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):

As I see it, the economics profession went astray because economists, as a group, mistook beauty, clad in impressive-looking mathematics, for truth. Until the Great Depression, most economists clung to a vision of capitalism as a perfect or nearly perfect system. That vision wasn't sustainable in the face of mass unemployment, but as memories of the Depression faded, economists fell back in love with the old, idealized vision of an economy in which rational individuals interact in perfect markets, this time gussied up with fancy equations. ... [The central cause of the profession's failure was the desire for an all-encompassing, intellectually elegant approach that also gave economists a chance to show off their mathematical prowess. -- Paul Krugman, "How Did the Economists Get It So Wrong?", New York Times, 2 Sep 2009, from Article

The complete list of quotes is available here.

General information

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Acknowledgement of support

Prior to his recent retirement, Bailey's research was 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.

Online demonstration tools

We operate two online tools 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:

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) 2016. All rights reserved.

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For some recent news articles in the general area of mathematics, computing, science and finance, 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:

Press reports

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: