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An investment has a 91.5% chance of making a profit of $40 million, a 4% chance of losing $10 million, a 3% of losing $20

An investment has a 91.5% chance of making a profit of $40 million, a 4% chance of losing $10 million, a 3% of losing $20 million, and a 1.5% chance of losing $30 million. A) What is the VaR for this investment when the confidence level is 90%, 94%, 95%, 98% or 99%? B) What is the expected shortfall when the confidence level is 97% or 99%? C) Suppose there is another independent investment with the following profile: a 90% change of making $22 million, a 7% chance of losing $12 million, and a 3% chance of losing $19 million. What is the VaR for a portfolio consisting of the two investments when the confidence level is 99.5%? D) What is the expected shortfall for the portfolio in C) when the confidence level is 99.5%? E) Does VaR in C) satisfy the subadditivity condition? How about the expected shortfall in D)? (Hint: do part C) in a spreadsheet by first calculating all the joint probabilities and gains/losses and then sort from gain to loss.)

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