A Dual Characterisation of Regulatory Arbitrage for Expected Shortfall

18 Pages Posted: 7 May 2019

See all articles by Martin Herdegen

Martin Herdegen

University of Warwick - Department of Statistics

Nazem Khan

University of Warwick - Department of Statistics

Date Written: April 9, 2019

Abstract

We study portfolio selection in a one-period financial market with an Expected Shortfall (ES) constraint. Unlike in classical mean-variance portfolio selection, it can happen that no efficient portfolios exist. We call this situation regulatory arbitrage and show that the presence or absence of regulatory arbitrage for ES is intimately linked to the fine structure of equivalent martingale measures (EMMs) for the discounted risky assets. More precisely, we prove that the market does not admit regulatory arbitrage for ES at confidence level α if and only if there exists an EMM Q ≈ P such that ll dQ/dP ll < 1/α.

Keywords: portfolio selection, Expected Shortfall, efficient frontier, regulatory arbitrage, fundamental theorem of asset pricing

JEL Classification: G11, D81, C61

Suggested Citation

Herdegen, Martin and Khan, Nazem, A Dual Characterisation of Regulatory Arbitrage for Expected Shortfall (April 9, 2019). Available at SSRN: https://ssrn.com/abstract=3368865 or http://dx.doi.org/10.2139/ssrn.3368865

Martin Herdegen (Contact Author)

University of Warwick - Department of Statistics ( email )

Coventry CV4 7AL
United Kingdom

Nazem Khan

University of Warwick - Department of Statistics ( email )

Coventry CV4 7AL
United Kingdom

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