Simplified Mean-Variance Portfolio Optimisation

36 Pages Posted: 18 Jan 2012 Last revised: 13 Jun 2012

See all articles by Claudio Fontana

Claudio Fontana

Université Paris VII Denis Diderot

Martin Schweizer

ETH Zurich; Swiss Finance Institute

Date Written: September 30, 2011


We propose a simplified approach to mean-variance portfolio problems by changing their parametrisation from trading strategies to final positions. This allows us to treat, under a very mild no-arbitrage-type assumption, a whole range of quadratic optimisation problems by simple mathematical tools in a unified and model-independent way. We provide explicit formulas for optimal positions and values, connections between the solutions to the different problems, two-fund separation results, and explicit expressions for indifference values.

Keywords: mean-variance, portfolio choice, hedging, indifference valuation, Markowitz problem, two-fund separation, no approximate profits, minimum variance, Sharpe ratio

JEL Classification: G11, C61, D81

Suggested Citation

Fontana, Claudio and Schweizer, Martin, Simplified Mean-Variance Portfolio Optimisation (September 30, 2011). Swiss Finance Institute Research Paper No. 11-68. Available at SSRN: or

Claudio Fontana

Université Paris VII Denis Diderot ( email )

avenue de France
Paris, 75205

Martin Schweizer (Contact Author)

ETH Zurich ( email )

Mathematik, HG G51.2
Raemistrasse 101
CH-8092 Zurich

Swiss Finance Institute

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4

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