Mathematicians Against Fraudulent Financial and Investment Advice (MAFFIA)
- Three MAFFIA papers are on SSRN's Econometric/Math Methods All Time Top Ten list. The Social Science Research Network's Econometrics: Mathematical Methods and Programming eJournal distributes working and accepted paper abstracts in the area of mathematical methods applied to econometrics. In SSRN's list as of 6 June 2015 of the All Time Top Ten papers (by download count), three papers from this list, namely #5, #7 and #10, are authored or co-authored by members of our MAFFIA research group. For details, see the Math Investor blog.
- Backtest overfitting demonstration is now available. An online simulator is now available to demonstrate the effects of backtest overfitting. The simulator "discovers" an "optimal" strategy, based on a computer search over backtest data, yet when this "optimal" strategy is tried on new data, it typically falls flat. The intent here is to demonstrate how easy it is to statistically overfit an investment strategy.
- Tenure-maker overfitting demonstration is now available. A related online demonstration, named the Tenure-maker, extends the demonstration of backtest overfitting to more general strategies.
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):
About H.E. Smith: In the book "Elementary Number Theory" (Chelsea, New York, 1958. An English translation of vol. 1 of the German book Vorlesungen ueber Zahlentheorie), p.31, the author, Edmund Landau, mentions the question whether the infinite series $\sum \mu(n)/n$ converges (TEX notation; \mu is the Moebius function). After giving a reference to the answer in Part 7 of the same V.u.Z, and without saying what the answer is, Landau writes: "Gordan used to say something to the effect that 'Number Theory is useful since one can, after all, use it to get a doctorate with.' In 1899 I received my doctorate by answering this question." -- This is taken from Alexander Macfarlane, Ten British Mathematicians of the Nineteenth Century, 1916, pg. 63-64. A copy of the book is available on the Project Gutenberg website: Gutenberg
The complete list of quotes is available
This website is operated by
- David H. Bailey, Lawrence Berkeley National Laboratory (retired), and Research Associate, University of California, Davis, Department of Computer Science.
- Marcos Lopez de Prado, Senior Managing Director, Guggenheim Partners, New York City; also Research Affiliate, Lawrence Berkeley National Laboratory.
- Qiji Jim Zhu, Professor of Mathematics, Western Michigan University.
Please send any comments or questions for this site to:
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.
For full details, PLEASE READ this disclaimer and copyright notice.
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:
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)