Hull: Options, Futures, and Other Derivatives, Tenth Edition
Chapter 22: Value at Risk and Expected Shor!all
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?
A. $0.145 million
B. $0.14 million
C. $0.13 million
D. $0.10 million
Answer: B
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 shor4all?
A. $0.145 million
B. $0.14 million
C. $0.13 million
D. $0.10 million
Answer: A
As explained in the answer to the previous ques5on the VaR level is $0.14 million.
Condi5onal 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 condi5onal that it is greater
than $0.14 million is therefore $0.145 million. This is the expected shor4all.
4. Which of the following is true of the historical simula5on method for calcula5ng VaR?
A. It 7ts historical data on the behavior of variables to a normal distribution
B. It 7ts historical data on the behavior of variables to a lognormal distribution
C. It assumes that what will happen in the future is a random sample from what has
happened in the past
D. It uses Monte Carlo simula5on to create random future scenarios
Answer: C
The historical simula5on 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.
5. The 10-day VaR is often assumed to be which of the following
A. The 1-day VaR mul5plied by 10
B. The 1-day VaR mul5plied by the square root of10
C. The 1-day VaR divided by 10
D. The 1-day VaR divided by the square root of 10
Answer: B
The Basel commi:ee rules allow the 10-VaR to be calculated as the one-day VaR mul5plied
by the square root of 10. This is exactly true when losses on successive days have
independent normal distribu5ons with mean zero.
6. Which was the minimum capital requirement for market risk in the 1996 BIS Amendment?
A. At least 3 5mes the 10-day VaR with a 99% confidence level
