Question 1

Consider a two-asset portfolio invested with $10 in each asset. The mean returns of the two assets are $10 \%$ and $15 \%$ . The correlation of returns is 50%. The standard deviation of returns is 20% and 30%, respectively. What is the 99%-VaR of this portfolio?

Accepted Answer

A)  6.22 
B)  7.66 
C)  8.40 
D)  10.58

Question 2

You invest $100 in a corporate bond. You estimate that with probability 0.95, the corporation will pay back the promised amount of $110 at the end of one year; with probability 0.04, the corporation will default and the recovered amount will be $70; and with probability 0.01, the corporation will default and you will recover nothing. The 98%-VaR in this scenario is

Accepted Answer

A)  $30 
B)  $40 
C)  $70 
D)  $100

Question 3

Given two portfolios $P _ { 1 }$ and $P _ { 2 }$ , which risk measure $R ( )$ does not always satisfy the "sub-addivity" property (i.e., that $R \left( P _ { 1 } + P _ { 2 } \right) \leq R \left( P _ { 1 } \right) + R \left( P _ { 2 } \right)$ where $R ( )$ is the measure of portfolio risk)?

Accepted Answer

A)  VaR. 
B)  Expected shortfall. 
C)  Variance. 
D)  Standard deviation.

Question 4

Which of the following measures of risk does not have the linear homogeneity property?

Accepted Answer

A)  VaR. 
B)  Expected shortfall. 
C)  Variance. 
D)  Standard deviation.

Question 5

Monte Carlo is widely-used approach for computing VaR. Relative to other methods which of the following is a benefit of using this approach?

Accepted Answer

A)  It is fully flexible in parameterizing the forward-looking distribution. 
B)  It always requires very few parameters. 
C)  It always uses normality. 
D)  It is the fastest approach to computing VaR.

Question 6

You invest $100 each in two bonds. Each bond will pay you $110 at the end of the year with probability 0.98 and nothing with probability 0.02. The correlation between the bonds is zero. In this scenario, the 95%-VaR of your portfolio is

Accepted Answer

A)  $- 20$ . 
B)  Zero. 
C)  $90 
D)  $200

Question 7

Value-at-Risk (VaR) is most closely defined as

Accepted Answer

A)  The probability of a specified level of negative return of a portfolio in the left tail of its profit-and-loss distribution. 
B)  The dollar loss at which a pre-specified cumulative probability occurs in the left tail of the profit-and-loss distribution. 
C)  The probability of a negative return below a specified threshold in the left tail of the distribution. 
D)  The negative return rate for which a pre-specified probability lies in the left tail of the distribution.

Question 8

A portfolio has a current value of $1000. The annual profit $X$ is distributed normally with mean 100 and standard deviation 100. What is the 99%-VaR?

Accepted Answer

A)  $- 133$ 
B)  $- 65$ 
C)  $65$ 
D)  $133$

Question 9

If every position in a portfolio is doubled in size, the risk contribution of the original portion of the portfolio, as measured by VaR, will

Accepted Answer

A)  Remain the same as before. 
B)  Double. 
C)  Halve. 
D)  More than double.

Question 10

You invest $100 in a corporate bond. You estimate that with probability 0.95, the corporation will pay back the promised amount of $110 at the end of one year; with probability 0.04, the corporation will default and the recovered amount will be $70; and with probability 0.01, the corporation will default and you will recover nothing. The 99%-VaR in this scenario is

Accepted Answer

A)  $30 
B)  $40 
C)  $70 
D)  $100

Question 11

Which of the following risk measures is not translation invariant (i.e., does not satisfy the property that if we add a risk-free asset to a portfolio with a return of$r$ , the risk of the portfolio should come down by the extent of this addition)?

Accepted Answer

A)  VaR. 
B)  Expected shortfall. 
C)  Kurtosis. 
D)  Standard deviation.

Question 12

You invest $100 in a corporate bond. You estimate that with probability 0.94, the corporation will pay back the promised amount of $110 at the end of one year; with probability 0.04, the corporation will default and the recovered amount will be $70; and with probability 0.02, the corporation will default and you will recover nothing. The 90%-VaR in this scenario is

Accepted Answer

A)  $30 
B)  $40 
C)  $70 
D)  $100

Question 13

Which of the following best characterizes the mathematical properties of the risk measure VaR?

Accepted Answer

A)  It is a dollar quantity. 
B)  It is a measure of first moment of returns. 
C)  It is a measure of the second moment of returns. 
D)  It is a percentage loss rate.

Question 14

You invest $100 each in two bonds. Each bond will pay you $110 at the end of the year with probability 0.98 and nothing with probability 0.02. The correlation between the bonds is zero. In this scenario, the 98%-VaR of your portfolio is

Accepted Answer

A)  $- 20$ . 
B)  Zero. 
C)  $90 
D)  $200

Exam 20: Value at Risk

Consider a two-asset portfolio invested with $10 in each asset. The mean returns of the two assets are $10 \%$ and $15 \%$ . The correlation of returns is 50%. The standard deviation of returns is 20% and 30%, respectively. What is the 99%-VaR of this portfolio?

Given two portfolios $P _ { 1 }$ and $P _ { 2 }$ , which risk measure $R ( )$ does not always satisfy the "sub-addivity" property (i.e., that $R \left( P _ { 1 } + P _ { 2 } \right) \leq R \left( P _ { 1 } \right) + R \left( P _ { 2 } \right)$ where $R ( )$ is the measure of portfolio risk) ?

Which of the following measures of risk does not have the linear homogeneity property?

Monte Carlo is widely-used approach for computing VaR. Relative to other methods which of the following is a benefit of using this approach?

You invest $100 each in two bonds. Each bond will pay you $110 at the end of the year with probability 0.98 and nothing with probability 0.02. The correlation between the bonds is zero. In this scenario, the 95%-VaR of your portfolio is

Value-at-Risk (VaR) is most closely defined as

A portfolio has a current value of $1000. The annual profit $X$ is distributed normally with mean 100 and standard deviation 100. What is the 99%-VaR?

If every position in a portfolio is doubled in size, the risk contribution of the original portion of the portfolio, as measured by VaR, will

Which of the following risk measures is not translation invariant (i.e., does not satisfy the property that if we add a risk-free asset to a portfolio with a return of $r$ , the risk of the portfolio should come down by the extent of this addition) ?

Which of the following best characterizes the mathematical properties of the risk measure VaR?

You invest $100 each in two bonds. Each bond will pay you $110 at the end of the year with probability 0.98 and nothing with probability 0.02. The correlation between the bonds is zero. In this scenario, the 98%-VaR of your portfolio is

Exam 20: Value at Risk

Consider a two-asset portfolio invested with $10 in each asset. The mean returns of the two assets are 10%10 \%10% and 15%15 \%15% . The correlation of returns is 50%. The standard deviation of returns is 20% and 30%, respectively. What is the 99%-VaR of this portfolio?

Which of the following measures of risk does not have the linear homogeneity property?

Monte Carlo is widely-used approach for computing VaR. Relative to other methods which of the following is a benefit of using this approach?

You invest $100 each in two bonds. Each bond will pay you $110 at the end of the year with probability 0.98 and nothing with probability 0.02. The correlation between the bonds is zero. In this scenario, the 95%-VaR of your portfolio is

Value-at-Risk (VaR) is most closely defined as

A portfolio has a current value of $1000. The annual profit XXX is distributed normally with mean 100 and standard deviation 100. What is the 99%-VaR?

If every position in a portfolio is doubled in size, the risk contribution of the original portion of the portfolio, as measured by VaR, will

Which of the following risk measures is not translation invariant (i.e., does not satisfy the property that if we add a risk-free asset to a portfolio with a return of rrr , the risk of the portfolio should come down by the extent of this addition) ?

Which of the following best characterizes the mathematical properties of the risk measure VaR?

You invest $100 each in two bonds. Each bond will pay you $110 at the end of the year with probability 0.98 and nothing with probability 0.02. The correlation between the bonds is zero. In this scenario, the 98%-VaR of your portfolio is

Consider a two-asset portfolio invested with $10 in each asset. The mean returns of the two assets are $10 \%$ and $15 \%$ . The correlation of returns is 50%. The standard deviation of returns is 20% and 30%, respectively. What is the 99%-VaR of this portfolio?

A portfolio has a current value of $1000. The annual profit $X$ is distributed normally with mean 100 and standard deviation 100. What is the 99%-VaR?

Which of the following risk measures is not translation invariant (i.e., does not satisfy the property that if we add a risk-free asset to a portfolio with a return of $r$ , the risk of the portfolio should come down by the extent of this addition) ?