1. Suppose that each of two investments has a 0.9% chance of a loss of $10...
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1. Suppose that each of two investments has a 0.9% chance of a loss of $10 million and a 99.1% chance of a loss of $1 million. The investments are independent of each other. (a) What is the VaR and the expected shortfall (ES) for one of the investments when the confidence level is 99% and the time horizon is one year? (6 marks) (b) What is the VaR and the expected shortfall (ES) for a portfolio consisting of the two investments when the confidence level is 99% and the time horizon is one year? (6 marks) (c) Check whether VaR or expected shortfall satisfies the subadditivity condition for a coherent risk measure for the investments. (4 marks) 1. Suppose that each of two investments has a 0.9% chance of a loss of $10 million and a 99.1% chance of a loss of $1 million. The investments are independent of each other. (a) What is the VaR and the expected shortfall (ES) for one of the investments when the confidence level is 99% and the time horizon is one year? (6 marks) (b) What is the VaR and the expected shortfall (ES) for a portfolio consisting of the two investments when the confidence level is 99% and the time horizon is one year? (6 marks) (c) Check whether VaR or expected shortfall satisfies the subadditivity condition for a coherent risk measure for the investments. (4 marks)
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