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Hull: Options, Futures, and Other Derivatives, Ninth Edition Chapter 22: Value at Risk Multiple Choice Test Bank: Questions with Answers 1. Which of the following is true of the 99.9% value at risk? A. There is 1 chance in 10 that the loss will be greater than the value of risk B. There is 1 chance in 100 that the loss will be greater than the value of risk C. There is 1 chance in 1000 that the loss will be greater than the value of risk D. None of the above Answer: C A 99.9% VaR means that there is a 0.1% chance of the loss exceeding the VaR level. This is 1 chance in 1000. 2. The gain from a project is equally likely to have any value between -\$0.15 million and +\$0.85 million. What is the 99% value at risk? The gain is uniformly distributed between −0.15 and +0.85 million dollars. The probability that it will be between −0.15 and −0.14 million dollars is therefore 1%. This means that there is a 99% chance that the loss will not be greater than \$0.14 million. This is the 99% VaR. 3. The gain from a project is equally likely to have any value between −\$0.15 million and +\$0.85 million. What is the 99% expected shortfall? As explained in the answer to the previous question the VaR level is \$0.14 million. Conditional on the loss being greater than \$0.14 million it is equally likely to have any value between \$0.14 million and \$0.15 million. The expected loss conditional that it is greater than \$0.14 million is therefore \$0.145 million. This is the expected shortfall. 4. Which of the following is true of the historical simulation method for calculating VaR?

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The historical simulation method assumes that the percentage changes in all market variables during the next day is a random sample from the percentage changes in a certain number of past days.
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• Fall '13
• yuriyzabolotnyuk

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