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; Abu Dhabi Investment Authority; True Positive Technologies

Date Written: February 16, 2013


* 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 and 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

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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