Question 1

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 99%-VaR of your portfolio is

Accepted Answer

The answer of You invest $100 each in two bonds....

Question 2

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

Accepted Answer

The answer of Which of the following measures of risk...

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

VaR (Value at Risk) does not always satisfy the sub-additivity property, which means that the risk of a combined portfolio can be greater than the sum of the risks of the individual portfolios. This is a limitation of VaR as a risk measure, especially when assessing the risk of diversified portfolios.

Question 4

Identifying the risk contribution of an asset to a portfolio is more difficult than identifying its return contribution because

Accepted Answer

Identifying the risk contribution of an asset to a portfolio is more difficult than identifying its return contribution because risk is not additive like return. Adding an asset with a specific level of risk does not necessarily increase the risk of the overall portfolio in a straightforward manner. Therefore, it can be challenging to determine the exact risk contribution of a single asset in a portfolio.

Question 5

The expected shortfall (ES) measure does not satisfy the following coherence property of risk measures:

Accepted Answer

Expected shortfall (ES) satisfies all the listed coherence properties: linear homogeneity, sub-additivity, and translation invariance, making none of the options correct.

Question 6

"Subadditivity" is the requirement of a coherent risk measure that

Accepted Answer

Subadditivity requires that the risk of the combination of two portfolios be no greater than the sum of the risks of the two portfolios. This means that the risk measure is consistent with the idea that diversification can lower overall risk, as the risk of the combined portfolio should be less than the sum of the risks of the individual portfolios.

Question 7

Worst-case scenario analysis develops a measure that computes, say, for one year's returns

Accepted Answer

Worst-case scenario analysis focuses on the average of the worst outcomes across multiple trials, not just a single worst outcome or meanest possible outcome.

Question 8

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 are the risk-contribution proportions of each asset to the 99%-VaR of this portfolio?

Accepted Answer

The risk contribution of each asset to the portfolio's VaR is determined by the marginal VaR, which depends on the asset's weight, standard deviation, and correlation with the portfolio. Calculating these contributions shows that the proportions are approximately 36% for the first asset and 64% for the second asset.

Question 9

VaR fails the following requirement of a "coherent" risk measure:

Accepted Answer

VaR fails the subadditivity requirement of a "coherent" risk measure, which means the risk measure is not additive. This means that the risk measure of a portfolio consisting of individual assets will not equal the sum of the risk measures of the assets. This failure makes VaR deficient as a measure of risk.

Question 10

"Monotonicity" is the requirement of a risk-measure that if Portfolio A dominates Portfolio B (in the sense of always doing at least as well as B in every state of the world and strictly better in some states), then the risk of Portfolio A should be less than the risk of Portfolio B. Which of the following statements is correct?

Accepted Answer

The answer of "Monotonicity" is the requirement of a risk-measure...

Question 11

VaR-bases risk decomposition is the calculation that allocates the total VaR of a portfolio to each of its assets or subportfolios. Which of the following statements is most valid?

Accepted Answer

Risk decomposition is based on the assumption that VaR is linearly homogeneous in its constituents, meaning that the risk of a portfolio can be decomposed into the risks of its individual assets or subportfolios. This assumption holds regardless of the distributional assumptions or simulation method used to calculate VaR. The other answer choices are not accurate or relevant to the concept of risk decomposition.

Question 12

Consider a $900 portfolio with three assets, each held in equal value. The VaR of the portfolio is such that an increase in $1 of any of the asset holdings results in a $0.05 increase in VaR. The VaR of this portfolio is approximately equal to:

Accepted Answer

Since the portfolio is equally divided among three assets, each asset is worth $300. An increase of $1 in any asset increases the VaR by $0.05, so the VaR per dollar is $0.05. Therefore, the VaR for the entire $900 portfolio is $900 * $0.05 = $45.

Question 13

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

Translation invariance implies that if a constant is added to all outcomes of a portfolio, the risk measure should adjust accordingly. VaR, Expected Shortfall, and Standard Deviation are translation invariant because adding a risk-free asset (constant return) to a portfolio directly reduces the risk by that amount. Kurtosis, however, measures the "tailedness" of the distribution and is not affected by shifting the distribution up or down (adding a constant to all outcomes), hence it does not satisfy the property of translation invariance in the context of risk measurement.

Question 14

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

Doubling the size of every position in a portfolio will double the risk contribution of the original portion of the portfolio, as measured by VaR.

Quiz 20: Value at Risk

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 99%-VaR of your portfolio is

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

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) ?

Identifying the risk contribution of an asset to a portfolio is more difficult than identifying its return contribution because

The expected shortfall (ES) measure does not satisfy the following coherence property of risk measures:

"Subadditivity" is the requirement of a coherent risk measure that

Worst-case scenario analysis develops a measure that computes, say, for one year's returns

VaR fails the following requirement of a "coherent" risk measure:

VaR-bases risk decomposition is the calculation that allocates the total VaR of a portfolio to each of its assets or subportfolios. Which of the following statements is most valid?

Consider a $900 portfolio with three assets, each held in equal value. The VaR of the portfolio is such that an increase in $1 of any of the asset holdings results in a $0.05 increase in VaR. The VaR of this portfolio is approximately equal to:

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) ?

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

Quiz 20: Value at Risk

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 99%-VaR of your portfolio is

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

Identifying the risk contribution of an asset to a portfolio is more difficult than identifying its return contribution because

The expected shortfall (ES) measure does not satisfy the following coherence property of risk measures:

"Subadditivity" is the requirement of a coherent risk measure that

Worst-case scenario analysis develops a measure that computes, say, for one year's returns

VaR fails the following requirement of a "coherent" risk measure:

VaR-bases risk decomposition is the calculation that allocates the total VaR of a portfolio to each of its assets or subportfolios. Which of the following statements is most valid?

Consider a $900 portfolio with three assets, each held in equal value. The VaR of the portfolio is such that an increase in $1 of any of the asset holdings results in a $0.05 increase in VaR. The VaR of this portfolio is approximately equal to:

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) ?

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) ?