Deck 30: Structural Models of Default Risk

Question 1

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

Answer 1

B.

Question 2

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

Answer 2

C

Question 3

Credit spreads in the Merton (1974) model will be increasing, ceteris paribus, when
(a) Stock volatility decreases.
(b) The growth rate of the firm decreases.
(c) Leverage increases.
(d) The risk-free rates increase.

Answer 3

C

Question 4

The Geske model generalizes the Merton model to allow for
(a) Coupon debt.
(b) Jumps in the firm value process.
(c) Non-normality in the firm value process.
(d) Perpetual convertible preferred shares.

Question 5

Credit-scoring models primarily rely on:
(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.

Question 6

An obstacle in implementation of the Merton model is that
(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 7

Equity and debt in a firm are option-like mainly because
(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 8

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 :

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 9

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

Question 10

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

Question 11

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

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 12

Equity holders in a leveraged firm have
(a) A long put option to sell the firm's assets to the bond holders.
(b) A long call option on the firm's assets, bought from the bond holders.
(c) A short call option on the firm's assets, sold to the bond holders.
(d) A short put option on the firm's assets, sold to the bond holders.

Question 13

Zero-coupon debt value rises when, ceteris paribus
(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 14

A firm has one-year zero-coupon debt with face value $7 billion. Assuming the firm value at the end of the year is normally distributed with a mean of 10 billion and a standard deviation of 2 billion, , what is the probability that the firm's assets will not be sufficient to repay the debt at the end of the year?
(a) 0.14%
(b) 4.44%
(c) 5.39%
(d) 6.68%

Question 15

Equity and debt in a firm are option-like. Which of the following options are they?
(a) Equity is akin to a short call and debt is akin to a package containing a long put.
(b) Equity is akin to a long call and debt is akin to a package containing a short put.
(c) Equity is akin to a short put and debt is akin to a package containing a long call.
(d) Equity is akin to a long put and debt is akin to a package containing a short call.

Question 16

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?
(a) 1.50
(b) 2.00
(c) 3.00
(d) 7.00

Question 17

Altman's Z-score model may be used to:
(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 18

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?
(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 19

The Merton (1974) model assumes that the value of the firm is distributed
(a) Normally.
(b) Lognormally.
(c) Exponentially.
(d) None of the above.

Question 20

In Altman's Z-score model, which of the following variables has a negative coefficient in the discriminant function that comes out of the model? (A negative coefficient would mean that the Z-score is decreasing in the variables.)
(a) Working Capital/Total Assets
(b) Market Value of Equity/Book Value of Debt
(c) Sales/Total Assets
(d) None of the above.

Question 21

A firm's current value is 1 billion. The firm has one-year zero-coupon debt of face value €0.6 billion. Assume an expected growth rate of the firm's assets of 0% and a standard deviation of asset value of 0.3 billion. If the firm asset value at year end is normally distributed, what is the probability that the firm's assets will not be sufficient to repay the debt at the end of the year?
(a) 1.23%
(b) 4.11%
(c) 7.34%
(d) 9.12%

Question 22

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.

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

Question 23

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?
(a) 10.0%
(b) 19.2%
(c) 24.2%
(d) 35.4%

Question 24

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:

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

Question 25

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?
(a) 17.12%
(b) 19.23%
(c) 20.02%
(d) 21.22%

Question 26

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%?

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