IAI Actuarial Core Principles · Economic Modelling · Measures of investment risk
A regulator prefers a risk measure that satisfies subadditivity, so diversification never appears to increase measured risk. Which choice is most consistent with this preference?
Tail value at risk is the best fit. It is subadditive, so combining portfolios cannot raise measured risk above the sum of the parts, whereas VaR and shortfall probability can violate this property for some distributions.
- AValue at Risk at 99%
- BProbability of shortfall
- CTail value at risk (expected shortfall)Correct
- DRange of returns
- Mean return
Explanation
TVaR is subadditive, so the risk of a combined portfolio never exceeds the sum of individual risks. VaR and shortfall probability can violate subadditivity for non-elliptical distributions. Range and mean are not coherent risk measures of this type.
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