Mathematicians Against Fraudulent Financial and Investment Advice (MAFFIA)
This site was created out of growing concern with the usage of less-than-fully rigorous mathematical and statistical methodologies in the financial/investment world. One example is the increasing prevalence of backtest overfitting, due in part to the ease of generating large numbers of model variations (more than statistically justified) using modern computer technology. Indeed, such statistical errors are likely the primary reason that investment strategies which look good on paper often fall flat in practice.
We are also concerned with the proliferation of quasi-mathematical investment advice and financial columns in the past few years, which appear to be based on sophisticated mathematics and statistics, but which, upon more rigorous analysis, are at best questionable. We encourage the reader to search the Internet for terms such as "stochastic oscillators," "Fibonacci ratios," "cycles," "Elliot wave," "Golden ratio," "parabolic SAR," "pivot point," "momentum," and others in the context of finance. Although such terms clearly evoke precise mathematical concepts, in fact, in almost all cases, their usage is at best scientifically unsound.
Historically scientists have led the way in exposing those who utilize pseudoscience to extract a commercial benefit. Even in the 18th century, physicists exposed the nonsense of astrologers. Yet mathematicians in the 21st century have remained disappointingly silent with the regards to those in the investment community who, knowingly or not, misuse mathematical techniques such as probability theory, statistics and stochastic calculus. Our silence is consent, making us accomplices in these abuses.
This blog and website were established with these concerns in mind. Nonetheless, our approach here is not one of confrontation, but instead one of research to better understand and mitigate these difficulties, education to assist other professionals in the field, together with unbiased testing and analysis. If you identify with our concerns, let us know and spread the word. Together we can make a difference. Contact us at
Consider also joining our MAFFIA-News email list, to receive notices of articles, blogs and other items of interest to the financial mathematica arena (low frequency -- just one post every week or two). Just send us your Google-registered email address. To register a non-Gmail address with Google, go to the Google account page, then click on "I prefer to use my current email address."
<== This graph shows the trade-off between the number of trials N and the minimum backtest length needed to prevent spurious strategies to be generated with a Sharpe ratio in-sample of 1, when the underlying data has mean zero. Here "backtest" means the usage of historical data to judge the performance of an investment strategy, and "Sharpe ratio" is a widely used measure of investment portfolio performance. For instance, if only five years of daily data are available, no more than 45 independent model configurations should be tried. One implication of this data is that a backtest which does not report the number of trials N used to produce the selected configuration makes it impossible to assess the risk of overfitting. For details, see our paper Pseudo-mathematics and financial charlatanism: The effects of backtest overfitting on out-of-sample performance.
Quote of the day (refresh browser to select another):
Now that we can stand back from the story, the birth of our modern number-system [in 4-5th Century India] seems a colossal event in the history of humanity, as momentous as the mastery of fire, the development of agriculture, or the invention of writing, of the wheel, or of the steam engine. -- Georges Ifrah, The Universal History of Numbers: From Prehistory to the Invention of the Computer, translated from French, John Wiley, 2000, pg. 346.
The complete list of quotes is available
- NEW! An online tool is now available to demonstrate the effects of backtest overfitting. Click HERE for details.
This website is operated by
- David H. Bailey, Lawrence Berkeley National Laboratory (recently retired); University of California, Davis, Department of Computer Science.
- Jonathan M. Borwein, Laureate Professor and Director, Priority Research Centre for Computer-Assisted Research Mathematics and its Applications (CARMA), University of Newcastle, Newcastle, Australia.
- Marcos Lopez de Prado, Senior Managing Director, Guggenheim Partners, New York City.
- Qiji Jim Zhu, Professor of Mathematics, Western Michigan University.
Please send any comments or questions for this site to:
Recent press reports:
For additional press reports, see the Press reports page.
- 28 Jun 2014: Jason Zweig, columnist for the Wall Street Journal, commented our our research in his article Huge Returns at Low Risk? Not So Fast. He first mentioned two humorous examples of investment strategies that would have been hugely successful if implemented over the past 20 years or so, but only by statistical accident. Then in reference to a recent claim of a strategy that has a "100% ... probability of outperformance," he quotes one of us as responding, tongue in check, "Popes have been trying to achieve infallibility for 2000 years, and these people have finally done it."
- 10 May 2014: John Rekenthaler, Vice President of Research for Morningstar, presented a synopsis of our "Pseudo-Mathematics" paper. He relayed our recommendation that it would "behoove the investment community to adopt a similar policy" to one now being promoted in the pharmaceutical industry, namely to make all test results public.
- 28 Apr 2014: The present authors' paper was mentioned in a Pacific Standard article by Ryan Jacobs. It quotes one of us saying, "What you end up doing is that the models that you derive or you select tend to just focus on idiosyncrasies of the data, and don't have any real fundamental forward predictive power."
- 23 Apr 2014: After the talk by Bailey and Marcos Lopez de Prado at the "Battle of the Quants" meeting in New York City in March (see below), Bailey was invited to do a video interview for Institutional Investor Journals. This video is now available online Here.
- 17 Apr 2014: The present authors were featured in a Barron's article by Brendon Conway. We were quoted as saying, "The higher the number of configurations tried, the greater is the probability that the backtest is overfit."
- 16 Apr 2014: The present authors were featured in a Financial Times article by Stephen Foley. He summarizes our paper by saying, "The authors' argument is that, by failing to apply mathematical rigour to their methods, many purveyors of quantitative investment strategies are, deliberately or negligently, misleading clients." If you cannot view the article due the pay wall, a PDF copy is available Here.
- 11 Apr 2014: The present authors were featured in a Bloomberg News article. It quotes us as saying, "We strongly suspect that such back-test overfitting is a large part of the reason why so many algorithmic or systematic hedge funds do not live up to the elevated expectations generated by their managers."
- 10 Apr 2014: The present authors' paper "Pseudo-Mathematics and Financial Charlatanism: The Effects of Backtest Overfitting on Out-of-Sample Performance" was published by the American Mathematical Society. It is available free of charge from the AMS website, or from the SSRN website (preprint version).
- 26 Mar 2014: On Tuesday March 26, 2014, Marcos Lopez de Prado and David H. Bailey, two of the bloggers on this site, jointly presented a talk How to spot backtest overfitting at the Battle of the Quants meeting in New York City.
- 16 Jan 2014: An article by Michael Oliver Weinberg at HedgeFundIntelligence.com mentions this site with the comment "we have some more intelligent colleagues with PhDs in mathematics who for sport run a website that exposes forecasters who make erroneous statistical assumptions and representations, and we tremble at the thought of falling into their cross hairs."
For other current news in the area of financial mathematics, see the Mathematical Investor news column. This listing is updated frequently.
Acknowledgement of support
Bailey's research has been supported in part by the Director, Office of Computational and Technology Research, Division of Mathematical, Information, and Computational Sciences of the U.S. Department of Energy, under contract number DE-AC02-05CH11231. Borwein's research is supported in part by MITACS, by the Australian Research Council and the University of Newcastle. Lopez de Prado's research is sponsored by Guggenheim Partners, LLC. Zhu's research is sponsored by Western Michigan University.
Backtest overfitting demonstration
An online tool is now available to demonstrate the effects of backtest overfitting.
The "Mathematical Investor" blog is now online. It contains essays, philosophical musings, and news in the realm of financial mathematics, computing and scientific research.
Books that are published by the owners of this site, as well as some others of interest in the financial mathematics and the larger arena of scientific and mathematical computing, will be highlighted in our books directory:
Jonathan Borwein leads the Priority Research Centre for Computer-Assisted Research Mathematics and its Applications (CARMA) at the University of Newcastle, Australia. The researchers in this centre are active in financial mathematics and computational mathematics in general. Here is an index to the resources at the CARMA site:
The Conversation articles
Bailey and Borwein have also authored a series of articles for The Conversation, an international forum of academic research and discussion based in Melbourne, Australia. A listing of these articles is available here:
Disclaimer and copyright
Material on this site, including papers linked to in the papers directory, articles on the blog, and software available on this site, are provided for research purposes only and do not necessarily reflect the views or policies of the respective institutions or funding agencies of the site editors. No material on this site should be interpreted as a directive to buy or sell any particular securities or to adopt any particular investment strategy, or as a forecast of future market prices or trends. Software available on this site is provided "as-is" and without any express or implied warranties, including, without limitation, the implied warranties of merchantability and fitness for a particular purpose. All material available on this site is copyrighted (c) 2014.
For full details, PLEASE READ this disclaimer and copyright notice.
Huffington Post articles
Bailey and Borwein have authored a series of articles for the Huffington Post, a very widely read online news and discussion forum based in the U.S., with over 9000 contributors and many thousands of regular readers. It was recently named the world's most influential blog/news site in an article in the U.K. Guardian. A listing of the articles by Bailey and Borwein is available here:
For some recent news in the general area of financial mathematics, see the News page:
Other Sites of interest
For a list of numerous other websites with interesting and useful information relevant to mathematics in general and financial mathematics in particular, see the Other site page:
Here are some papers on the general topic of financial mathematics, authored by the editors of this site and by others, that are deemed of interest to readers of this community:
Here are some press reports mentioning one or more of us, particularly in the realm of mathematics in general or financial mathematics in particular:
For some freely downloadable software for financial math research, see the Software page:
Here are some recent presentations by the site owners in the area of financial mathematics:
- Talks (under construction)