Risk Management with Weighted VaR

46 Pages Posted: 17 Apr 2017  

Pengyu Wei

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

Date Written: April 13, 2017


This article studies 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). 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 admit no optimal solution; the second can necessitate portfolio insurance endogenously; the third will allow economic agents to engage in “regulatory capital arbitrage”, incurring larger losses when losses occur, which includes VaR and ES, two popular regulatory risk measures.

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 (April 13, 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 States

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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