Mathematical Appendices to: 'The Probability of Backtest Overfitting'

Journal of Computational Finance (Risk Journals), 2015, Forthcoming

8 Pages Posted: 23 Feb 2015 Last revised: 5 Jul 2015

See all articles by David H. Bailey

David H. Bailey

Lawrence Berkeley National Laboratory; University of California, Davis

Jonathan Borwein

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

Marcos Lopez de Prado

Cornell University - Operations Research & Industrial Engineering; Abu Dhabi Investment Authority; True Positive Technologies

Qiji Jim Zhu

Western Michigan University

Date Written: February 22, 2015

Abstract

We carry out several test cases to illustrate how the Probability of Backtest Overfitting (PBO) performs under different scenarios. We also assess the accuracy of PBO using two alternative approaches (Monte Carlo Methods and Extreme Value Theory).

The paper "The Probability of Backtest Overfitting" to which these Appendices apply is available at the following URL: http://ssrn.com/abstract=2326253

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 and Borwein, Jonathan and López de Prado, Marcos and López de Prado, Marcos and Zhu, Qiji Jim, Mathematical Appendices to: 'The Probability of Backtest Overfitting' (February 22, 2015). Journal of Computational Finance (Risk Journals), 2015, Forthcoming, Available at SSRN: https://ssrn.com/abstract=2568435 or http://dx.doi.org/10.2139/ssrn.2568435

David H. 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
Apt 153
Davis, CA 95616
United States

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

Jonathan Borwein

Royal Society of Canada

University of Newcastle (Australia)

Australian Academy of Science (deceased)

Marcos López de Prado (Contact Author)

Abu Dhabi Investment Authority ( email )

211 Corniche Road
Abu Dhabi, Abu Dhabi PO Box3600
United Arab Emirates

HOME PAGE: http://www.adia.ae

Cornell University - Operations Research & Industrial Engineering ( email )

237 Rhodes Hall
Ithaca, NY 14853
United States

HOME PAGE: http://www.orie.cornell.edu

True Positive Technologies ( email )

NY
United States

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

Qiji Jim Zhu

Western Michigan University ( email )

Kalamazoo, MI 49008
United States

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