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.

Question

(Express all the following answers in million dollars: 100 million = 100, 1.3 million = 1.3)

1. The VaR0.95 for each single investment is = ?

2. The VaR0.98 for each single investment is = ?

3. The ES0.95 for each single investment is = ?

4. What is the VaR for a portfolio consisting of the two investments when the confidence level is 95%?

5. What is the expected shortfall for a portfolio consisting of the two investments when the confidence level is 95%? (round off to the second decimal place)

Remember: VaR0.95 means Value-at-Risk at 95% confidence level, ES means Expected Shortfall.

Answer 1

Var0.95 = 1
Aar0.98 = 5

Answer 2

Var0.95 = 1
Var 0.98= 5
Es 0.95 = 4.4

Answer 3

confidence level is 95% = 4
shortfall for a portfolio consisting of the two investments when the confidence level is 95% = 6.18

Answer 4

a)1
b)5
c)4.4
d)4
e)6.14