Question 1

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.

Accepted Answer

The Geske model generalizes the Merton model by allowing for coupon debt, which means it can handle scenarios where the firm has debt obligations that include regular interest payments, unlike the Merton model that primarily deals with zero-coupon bonds.

Question 2

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.

Accepted Answer

Equity is like a long call option because owning equity gives the holder the right, but not the obligation, to participate in the profits of the business. Debt, on the other hand, is like a short put option because the holder receives fixed interest payments and has the obligation to repay the principal at maturity. Additionally, the option-like characteristics of debt and equity come from the fact that their values are linked to the success or failure of the firm, which makes them similar to options whose values depend on the price of the underlying asset.

Question 3

The Merton (1974)model assumes that the value of the firm is distributed
A)Normally.
B)Lognormally.
C)Exponentially.
D)None of the above.

Accepted Answer

The Merton (1974) model assumes that the value of the firm is distributed lognormally, meaning that the logarithm of the value of the firm is normally distributed.

Question 4

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.

Accepted Answer

Credit-scoring models primarily rely on information from the firm's financials, such as income statements, balance sheets, and cash flow statements, to assess the creditworthiness of a borrower.

Question 5

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.

Accepted Answer

The answer of Which of the following statements best describes...

Question 6

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.

Accepted Answer

Altman's Z-score model is a widely used model that assesses the credit quality of a firm based on certain financial ratios. The model calculates a score that can be used to rank-order firms, discriminate between firms that are likely to default and those that are not likely to do so, and rate firms based on their creditworthiness. Therefore, the correct answer is D, i.e., "All of the above."

Question 7

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.

Accepted Answer

Equity holders can be viewed as holding a call option on the firm's assets, with the strike price being the debt level. An increase in the volatility of the firm's assets increases the value of this option, making equity holders better off.

Question 8

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.

Accepted Answer

A decrease in the value of a firm's assets and an increase in the volatility of its assets both increase the likelihood of default and lower investor confidence, leading to higher credit spreads. Option A is incorrect because an increase in asset value is typically viewed positively and would typically lead to tighter credit spreads. Option B is incorrect because lower asset volatility would also typically lead to tighter credit spreads, as it implies less risk. Option D is incorrect as a decrease in asset value and a decrease in asset volatility both imply less risk and would lead to tighter credit spreads.

Question 9

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.

Accepted Answer

Using equity prices to back out firm volatility is a popular and effective way to overcome unobserved firm volatility in the implementation of the Merton model. This approach involves using the market value of equity and the risk-free rate to estimate the firm's equity volatility, which can then be used to derive the asset volatility necessary for the model. This approach is widely used in practice and has been found to produce robust results.

Question 10

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%

Accepted Answer

The volatility of the firm's assets can be derived using the Merton model, which links the value of the firm's equity, the value of its debt, the risk-free rate, and the volatility of the firm's assets. Given the information, the correct answer involves applying the Merton model formulas, which require complex calculations not directly provided in the question. However, the correct choice, based on the Merton model's application to the given values, is 19.2%.

Question 11

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.

Accepted Answer

Zero-coupon debt value increases when the firm's assets rise in value because the likelihood of repayment increases. It also rises when the volatility of the firm's assets declines, as lower volatility means less risk of default. Additionally, as the maturity of the debt declines, the time until repayment is shorter, reducing the risk of default, thus increasing the debt's value.

Question 12

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.

Accepted Answer

if volatility decreases,risk falls,and spreads fall.The growth rate of the firm does not matter,as the spreads are determined in a risk-neutral setting and the growth rate does not enter the formula for spreads.When risk-free rates increase,the put option that proxies for the spread declines in value and spreads will in fact decrease.But spreads do increase when leverage increases.

Question 13

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.

Accepted Answer

can become horribly complicated even for three or more debt maturities.The case of two debt maturities is the Geske (1976)model.

Question 14

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.

Accepted Answer

Equity is option-like because shareholders have limited liability, similar to an option where the downside is limited to the premium paid.

Question 15

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.

Accepted Answer

Equity holders in a leveraged firm essentially have a long call option on the firm's assets, bought from the bond holders. This is because they have the right, but not the obligation, to "buy" the firm's assets by paying off the firm's debt, similar to how a call option gives the holder the right to buy an asset at a specified price. If the firm does well, equity holders can benefit from the upside, much like exercising a call option when the underlying asset's price is above the strike price.

Question 16

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.

Accepted Answer

The value of zero-coupon risky debt in a firm can be conceptualized as the value of risk-free debt minus the value of a put option on the firm's assets. This is because the risky debt holders are essentially selling a put option on the firm's assets to the equity holders, which gives the equity holders the right to "sell" the firm to the debt holders (by defaulting) if the firm's value falls below a certain level (the debt's face value).

Question 17

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%

Accepted Answer

The answer of A firm has one-year zero-coupon debt with...

Question 18

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.

Accepted Answer

Altman's Z-score model does not include a variable with a negative coefficient in its discriminant function. All the variables listed (Working Capital/Total Assets, Market Value of Equity/Book Value of Debt, Sales/Total Assets) are positively associated with the Z-score, meaning as they increase, the Z-score increases, indicating a lower probability of bankruptcy.

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 :
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
 $\sigma \sqrt { T - t }$
)

Accepted Answer

In the Merton model, to switch from the risk-neutral measure to the real-world measure, the drift term $\mu$ (the firm's asset growth rate) should replace the risk-free rate $r$ in the calculation of $N(d_2)$.

Question 20

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

Accepted Answer

The distance-to-default is calculated as (Value of the firm - Face value of debt) / Standard deviation of firm asset value. Here, it is ($10 billion - $7 billion) / $2 billion = 1.50.

Quiz 30: Structural Models of Default Risk

The Geske model generalizes the Merton model to allow for

Equity and debt in a firm are option-like.Which of the following options are they?

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

Credit-scoring models primarily rely on:

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

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

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

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

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

Zero-coupon debt value rises when,ceteris paribus

Credit spreads in the Merton (1974) model will be increasing,ceteris paribus,when

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?

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

Equity holders in a leveraged firm have

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

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. )

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 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?