bullet to correct this problem, just raising awareness of this issue could prevent some damages.
Very little effort could take us a long way. If you believe that something should be done about protecting the good name of Mathematics, please spread the word, or even better, join the MAFFIA!