Question 1

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

Accepted Answer

Using equity prices to back out firm volatility is a popular way to overcome the issue of unobserved firm volatility in the implementation of the Merton model. This approach involves using the relationship between the price of the firm's equity and its implied volatility to estimate the firm's volatility.

Question 2

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

Accepted Answer

A decrease in the value of a firm's assets indicates a higher likelihood of default, leading to an increase in credit spreads. The increase in volatility of its assets will also lead to an increase in credit spreads as it indicates a higher level of risk.

Question 3

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

Accepted Answer

According to the Merton (1974) model, credit spreads will increase with an increase in leverage.

Question 4

The Geske model generalizes the Merton model to allow for

Accepted Answer

The Geske model generalizes the Merton model by allowing for coupon debt, which means it can model firms with debt that pays periodic interest, unlike the Merton model that primarily deals with zero-coupon or bullet debt.

Question 5

Credit-scoring models primarily rely on:

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 6

An obstacle in implementation of the Merton model is that

Accepted Answer

The Merton model assumes simple capital structures while capital structures in practice are complex. Also, the volatility of firm asset value is unobserved, making it difficult to accurately estimate the model's inputs.

Question 7

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

Accepted Answer

Equity is option-like because shareholders have limited liability, similar to holding a call option where the downside is limited to the premium paid (or the initial investment in equity), while the upside is potentially unlimited.

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 :

Accepted Answer

In the Merton model, under the real-world probability measure, the drift term $\mu$ is used instead of the risk-neutral drift $r$ when calculating $N(d_2)$.

Question 9

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

Accepted Answer

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

Question 10

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

Accepted Answer

Zero-coupon means that there are no periodic interest payments and the bond is sold at a discount to its face value. In the case of risky debt, the value of the bond is equal to the risk-free debt minus a put option on the firm's assets. The put option represents the bondholder's right to sell back the bond to the firm in case of default. Therefore, option B is the correct choice. The other choices involve call options which are not typically associated with debt instruments.

Question 11

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

Accepted Answer

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

Question 12

Equity holders in a leveraged firm have

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.

Question 13

Zero-coupon debt value rises when, ceteris paribus

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 the firm's value dropping below the debt value. Additionally, as the maturity of the debt declines, the time horizon for potential default decreases, thus increasing the debt's value.

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?

Accepted Answer

The probability that the firm's assets will not be sufficient to repay the debt is the probability that the firm value is less than $7 billion. This is calculated using the cumulative distribution function (CDF) of a normal distribution. The Z-score is (7-10)/2 = -1.5. The probability corresponding to a Z-score of -1.5 is approximately 6.68%.

Question 15

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

Accepted Answer

Equity behaves like a long call option because it gives the holder the right, but not the obligation, to purchase the underlying asset (the value of the firm) at a certain price (the share price). Debt behaves like a short put option because it reflects a fixed obligation to purchase the underlying asset (pay back the loan) at a certain price (the interest rate). A package containing a short put option would be a combination of short-term debt and equity, while a package containing a long put option would be a combination of long-term debt and equity. Therefore, option B is the best choice because it accurately reflects the nature of equity and debt as option-like instruments.

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?

Accepted Answer

The "distance-to-default" in the Moody's KMV approach is calculated as the difference between the firm's current value and the debt's face value, divided by the standard deviation of the firm's asset value. Here, it is ($10 billion - $7 billion) / $2 billion = $3 billion / $2 billion = 1.50.

Question 17

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

Accepted Answer

Altman's Z-score model is a financial model used to assess the likelihood of a company going bankrupt. The model uses multiple financial ratios and other company data to calculate a score, which can then be used to rank-order firms based on credit quality, discriminate between firms that are likely to default and those that are not likely to do so, and rate firms. Therefore, the correct answer is 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?

Accepted Answer

The nested compound option model is not a simplification, but a more complex approach that considers multiple debt maturities. Choices B and C both collapse debt to simpler forms, simplifying the analysis.

Question 19

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

Accepted Answer

The Merton model assumes that the value of the firm follows a lognormal distribution. This distribution is commonly used in finance to model the prices of assets over time, where the logarithm of the prices follows a normal distribution.

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.)

Accepted Answer

All the variables listed in options A, B, and C have positive coefficients in Altman's Z-score model, meaning they contribute positively to the Z-score calculation. A negative coefficient would decrease the Z-score, but none of these variables do that.

Quiz 30: Structural Models of Default Risk