Mean–variance approximations to expected utility

• Published in: European journal of operational research Vol. 234; no. 2; pp. 346 - 355
• Main Author: Markowitz, Harry
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 16.04.2014; Elsevier Sequoia S.A
• Subjects: Approximation; Errors; Expected utility; Gaussian; Geometric mean; Mean-absolute deviation; Mean–variance analysis; Normal distribution; Operational research; Semivariance; Studies; Utilities; Utility functions; Value at risk; Variance analysis; Semivariance; Value at risk; Expected utility; Geometric mean; Mean-absolute deviation; Mean–variance analysis
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2012.08.023

► Critically evaluates attacks on assumptions of modern portfolio theory. ► Argues attacks confuse sufficient versus necessary conditions for applying theory. ► Reviews a half-century of research on mean–variance approximations to expected utility. It is often asserted that the application of mean–variance analysis assumes normal (Gaussian) return distributions or quadratic utility functions. This common mistake confuses sufficient versus necessary conditions for the applicability of modern portfolio theory. If one believes (as does the author) that choice should be guided by the expected utility maxim, then the necessary and sufficient condition for the practical use of mean–variance analysis is that a careful choice from a mean–variance efficient frontier will approximately maximize expected utility for a wide variety of concave (risk-averse) utility functions. This paper reviews a half-century of research on mean–variance approximations to expected utility. The many studies in this field have been generally supportive of mean–variance analysis, subject to certain (initially unanticipated) caveats.