Risk Management with Weighted VaR

62 Pages Posted: 17 Apr 2017 Last revised: 25 May 2017

Pengyu Wei

University of Oxford - Mathematical Institute; University of Oxford - Man Institute of Quantitative Finance

Date Written: May 23, 2017

Abstract

This article studies the optimal portfolio selection of expected utility maximizing investors who must also manage their market-risk exposures. The risk is measured by a so-called weighted Value-at-Risk (WVaR) risk measure, which is a generalization of both Value-at-Risk (VaR) and Expected Shortfall (ES). The feasibility, well-posedness, and existence of the optimal solution are examined. We obtain the optimal solution (when it exists) and show how risk measures change asset allocation patterns. In particular, we characterize three classes of risk measures: the first class will lead to models that do not admit an optimal solution; the second class can give rise to endogenous portfolio insurance; and the third class, which includes VaR and ES, two popular regulatory risk measures, will allow economic agents to engage in “regulatory capital arbitrage,” incurring larger losses when losses occur.

Keywords: portfolio selection, risk measure, weighted Value-at-Risk, Value-at-Risk, Expected Shortfall, portfolio insurance, regulatory capital arbitrage

JEL Classification: G11, C61

Suggested Citation

Wei, Pengyu, Risk Management with Weighted VaR (May 23, 2017). Available at SSRN: https://ssrn.com/abstract=2952596 or http://dx.doi.org/10.2139/ssrn.2952596

Pengyu Wei (Contact Author)

University of Oxford - Mathematical Institute ( email )

United Kingdom

University of Oxford - Man Institute of Quantitative Finance ( email )

University of Oxford, Eagle House
Walton Well Road
Oxford, OX2 6ED
United Kingdom

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