Deck 22: Value at Risk

Question 1

An investor has $2,000 invested in stock A and $5,000 in stockB.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? Assume that returns are multivariate normal (Note that N(-2.326)=0.01)

A)$177
B)$135
C)$215
D)$331

Answer 1

A
The standard deviation of the change in the stock A position in one day is 2,000×0.015= $30.The standard deviation of the change in the value of the stock B position in one day is 5,000×0.01 = $50.The variance of the combined position is 30² +50² +2×0.8×30×50 = 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.

Question 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% expected shortfall?

A)$0.145 million
B)$0.14 million
C)$0.13 million
D)$0.10 million

Answer 2

A
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.

Question 3

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

Answer 3

B
The 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 mean zero.

Question 4

Which of the following is true

A)Expected shortfall is always less than VaR
B)Expected shortfall is always greater than VaR
C)Expected shortfall is sometimes greater than VaR and sometimes less than VaR
D)Expected shortfall is a measure of liquidity risk wheras VaR is a measure of market risk

Question 5

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

Question 6

A German bank has exposure to the S&P500.Which of the following is true

A)The S&P 500 index should be always be measured in U.S.dollars when VaR is calculated
B)The S&P 500 index should be always be measured in euros when VaR is calculated
C)Either A or B can be done
D)The S&P 500 index should be measured in euros only if the bank has not got a U.S.subsidiary.

Question 7

In the case of interest rate movements the most important factor corresponds to

A)A parallel shift
B)A slope change
C)A bowing
D)An increase in short rates

Question 8

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

Question 9

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

Question 10

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

Question 11

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

Question 12

In a principal components analysis which of the following is the quantity of a particular factor in an observation

A)Factor loading
B)Factor score
C)Factor size
D)Factor rating

Question 13

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

Question 14

In the case of interest rate movements the second most important factor corresponds to

A)A parallel shift
B)A slope change
C)A bowing
D)An increase in short rates

Question 15

Consider a position in options on a particular stock.The position has 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,dx

A)dP=12dx
B)dP=1.2dx
C)dP=120dx
D)dP=22dx

Question 16

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

Question 17

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

Question 18

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)Back testing
C)EWMA
D)The model-building approach

Question 19

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

Question 20

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 relation 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 dx
B)dP = 2 times the square of dx
C)dP = 20 times the square of dx
D)dP = 200 times the square of dx