A Journey Through the 'Mathematical Underworld' of Portfolio Optimization

26 Pages Posted: 11 Feb 2013 Last revised: 5 Jul 2015

See all articles by Marcos Lopez de Prado

Marcos Lopez de Prado

Cornell University - Operations Research & Industrial Engineering; AQR Capital Management, LLC

Date Written: February 16, 2013

Abstract

* It has been estimated that the current size of the asset management industry is approximately US$58 trillion.

* Portfolio optimization is one of the problems most frequently encountered by financial practitioners. It appears in various forms in the context of Trading, Risk Management and Capital Allocation.

* The Critical Line Algorithm (CLA) is the only algorithm specifically designed for inequality-constrained portfolio optimization problems, which guarantees that the exact solution is found after a predefined number of iterations.

* Surprisingly, open-source implementations of CLA in a scientific language appear to be inexistent or unavailable.

* The lack of publicly available CLA software, commercially or open-source, means that trillions of dollars are likely to be suboptimally allocated as a result of practitioners using general-purpose quadratic optimizers.

* We believe that a large amount of financial firms and practitioners will benefit from our robust implementation of CLA in a scientific language.

The code is available in the author's website.

Keywords: portfolio selection, quadratic programming, portfolio optimization, constrained efficient frontier, turning point, Kuhn-Tucker conditions, risk aversion

JEL Classification: C02, G11, G14, D53

Suggested Citation

López de Prado, Marcos, A Journey Through the 'Mathematical Underworld' of Portfolio Optimization (February 16, 2013). Available at SSRN: https://ssrn.com/abstract=2214771 or http://dx.doi.org/10.2139/ssrn.2214771

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

AQR Capital Management, LLC

One Greenwich Plaza
Greenwich, CT 06830
United States

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

Register to save articles to
your library

Register

Paper statistics

Downloads
1,649
rank
9,692
Abstract Views
5,502
PlumX Metrics