ECOM055 – Risk Management For Banking
Problem Set 9
Based on Book Chapter 12 风险管理作业代做
12.13.
Suppose that each of two investments has a 4% chance of a loss of $10 million, a 2% chance of a loss of $1 million, and a 94% chance of a profit of $1 million. They are independent of each other.
(a) What is the VaR for one of the investments when the confidence level is 95%?
(b) What is the expected shortfall (ES) when the confidence level is 95%?
(c) What is the VaR for a portfolio consisting of the two investments when the confidence level is 95%?
(d) What is the expected shortfall for a portfolio consisting of the two investments when the confidence level is 95%?
(e) Show that, in this example, VaR does not satisfy the subadditivity condition whereas expected shortfall does.
12.14.
Suppose that daily changes for a portfolio have first-order autocorrelation with autocorrelation parameter 0.12. The 10-day VaR, calculated by multiplying the one-day VaR by , is $2 million. What is a better estimate of the VaR that takes account of autocorrelation?
12.16.
The change in the value of a portfolio in three months is normally distributed, with a mean of $500,000 and a standard deviation of $3 million. Calculate the VaR and ES for a confidence level of 99.5% and a time horizon of three months.
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