Question 1

Credit-scoring models primarily rely on:

Accepted Answer

A)  Information from the equity markets. 
B)  Information from the debt markets. 
C)  Information from the firm's financials. 
D)  Information from the credit markets. 
A)  Information from the equity markets. 
B)  Information from the debt markets. 
C)  Information from the firm's financials. 
D)  Information from the credit markets. C

Question 2

Suppose the current value of a firm's assets is $100 million, and the value of equity in the firm is $40 million. Suppose too that the firm has only one issue of debt outstanding: zero-coupon debt with a maturity of three years, and a face value of $70 million. Finally, suppose that the risk-free rate of interest is 4% (continuously-compounded terms) for all maturities. Assuming that firm value evolves according to a lognormal diffusion (as in Merton, 1974), what is the volatility of the firm's assets?

Accepted Answer

A)  10.0% 
B)  19.2% 
C)  24.2% 
D)  35.4% 
A)  10.0% 
B)  19.2% 
C)  24.2% 
D)  35.4% B

Question 3

Based on your understanding of structural models of default, equity holders are better off when, holding all else constant

Accepted Answer

A)  The volatility of the firm's assets increases. 
B)  The value of the firm's assets decreases. 
C)  The debt maturity is shorter. 
D)  All of the above. 
A)  The volatility of the firm's assets increases. 
B)  The value of the firm's assets decreases. 
C)  The debt maturity is shorter. 
D)  All of the above. A

Question 4

The Merton (1974) model assumes that the value of the firm is distributed

Accepted Answer

A)  Normally. 
B)  Lognormally. 
C)  Exponentially. 
D)  None of the above. 
A)  Normally. 
B)  Lognormally. 
C)  Exponentially. 
D)  None of the above.

Question 5

Equity and debt in a firm are option-like mainly because

Accepted Answer

A)  You can choose one or the other. 
B)  They are both non-linear securities. 
C)  The equity has limited liability. 
D)  They may be redeemed or repurchased. 
A)  You can choose one or the other. 
B)  They are both non-linear securities. 
C)  The equity has limited liability. 
D)  They may be redeemed or repurchased.

Question 6

Suppose that the asset value of a firm evolves according to a lognormal diffusion, as in Merton (1974). The current value of the firm's assets is $100 million, and its volatility is 24.24%. Suppose too that the firm has only one issue of debt outstanding: zero-coupon debt with a maturity of three years, and a face value of $70 million. Finally, suppose that the risk-free rate of interest is 4% (continuously-compounded terms) for all maturities. What is the risk-neutral probability of the firm defaulting at maturity of the debt?

Accepted Answer

A)  17.12% 
B)  19.23% 
C)  20.02% 
D)  21.22% 
A)  17.12% 
B)  19.23% 
C)  20.02% 
D)  21.22%

Question 7

A firm's current value is £ 1 billion . The firm has one-year zero-coupon debt outstanding with a face value of £ 0.6 billion. What is the one-year "distance to default" (in the Moody's KMV approach) if the standard deviation of firm value is 30%?

Accepted Answer

A)  1.33 
B)  1.71 
C)  2.34 
D)  3.12 
A)  1.33 
B)  1.71 
C)  2.34 
D)  3.12

Question 8

The structural model framework is a parsimonious one, yet needs to accommodate complex capital structures. Which of the following approaches is not a simplification of the complexity of the real-world situation?

Accepted Answer

A)  The nested compound option model for multiple debt maturities. 
B)  Collapsing debt to a fixed horizon equal to all of short-term debt and a percentage of long-term debt (the KMV approach). 
C)  Collapsing debt to a single horizon equal to the duration of the outstanding debt of all maturities. 
D)  None of the above. 
A)  The nested compound option model for multiple debt maturities. 
B)  Collapsing debt to a fixed horizon equal to all of short-term debt and a percentage of long-term debt (the KMV approach). 
C)  Collapsing debt to a single horizon equal to the duration of the outstanding debt of all maturities. 
D)  None of the above.

Question 9

The Geske model generalizes the Merton model to allow for

Accepted Answer

A)  Coupon debt. 
B)  Jumps in the firm value process. 
C)  Non-normality in the firm value process. 
D)  Perpetual convertible preferred shares. 
A)  Coupon debt. 
B)  Jumps in the firm value process. 
C)  Non-normality in the firm value process. 
D)  Perpetual convertible preferred shares.

Question 10

Given a firm value of $V = 100$ , debt face value of $D = 60$ , asset volatility of $\sigma = 30 \%$ , and a risk free rate of $r = 3 \%$ , conditional on default, the expected recovery rate in the Merton model for debt of maturity five years will be:

Accepted Answer

A)  40% 
B)  50% 
C)  60% 
D)  70% 
A)  40% 
B)  50% 
C)  60% 
D)  70%

Question 11

Altman's Z-score model may be used to:

Accepted Answer

A)  Rank-order firms based on credit quality. 
B)  Discriminate between firms that are likely to default and those that are not likely to do so. 
C)  Rate firms. 
D)  All of the above. 
A)  Rank-order firms based on credit quality. 
B)  Discriminate between firms that are likely to default and those that are not likely to do so. 
C)  Rate firms. 
D)  All of the above.

Question 12

Unobserved firm volatility is an obstacle in the implementation of the Merton model. One popular way to overcome this is to

Accepted Answer

A)  Use the model only on non-financial firms. 
B)  Use equity prices to back out firm volatility. 
C)  Use equity volatility in place of asset volatility in implementing the model. 
D)  Use data on closely-related firms from the same sector to infer this volatility. 
A)  Use the model only on non-financial firms. 
B)  Use equity prices to back out firm volatility. 
C)  Use equity volatility in place of asset volatility in implementing the model. 
D)  Use data on closely-related firms from the same sector to infer this volatility.

Question 13

Which of the following statements best describes the relation of the real-world ( $P$ ) and risk-neutral ( $Q$ ) probabilities of default?

Accepted Answer

A)  $P \leq Q$ 
B)  $P = Q$ 
C)  $P \geq Q$ 
D)  Depends on the parameters of the firm for which this is being considered. 
A)  $P \leq Q$ 
B)  $P = Q$ 
C)  $P \geq Q$ 
D)  Depends on the parameters of the firm for which this is being considered.

Question 14

An obstacle in implementation of the Merton model is that

Accepted Answer

A)  The model assumes simple capital structures while capital structures in practice are complex. 
B)  The volatility of firm asset value is unobserved. 
C)  Both (a) and (b). 
D)  Neither (a) nor (b). 
A)  The model assumes simple capital structures while capital structures in practice are complex. 
B)  The volatility of firm asset value is unobserved. 
C)  Both (a) and (b). 
D)  Neither (a) nor (b).

Question 15

Suppose that a firm's value $V$ grows over one year at a simple rate $^\circ R$ that has a mean of $0.10$ and a variance of $0.04$ . If the firm's current value is $10 billion and it has one-year zero-coupon debt of face value $7 billion, what is the probability that the firm's assets will not be sufficient to repay the debt at the end of the year? Assume the firm value at the end of the year is normally distributed.

Accepted Answer

A)  1.15% 
B)  2.28% 
C)  3.39% 
D)  5.12% 
A)  1.15% 
B)  2.28% 
C)  3.39% 
D)  5.12%

Question 16

Zero-coupon debt value rises when, ceteris paribus

Accepted Answer

A)  The firm's assets rise in value. 
B)  The volatility of the firm's assets declines. 
C)  The maturity of the debt declines. 
D)  All of the above. 
A)  The firm's assets rise in value. 
B)  The volatility of the firm's assets declines. 
C)  The maturity of the debt declines. 
D)  All of the above.

Question 17

Which of the following scenarios is most likely to lead to an increase in a firm's credit spreads?

Accepted Answer

A)  The firm's assets increase in value and the volatility of its assets also increases. 
B)  The firm's assets increase in value and the volatility of its assets decreases. 
C)  The firm's assets decrease in value and the volatility of its assets increases. 
D)  The firm's assets decrease in value and the volatility of its assets decreases. 
A)  The firm's assets increase in value and the volatility of its assets also increases. 
B)  The firm's assets increase in value and the volatility of its assets decreases. 
C)  The firm's assets decrease in value and the volatility of its assets increases. 
D)  The firm's assets decrease in value and the volatility of its assets decreases.

Question 18

A firm's current value is $10 billion. The firm has one-year zero-coupon debt with face value $7 billion. The standard deviation of firm asset value is $2 billion. What is the firm's "distance-to-default" as measured by the Moody's KMV approach?

Accepted Answer

A)  1.50 
B)  2.00 
C)  3.00 
D)  7.00 
A)  1.50 
B)  2.00 
C)  3.00 
D)  7.00

Question 19

In order to obtain the probability of default in the Merton (1974) model under the real-world probability measure, we need to make the following change in calculating $N \left( d _ { 2 } \right)$ in the formula :

Accepted Answer

A)  Replace $\mu$ (the firm's asset growth rate) with $r$ (the risk-free rate). 
B)  Replace $r$ with $\mu$ . 
C)  Replace $\sigma$ (the firm's asset volatility) with $d _ { 1 } \sqrt { T - t }$ . 
D)  Replace $d _ { 2 }$ with $\sigma \sqrt { T - t }$ . 
A)  Replace $\mu$ (the firm's asset growth rate) with $r$ (the risk-free rate). 
B)  Replace $r$ with $\mu$ . 
C)  Replace $\sigma$ (the firm's asset volatility) with $d _ { 1 } \sqrt { T - t }$ . 
D)  Replace $d _ { 2 }$ with $\sigma \sqrt { T - t }$ .

Question 20

Zero-coupon risky debt value in a firm is equal to

Accepted Answer

A)  Risk free debt plus a call option on the firm's assets. 
B)  Risk free debt minus a put option on the firm's assets. 
C)  Equity value minus a call option on the firm's assets. 
D)  Firm value minus a put option on the firm's assets. 
A)  Risk free debt plus a call option on the firm's assets. 
B)  Risk free debt minus a put option on the firm's assets. 
C)  Equity value minus a call option on the firm's assets. 
D)  Firm value minus a put option on the firm's assets.

Exam 30: Structural Models of Default Risk

Credit-scoring models primarily rely on:

Based on your understanding of structural models of default, equity holders are better off when, holding all else constant

The Merton (1974) model assumes that the value of the firm is distributed

Equity and debt in a firm are option-like mainly because

A firm's current value is £ 1 billion . The firm has one-year zero-coupon debt outstanding with a face value of £ 0.6 billion. What is the one-year "distance to default" (in the Moody's KMV approach) if the standard deviation of firm value is 30%?

The structural model framework is a parsimonious one, yet needs to accommodate complex capital structures. Which of the following approaches is not a simplification of the complexity of the real-world situation?

The Geske model generalizes the Merton model to allow for

Given a firm value of V=100V = 100V=100 , debt face value of D=60D = 60D=60 , asset volatility of σ=30%\sigma = 30 \%σ=30% , and a risk free rate of r=3%r = 3 \%r=3% , conditional on default, the expected recovery rate in the Merton model for debt of maturity five years will be:

Altman's Z-score model may be used to:

Unobserved firm volatility is an obstacle in the implementation of the Merton model. One popular way to overcome this is to

Which of the following statements best describes the relation of the real-world ( PPP ) and risk-neutral ( QQQ ) probabilities of default?

An obstacle in implementation of the Merton model is that

Zero-coupon debt value rises when, ceteris paribus

Which of the following scenarios is most likely to lead to an increase in a firm's credit spreads?

A firm's current value is $10 billion. The firm has one-year zero-coupon debt with face value $7 billion. The standard deviation of firm asset value is $2 billion. What is the firm's "distance-to-default" as measured by the Moody's KMV approach?

In order to obtain the probability of default in the Merton (1974) model under the real-world probability measure, we need to make the following change in calculating N(d2)N \left( d _ { 2 } \right)N(d2​) in the formula :

Zero-coupon risky debt value in a firm is equal to

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Given a firm value of $V = 100$ , debt face value of $D = 60$ , asset volatility of $\sigma = 30 \%$ , and a risk free rate of $r = 3 \%$ , conditional on default, the expected recovery rate in the Merton model for debt of maturity five years will be:

Which of the following statements best describes the relation of the real-world ( $P$ ) and risk-neutral ( $Q$ ) probabilities of default?

In order to obtain the probability of default in the Merton (1974) model under the real-world probability measure, we need to make the following change in calculating $N \left( d _ { 2 } \right)$ in the formula :