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?

Based on the diagram, match the trigonometric ratios with the corresponding ratios of the sides of the triangle. tiles : cosb sinb tanb sincposs matches: c/b b/a b/c c/a

How can constraints be used to model a real-world situation?

Acell phone company offers two plans to its subscribers. at the time new subscribers sign up, they are asked to provide some demographic information. the mean yearly income for a sample of 40 subscribers to plan a is $45,000 with a standard deviation of $9,200. for a sample of 25 subscribers to plan b, the mean income is $64,300 with a standard deviation of $7,100. at the 0.025 significance level, is it reasonable to conclude the mean income of those selecting plan b is larger? assume unequal population standard deviations. hint: for the calculations, assume the plan a as the first sample. what is the decision rule? (negative amount should be indicated by a minus sign. round your answer to 3 decimal places.) compute the value of the test statistic. (negative amount should be indicated by a minus sign. round your answer to 2 decimal places.) what is your decision regarding h0 ? reject h0 fail to reject h0 compute the p-value. less than 0.01 between 0.01 and 0.025 between 0.025 and 0.05 between 0.05 and 0.10 greater than 0.10