Identifying Value at Risk (VaR) and Expected Shortfall (Other (Not Listed) Sample)
12.5 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 for one of the investments when the confidence level is99%?(b) What is the expected shortfall for one of the investments when the confidence level is 99%?(c) What is the VaR for a portfolio consisting of the two investments when the confidence level is 99%?(d) What is the expected shortfall for a portfolio consisting of the two investments when the confidence level is 99%?(e) Show that in this example VaR does not satisfy the subadditivity condition where as expected shortfall does.
Risk Management
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Qstn a: What is the VaR for one of the investments when the confidence level is 99%?
In an event when the confidence level is 99%, this show is below 99.1% and as stated in the table its corresponding loss is $1 million. Thus, the VaR for the investment will be $1 million.
Qstn b: What is the expected shortfall for one of the investments when the confidence level is 99%?
If the confidence level is 99%, from the remaining 1%; most probably 0.1% will have a chance of incurring a $1 million loss. Whereas 0.9% has the chance of incurring a loss of $10 million respectively. This shows that there exist a 10% likelihood of losing $1 million and 90% probability of losing $10 million.
This implies that the prospected shortfall for a single investment can be computed as shown. The expected shortfall for a single investment which is:
0.1×$1 million + 0.9 × $10 million
= $9.1 million
Qstn c: What is the VaR for a portfolio
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