A Sharper Angle on Optimization

16 Pages Posted: 7 Oct 2009 Last revised: 19 Nov 2009

See all articles by Maxim Golts

Maxim Golts

Acadian Asset Management

Gregory C. Jones

affiliation not provided to SSRN

Date Written: October 5, 2009


The classical mean-variance optimization takes expected returns and variances and produces portfolio positions. In this paper we discuss the direction and the magnitude of the positions vector separately, and focus on the former. We quantify the distortions of the mean-variance optimization process by looking at the angle between the vector of expected returns and the vector of optimized portfolio positions. We relate this angle to the condition numbers of the covariance matrix and show how to control it by employing robust optimization techniques. The resulting portfolios are more intuitive and investment-relevant, in particular with lower leverage of the “noise” alphas at the expense of lower ex-ante Sharpe Ratio.

Keywords: mean-variance optimization, covariance matrix, condition number, leverage, Sharpe Ratio

JEL Classification: G11, C61

Suggested Citation

Golts, Maxim and Jones, Gregory C., A Sharper Angle on Optimization (October 5, 2009). Available at SSRN: https://ssrn.com/abstract=1483412 or http://dx.doi.org/10.2139/ssrn.1483412

Maxim Golts (Contact Author)

Acadian Asset Management ( email )

260 Franklin Street
Boston, MA 02110
United States

Gregory C. Jones

affiliation not provided to SSRN

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