Numeraire-Invariant Quadratic Hedging and Mean-Variance Portfolio Allocation

35 Pages Posted: 19 Oct 2021 Last revised: 24 Jun 2022

See all articles by Aleš Černý

Aleš Černý

Bayes Business School, City, University of London

Christoph Czichowsky

London School of Economics & Political Science (LSE) - Department of Mathematics

Jan Kallsen

CAU Kiel

Date Written: October 18, 2021

Abstract

The paper investigates quadratic hedging in a semimartingale market that does not necessarily contain a risk-free asset. An equivalence result for hedging with and without numeraire change is established. This permits direct computation of the optimal strategy without choosing a reference asset and/or performing a numeraire change. New explicit expressions for optimal strategies are obtained, featuring the use of oblique projections that provide unified treatment of the case with and without a risk-free asset. The analysis yields a streamlined computation of the efficient frontier for the pure investment problem in terms of three easily interpreted processes. The main result advances our understanding of the efficient frontier formation in the most general case where a risk-free asset may not be present. Several illustrations of the numeraire-invariant approach are given.

Keywords: mean-variance portfolio selection, quadratic hedging, numeraire change, oblique projection, opportunity-neutral measure

JEL Classification: G11, G12, C61

Suggested Citation

Černý, Aleš and Czichowsky, Christoph and Kallsen, Jan, Numeraire-Invariant Quadratic Hedging and Mean-Variance Portfolio Allocation (October 18, 2021). Available at SSRN: https://ssrn.com/abstract=3944947 or http://dx.doi.org/10.2139/ssrn.3944947

Aleš Černý (Contact Author)

Bayes Business School, City, University of London

Northampton Square
London, EC1V 0HB
United Kingdom

Christoph Czichowsky

London School of Economics & Political Science (LSE) - Department of Mathematics ( email )

Houghton Street
GB-London WC2A 2AE
United Kingdom

HOME PAGE: http://https://www.lse.ac.uk/Mathematics/people/Christoph-Czichowsky

Jan Kallsen

CAU Kiel

Kiel
Germany

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