1、Hull: Options, Futures, and Other Derivatives, Ninth EditionChapter 22: Value at Risk Multiple Choice Test Bank: Questions with Answers1. 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 riskB. There is 1 chance in 1
2、00 that the loss will be greater than the value of riskC. There is 1 chance in 1000 that the loss will be greater than the value of riskD. None of the above Answer: CA 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
3、 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 millionB. $0.14 millionC. $0.13 millionD. $0.10 million Answer: BThe gain is uniformly distributed between 0.15 and +0.85 million dollars. The probability that it will be between 0
4、.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?A
5、. $0.145 millionB. $0.14 millionC. $0.13 millionD. $0.10 million Answer: AAs 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 e
6、xpected 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? A. It fits historical data on the behavior of variables to a normal distributionB. It
7、fits historical data on the behavior of variables to a lognormal distributionC. It assumes that what will happen in the future is a random sample from what has happened in the pastD. It uses Monte Carlo simulation to create random future scenarios Answer: CThe historical simulation method assumes th
8、at 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 followingA. The 1-day VaR multiplied by 10B. The 1-day VaR multiplied by the square root of10 C.
9、 The 1-day VaR divided by 10D. The 1-day VaR divided by the square root of 10 Answer: BThe Basel committee rules allow the 10-VaR to be calculated as the one-day VaR multiplied by the square root of 10. This is exactly true when losses on successive days have independent normal distributions with me
10、an zero.6. 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 levelB. At least 3 times 7-day VaR with a 97% confidence levelC. At least 2 times 5-day VaR with a 95% confidence levelD. 1-day VaR with a 99% conf
11、idence levelAnswer: AThe 1996 amendment calculated capital as k times the 10-day 99% VaR where k was at least 3.7. 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 o
12、ne day 99% VaR? Assume that returns are multivariate normal (Note that N(-2.326)=0.01) A. $177B. $135C. $215D. $331 Answer: AThe standard deviation of the change in the stock A position in one day is 2,0000.015= $30. The standard deviation of the change in the value of the stock B position in one da
13、y is 5,0000.01 = $50. The variance of the combined position is 302+502+20.83050 = 5,800. The standard deviation is the square root of this or 76.16 and the 99% VaR is therefore 2.33 times 76.17 this or about $177.8. What is the method of testing how often a VaR with a certain confidence level was ex
14、ceeded in the past called?A. Stress testingB. Back testingC. EWMAD. The model-building approachAnswer: BBack testing involves examining how well a particular VaR methodology would have worked in the past. It counts exceptions, which are situations where the VaR level that would have been calculated,
15、 was exceeded.9. 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 lowB. VaR for a long call is too low and VaR for a long put is too highC. VaR for a long call is too high and VaR
16、 for a long put is too lowD. VaR for a long call is too high and VaR for a long put is too highAnswer: DWhen gamma is ignored, VaR for long option positions is too high and VaR for short option positions is too low. This is demonstrated for calls in Figures 22.5 and 22.6. The same can easily be seen
17、 to be true for puts.10. 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 gammaC. The quadratic model approximates daily changes using gamma, but not deltaD. None of the ab
18、ove Answer: AThe quadratic model uses delta and gamma to approximate daily changes as described in Section 22.511. Which of the following is true?A. Cash flow mapping is a way of calculating the present value of cash flowsB. Cash flow mapping is used to handle interest rate exposures in the model bu
19、ilding approachC. Cash flow mapping is used to handle interest rate exposures in the historical simulation approachD. None of the above Answer: BCash flow mapping is a way to handle interest rates when the model building approach is used. (See page 506-507)12. Which of the following describes stress
20、ed VaR?A. It is based on movements in market variables in stressed market conditionsB. It is VaR with a very high confidence levelC. It is VaR multiplied by a factor of 3D. None of the above Answer: AStressed VaR was introduced in Basel II.5. It calculates VaR based on movements in market variables
21、in stressed market conditions.13. A German bank has exposure to the S&P500. Which of the following is trueA. The S&P 500 index should be always be measured in U.S. dollars when VaR is calculatedB. The S&P 500 index should be always be measured in euros when VaR is calculatedC. Either A or B can be d
22、oneD. The S&P 500 index should be measured in euros only if the bank has not got a U.S. subsidiary.Answer: BAll foreign assets should be measured in the domestic currency.14. Which of the following is true of a covariance matrix?A. The numbers on the diagonal are variancesB. The numbers on the diago
23、nal are standard deviationsC. The numbers on the diagonal are all one. D. The numbers on the diagonal are all zero Answer: AThe diagonal numbers are variances. The off-diagonal numbers show the covariance between two variables.15. Consider a position in options on a particular stock. The position ha
24、s a delta of 12 and the stock price is 10. Which of the following is the approximate relation between the change in the portfolio value in one day, dP, and the return on the stock during the day, dxA. dP=12dxB. dP=1.2dxC. dP=120dxD. dP=22dxAnswer: CIf S is the stock price and the change in the stock
25、 price is dS, from the definition of delta we know that dP=12dS. This means that dP=12S(dS/S). dS/S is dx. In this case S=10 so that C is correct.16. A position in options on a particular stock has a delta of zero and a gamma of 4. The stock price is 10. Which of the following is the approximate rel
26、ation between the change in the portfolio value in one day, dP, and the return on the stock, dx A. dP = 4 times the square of dxB. dP = 2 times the square of dxC. dP = 20 times the square of dxD. dP = 200 times the square of dxAnswer: DIf S is the stock price and the change in the stock price is dS,
27、 the change in the portfolio value is 0.54(dS)2. This is 2S2(dS/S)2. dS/S is dx. In this case S=10 so that D is correct.17. In a principal components analysis which of the following is the quantity of a particular factor in an observationA. Factor loadingB. Factor scoreC. Factor sizeD. Factor rating
28、Answer: BThe quantity of a particular factor in the observation of changes on a particular day is known as the factor score.18. In the case of interest rate movements the most important factor corresponds toA. A parallel shiftB. A slope changeC. A bowingD. An increase in short ratesAnswer: AThe most
29、 important factor is the one corresponding to a parallel shift. This accounted for over 90% of the variance for the data in Section 22.9. 19. In the case of interest rate movements the second most important factor corresponds toA. A parallel shiftB. A slope changeC. A bowingD. An increase in short r
30、atesAnswer: BThe second most important factor is a slope change (or twist). In the example in Section 22.9 this accounted for about 7% of the variance in the data.20. Which of the following is trueA. Expected shortfall is always less than VaRB. Expected shortfall is always greater than VaRC. Expecte
31、d shortfall is sometimes greater than VaR and sometimes less than VaRD. Expected shortfall is a measure of liquidity risk wheras VaR is a measure of market riskAnswer: BExpected shortfall and VaR can both measure market risk. Expected shortfall is the expected loss level conditional on the loss level being greater than VaR. By definition expected shortfall must be greater than VaR.