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Hull: Fundamentals of Futures and Options Markets, Ninth Edition
Chapter 20: Value at Risk and Expected Shortfall
Multiple Choice Test Bank
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
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
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?
A. $0.145 million
B. $0.14 million
C. $0.13 million
D. $0.10 million
4. Which of the following is true of the historical simulation method for calculating VaR?
A. It fits historical data on the behavior of variables to a normal distribution
B. It fits 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 simulation to create random future scenarios
5. At the end of Thursday, the estimated volatility of asset A is 2% per day. During Friday asset A
produces a return of 3%. An EWMA model with lambda equal to 0.9 is used. What is an estimate
of the volatility of asset A at the end of Friday?
A. 2.08%
B. 2.10%
C. 2.12%
D. 2.14%
6. At the end of Thursday, the estimated volatility of asset B is 1% per day. During Friday asset B
produces a return of zero. An EWMA model with lambda equal to 0.9 is used. What is an
estimate of the volatility of asset A at the end of Friday?
A. 0.98%
B. 0.95%
C. 0.92%
D. 0.90%
7. At the end of Thursday, the estimated covariance between assets A and B is 0.0001. During
Friday asset A produces a return of 3% and asset B produces a return of zero. An EWMA model
with lambda equal to 0.9 is used. What is an estimate of the covariance at the end of Friday?
A. 0.000090
B. 0.000081
C. 0.000100
D. 0.000095
8. Which of the following is a definition of the covariance between X and Y?
A. Correlation between X and Y times variance of X times variance of Y
B. Variance of X times the variance of Y
C. Correlation between X and Y divided by the product of the standard deviation of X and
the standard deviation of Y
D. Correlation between X and Y times standard deviation of X times standard deviation of Y
9. Which of the following is true of a covariance matrix?
A. The numbers on the diagonal are variances
B. The numbers on the diagonal are standard deviations
C. The numbers on the diagonal are all one
D. The numbers on the diagonal are all zero
10. What does EWMA stand for?
A. Equally weighted moving average
B. Equally weighted median approximation
C. Exponentially weighted moving average
D. Exponentially weighted median average
11. Which of the following is true when lambda equals 0.95?
A. The weight given to the most recent observation is 0.95
B. The weight given to the observation one day ago is 95% of the weight given to the
observation two days ago
C. The weights given to observations add up to 0.95
D. The weights given to the observation two days ago is 95% of the weight given to the
observation one day ago
12. The 10-day VaR is often assumed to be which of the following
A. The 1-day VaR multiplied by 10
B. The 1-day VaR multiplied 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
13. Which was the minimum capital requirement for market risk in the 1996 BIS Amendment?
A. At least 3 times the 10-day VaR with a 99% confidence level
B. At least 3 times 7-day VaR with a 97% confidence level
C. At least 2 times 5-day VaR with a 95% confidence level
D. 1-day VaR with a 99% confidence level
14. An investor has $2,000 invested in stock A and $5,000 in stock B. The daily volatilities of A and B
are 1.5% and 1% respectively and the coefficient of correlation is 0.8. What is the one day 99%
VaR? (Note that N(-2.33)=0.01)
A. $177
B. $135
C. $215
D. $331
15. What is the method of testing how often a VaR with a certain confidence level was exceeded in
the past called?
A. Stress testing
B. Backtesting
C. EWMA
D. The model-building approach
16. If the volatility for a portfolio is 20% per year, what is the volatility per quarter?
A. 20%
B. 10%
C. 5%
D. 2%
17. Which of the following is true when delta, but not gamma, is used in calculating VaR for option
positions?
A. VaR for a long call is too low and VaR for a long put is too low
B. VaR for a long call is too low and VaR for a long put is too high
C. VaR for a long call is too high and VaR for a long put is too low
D. VaR for a long call is too high and VaR for a long put is too high
18. Which of the following is true?
A. The quadratic model approximates daily changes in using delta and gamma
B. The quadratic model approximates daily changes using delta, but not gamma
C. The quadratic model approximates daily changes using gamma, but not delta
D. None of the above
19. Which of the following is true?
A. Cash flow mapping is a way of calculating the present value of cash flows
B. Cash flow mapping is used to handle interest rate exposures in the model building
approach
C. Cash flow mapping is used to handle interest rate exposures in the historical simulation
approach
D. None of the above
20. Which of the following describes stressed VaR?
A. It is based on movements in market variables in stressed market conditions
B. It is VaR with a very high confidence level
C. It is VaR multiplied by a factor of 3
D. None of the above
