A risk manager oversees the risk measurement of two portfolios. Portfolio A has a VaR of USD 5 million and an ES of USD 10 million. Portfolio B has a VaR of USD 7 million and an ES of USD 15 million. When combining portfolios A and B, the risk manager observes that the VaR of the aggregate portfolio is USD 15 million and the ES is USD 20 million. This is because:
A. ES is subadditive, while VaR is not subadditive.
B. VaR is subadditive, while ES is not subadditive.
C. VaR satisfies positive homogeneity, while ES does not satisfy positive homogeneity.
D. ES satisfies positive homogeneity, while VaR does not satisfy positive homogeneity.
Answer:A
ES is a more aapropriate risk measure than VaR for the following reasons:
- ES is the coherent risk measure, VaR is not.
- ES meets the property of subadditivity and is more appropriate for solving optimization problems.
- ES gives an estimate of the magnitude of a loss for unfavorable events.VaR provides no estimate of how large a loss may be.
- ES has less restrictive assumptions regarding risk/return decision rules.