A Robust Estimator of the Efficient Frontier

16 Pages Posted: 18 Oct 2019 Last revised: 4 Mar 2020

See all articles by Marcos Lopez de Prado

Marcos Lopez de Prado

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

Date Written: October 15, 2016


Convex optimization solutions tend to be unstable, to the point of entirely offsetting the benefits of optimization. For example, in the context of financial applications, it is known that portfolios optimized in-sample often underperform the naïve (equal weights) allocation out-of-sample. This instability can be traced back to two sources: (i) noise in the input variables; and (ii) signal structure that magnifies the estimation errors in the input variables. A first innovation of this paper is to introduce the nested clustered optimization algorithm (NCO), a method that tackles both sources of instability.

Over the past 60 years, various approaches have been developed to address these two sources of instability. These approaches are flawed in the sense that different methods may be appropriate for different input variables, and it is unrealistic to expect that one method will dominate all the rest under all circumstances. Accordingly, a second innovation of this paper is to introduce MCOS, a Monte Carlo approach that estimates the allocation error produced by various optimization methods on a particular set of input variables. The result is a precise determination of what method is most robust to a particular case. Thus, rather than relying always on one particular approach, MCOS allows users to apply opportunistically whatever optimization method is best suited in a particular setting.

Presentation materials are available at: https://ssrn.com/abstract=3469964.

Keywords: Monte Carlo, convex optimization, de-noising, clustering, shrinkage.

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

Suggested Citation

López de Prado, Marcos and López de Prado, Marcos, A Robust Estimator of the Efficient Frontier (October 15, 2016). Available at SSRN: https://ssrn.com/abstract=3469961 or http://dx.doi.org/10.2139/ssrn.3469961

Marcos López de Prado (Contact Author)

Cornell University - Operations Research & Industrial Engineering ( email )

237 Rhodes Hall
Ithaca, NY 14853
United States

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

Abu Dhabi Investment Authority ( email )

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

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

True Positive Technologies ( email )

United States

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

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