Question

We have two independent investments. Each of them may have a 1% chance of a loss of 10 million dollars, a 2% chance of a loss of 5 million, a 3% chance of a loss of 1 million, and a 94% chance of a profit of 1 million.

(Express all the following answers in million dollars: 100 million = 100, 1.3 million = 1.3; round off all quantities to the second decimal place)

The VAR.5 for each single investment is

Answer 1

VaR at the 5% level for a single investment is 1.00 million (loss).

Reason: cumulative probabilities are 0.01 (−10), 0.03 (−5), 0.06 (−1); the 5% quantile falls at −1, so VaR5% = 1.00.