Suppose that two projects A and B have a 0.7% chance of a loss of $ 8 million, a 2.3% chance of a loss of $1 million, and a 97% chance of a profit of $1 million. The losses on these two investments are distributed independently of each other. Required:
a. What is the VaR for one of the investments when the confidence level is 99%?
b. What is the expected shortfall (ES) for one of the investments when the confidence level is 99%?
c. Show the probability distribution of losses/profits for a portfolio consisting of both investments. You need to determine all possible losses/gains on this portfolio and calculate corresponding probabilities.
d. What is the VaR when of the portfolio consisting of both investments when the confidence level is 99%?
e. What is the expected shortfall to a portfolio consisting of the two investments when the confidence level is 99%?
f. Based on your findings, what is your conclusion about the shortcoming of VaR as opposed to using ES?