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Pseudo-Mathematics and Financial Charlatanism: The Effects of Backtest Overfitting on Out-of-Sample Performance

Notices of the American Mathematical Society, 61(5), May 2014, pp.458-471

14 Pages Posted: 12 Aug 2013 Last revised: 5 Jul 2015

David H. Bailey

Lawrence Berkeley National Laboratory; University of California, Davis

Jonathan M. Borwein

University of Newcastle (Australia); Royal Society of Canada; Australian Academy of Science

Marcos Lopez de Prado

Guggenheim Partners, LLC; Lawrence Berkeley National Laboratory; Harvard University - RCC

Qiji Jim Zhu

Western Michigan University

Date Written: April 1, 2014

Abstract

We prove that high simulated performance is easily achievable after backtesting a relatively small number of alternative strategy configurations, a practice we denote “backtest overfitting”. The higher the number of configurations tried, the greater is the probability that the backtest is overfit. Because most financial analysts and academics rarely report the number of configurations tried for a given backtest, investors cannot evaluate the degree of overfitting in most investment proposals.

The implication is that investors can be easily misled into allocating capital to strategies that appear to be mathematically sound and empirically supported by an outstanding backtest. Under memory effects, backtest overfitting leads to negative expected returns out-of-sample, rather than zero performance. This may be one of several reasons why so many quantitative funds appear to fail.

Keywords: backtest, historical simulation, probability of backtest over-fitting, investment strategy, optimization, Sharpe ratio, minimum backtest length, performance degradation

JEL Classification: G0, G1, G2, G15, G24, E44

Suggested Citation

Bailey, David H. and Borwein, Jonathan M. and Lopez de Prado, Marcos and Zhu, Qiji Jim, Pseudo-Mathematics and Financial Charlatanism: The Effects of Backtest Overfitting on Out-of-Sample Performance (April 1, 2014). Notices of the American Mathematical Society, 61(5), May 2014, pp.458-471. Available at SSRN: https://ssrn.com/abstract=2308659 or http://dx.doi.org/10.2139/ssrn.2308659

David Bailey

Lawrence Berkeley National Laboratory ( email )

1 Cyclotron Road
Berkeley, CA 94720
United States

HOME PAGE: http://www.davidhbailey.com

University of California, Davis ( email )

One Shields Avenue
Davis, CA 95616
United States

HOME PAGE: http://www.davidhbailey.com

Jonathan Borwein

University of Newcastle (Australia) ( email )

University Drive
Callaghan, NSW 2308
Australia
+61 2 4921 5535 (Phone)

HOME PAGE: http://www.carma.newcastle.edu.au/jon

Royal Society of Canada ( email )

282 Somerset West
Ottawa, Ontario K2P 0J6
Canada

Australian Academy of Science ( email )

Ian Potter House
Gordon Street
Acton, ACT 2601
Australia

Marcos Lopez de Prado (Contact Author)

Guggenheim Partners, LLC ( email )

330 Madison Avenue
New York, NY 10017
United States

HOME PAGE: http://www.QuantResearch.org

Lawrence Berkeley National Laboratory ( email )

1 Cyclotron Road
Berkeley, CA 94720
United States

HOME PAGE: http://www.lbl.gov

Harvard University - RCC ( email )

26 Trowbridge Street
Cambridge, MA 02138
United States

HOME PAGE: http://www.rcc.harvard.edu

Qiji Zhu

Western Michigan University ( email )

Kalamazoo, MI 49008
United States

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