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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 |

**NEW!**An online tool is now available to demonstrate the effects of backtest overfitting. Click HERE for details.

- 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:

- 27 Jan 2015: Priyanjana Bengani, a writer for the publication
*Automated Trader*, discussed our paper Pseudo-mathematics and financial charlatanism at length, with comments by several analysts. Bailey was quoted saying, "when a statistical test is applied multiple times, the probability of obtaining false positives increases as a function of the number of trials." Lopez de Prado added, "A backtested strategy is doubly questionable if the time period covered by the backtest is not truly representative of what can be expected in the future." - 04 Dec 2014: Shawn Langlois, a MarketWatch.com columnist, quoted from our article How have 2014 market prophets fared in his column This 'hideously expensive' market has given the 'show horse' pundits fits.
- 03 Dec 2014: Brett Steenbarger, author of several books and a news column on market trading, mentioned our article How have 2014 market prophets fared in his article Do market prophets bring market profits? Steenbarger lamented that "the performance of funds has largely fallen short of benchmarks; the doomsayers have brought doom to their followers; and even those forecasters who beat the market over a prior ten year period are likely to underperform the following year."
- 30 Oct 2014: Michael P. Regan, columnist for
*Bloomberg News*, commented on our research in his article Beware Overfitting Models Even if They Win Baseball Bets. He mentioned our paper Statistical Overfitting and Backtest Performance and our new online tool demonstrating backtest overfitting. - 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.

For other current news in the area of financial mathematics, see the Mathematical Investor news column. This listing is updated frequently.

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