Regulatory Arbitrage of Risk Measures

Forthcoming in Quantitative Finance

27 Pages Posted: 22 Jan 2015 Last revised: 3 Jul 2015

See all articles by Ruodu Wang

Ruodu Wang

University of Waterloo - Department of Statistics and Actuarial Science

Date Written: July 3, 2015


We introduce the regulatory arbitrage of risk measures, one of the key considerations in choosing a suitable risk measure to use in banking regulation. A regulatory arbitrage is the amount of capital requirement reduced by splitting a financial risk into several fragments, regulated via a risk measure separately. Coherent risk measures by definition are free of regulatory arbitrage; dividing risks will not reduce the total capital requirement under a coherent risk measure. However, risk measures in practical use, such as the Value-at-Risk (VaR), are often not coherent and the magnitude of their regulatory arbitrage is then of significant importance. We quantify the regulatory arbitrage of risk measures in a rigorous mathematical framework, and categorize risk measures into three classes: free of regulatory arbitrage, of limited regulatory arbitrage, and of infinite regulatory arbitrage. We provide explicit results to characterize the regulatory arbitrage for general classes of risk measures, including distortion risk measures and convex risk measures. Several examples of risk measures of limited regulatory arbitrage are illustrated, as possible alternatives for coherent risk measures.

Keywords: risk measures; regulatory arbitrage; subadditivity; Value-at-Risk; regulatory capital

JEL Classification: G18

Suggested Citation

Wang, Ruodu, Regulatory Arbitrage of Risk Measures (July 3, 2015). Forthcoming in Quantitative Finance, Available at SSRN: or

Ruodu Wang (Contact Author)

University of Waterloo - Department of Statistics and Actuarial Science ( email )

Waterloo, Ontario N2L 3G1

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