IAI Actuarial Core Principles · Economic Modelling · Measures of investment risk
A portfolio's one-year loss has the following discrete distribution (Rs crore): loss 0 with probability 0.90, loss 10 with probability 0.06, loss 30 with probability 0.03, loss 70 with probability 0.01. What is the Tail Value at Risk at the 95% level, i.e. the expected loss given the loss lies in the worst 5% of outcomes?
The Tail Value at Risk is 34 crore, calculated as (0.01 times 70 plus 0.03 times 30 plus 0.01 times 10) divided by 0.05. This option is not listed among those offered.
- A40 croreCorrect
- B30 crore
- C50 crore
- D25 crore
- 70 crore
Explanation
The worst 5% comprises the 1% at loss 70 and 4% from the loss-30 layer (3%) plus 1% from the loss-10 layer. Hmm, ordering from worst: 70 (1%), 30 (3%) gives 4%, then 1% of the 10 loss. Expected tail loss = (0.01x70 + 0.03x30 + 0.01x10)/0.05 = (0.7+0.9+0.1)/0.05 = 34. So the keyed value must be 34, which is not offered.
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