Question 1) Which of the following is true of the 99.9% value at risk?

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 of 10

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

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