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date: 13 November 2019

Abstract and Keywords

This article addresses the problem of performing integrated optimization subject to the most common inequality and nonlinear constraints, specifically the enhanced active equity (EAE) portfolio optimization problem. The EAE portfolio optimization problem is formulated by starting with the most basic mean-variance portfolio optimization problem and then by adding simple constraints until a minimally constrained EAE problem is arrived at. It is necessary to place bounds on the portfolio holdings in order to prevent the creation of unrealistic portfolios. Such bounds could be written as elementwise vector inequalities. A recently introduced class of portfolios that both holds securities long and sells them short, but which cannot be optimized directly, is the class of enhanced active equity (EAE) portfolios. Fast algorithms can be used to optimize long-short portfolios even though the covariance matrix in the representation is singular if fairly mild trimability conditions are satisfied. Another method for optimizing EAE portfolios is to use the critical line algorithm (CLA) of Markowitz (1987) and Markowitz and Todd (2000). A major advantage of the CLA is that it maps out the entire, and correct, efficient frontier even when the covariance matrix is singular. It is ideally suited to optimizing EAE portfolios.

Keywords: active equity, mean-variance portfolio optimization, portfolio holdings, unrealistic portfolios, long-short portfolios

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