Default Risk Quantitative Methodologies

Kaplan Schweser Printable Quizzes - Default Risk: QuantitativeMethodologies

Quiz ID#: 11423056

Question 1 - #49704

Suppose a firm with a value of $80 million has a bond outstanding with a face value of $100 million that matures infive years. The current interest rate is 5 percent and the volatility of the firm is 20 percent. If the expected return onthe firm is 20 percent using the Merton model for probability of default, determine the probability that the firm willdefault on its debt (PD) and calculate the expected loss given default (LGD).

PD LGD

A) 0.78% $780,000

B) 56.50% $16,629,000

C) 2.21% $252,000

D) 6.51% $1,086,000

Your answer: A was incorrect. The correct answer was D)6.51% $1,086,000

Merton model of probability of default (PD) is:

where:

F = face value of the zero-coupon bond,V = value of the firmT = maturity date on bondσ = volatility of firm value

Expected loss given default (LGD) is:

What is the amount of the expected LGD?

Thus, the expected loss is $1,086,000.

Printable Quizzes http://www.schweser.com/online_program/test_engine/printable_answers...

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This question tested from Topic Area 2, Topic 19, AIM 1

Question 2 - #124940

Under the Merton model, the payoff at maturity to stockholders and bondholders approximates the payoff on a:

Stockholders Bondholders

A) Long call Short put

B) Short put Long call

C) Short call and risk-free bond Long put

D) Long call Short put and risk-free bond

Your answer: B was incorrect. The correct answer was D)Long call Short put and risk-free bond

The payoff to stockholders at maturity mimics the payoff on a long call (capped at 0 on the downside with no cap onthe upside). The payoff to bondholders mimics the payoff on a risk-free bond combined with a short put (capped at 0on the downside and the bond’s face value on the upside).


Question 3 - #38859

Suppose a fixed income portfolio manager buys a risky bond issue with a face amount of $100 million that matures inone year. To hedge the credit risk that the issuer of the debt will not pay the full amount, the debt holder buys a creditdefault put on the value of the issuing firm. What are the payoffs for holding a risky bond and the credit default put, ifthe value of the risky firm is $80 million? The risky debt payoff is:

A) $80 million and the credit default put payoff is $0 because it is out-of-the money.B) $20 million and the credit default put payoff is $80 million.C) $100 million and the credit default put payoff is $20 million.D) $80 million and the credit default put payoff is $20 million.

Your answer: C was incorrect. The correct answer was D) $80 million and the credit default put payoff is $20 million.

If the firm value is only $80 million, then the holder of risky debt will experience a $20 million loss unless they alsohave a position in a credit default put which would have a payoff of $20 million. Thus, the risky bond has a payoff of$80 million and the credit default put a payoff of $20 million so that the hedge payoff is $100 million.

Payoffs of Risky Bond Hedged with a Credit Default Put

Value of the FirmV 80

Payoff of Riskfree Bond,F 100

Short Put-Max(F-V,0) -20

Risky Debt=Riskfree Bond +short put 80

Credit Default Put Max(F-V,0) 20

Hedged Payoff 100


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Which of the following statements is (are) CORRECT?

One of the assumptions of the Merton model is that default can occur at any time.I.Logit and probit models are examples of parametric discrimination.II.Minimizing the maximum of Type I and Type II errors is an example of the Neyman-Pearson decision rule.III.The shape of the line on the GINI curve indicates the success of the classification system.IV.

A) I, II and III.B) I and IV.C) II and IV.D) III only.

Your answer: D was incorrect. The correct answer was C) II and IV.

Statement I is incorrect—The Merton model assumes that default can only occur at maturity. Statement II is correct.Statement III is incorrect—Minimizing the maximum of Type I and Type II errors is an example of Minimax. StatementIV is correct—The GINI curve is also known as cumulative accuracy profile.


Question 5 - #67457

Using the Merton model to value the firm’s debt and equity, which of the following scenarios is NOT possible?Assume the other three are true.

Equity = 0; Debt = $20.I.Equity = $10; Debt = $35.II.Equity = $10; Debt = $20.III.Equity = 0; Debt = $35.IV.

A) II only.B) III only.C) I only.D) IV only.

Your answer: C was incorrect. The correct answer was B) III only.

Equity cannot have a positive value until debt has reached its face value of $35.



Which of the following credit-scoring models attempts to classify firms as risky or non-risky by using hyperplanes thatdefine a boundary between groups?

A) Linear discriminant analysis.B) Parametric discrimination.C) Support vector machines.D) k-nearest neighbor.

Your answer: B was incorrect. The correct answer was C) Support vector machines.

Support vector machines attempt to define an equation that has firm characteristics as inputs and results in a


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boundary between different groups of firms. This boundary can either be a line, a plane, or a hyperplane.



A firm is valued at $1,000,000, and a zero-coupon bond with a $1,200,000 face value is the only debt issued by thefirm. Calculate the value of the firm’s equity.

A) −$200,000.B) $200,000.C) $1,000,000.D) $0.

Your answer: A was incorrect. The correct answer was D) $0.

Equity claimants receive the difference between firm value (VT) and the face value of the bond (F) if firm valueexceeds bond value. If bond value exceeds firm value, equity claimants receive nothing. The payoff on equity (ST) istherefore:

ST = Max(VT − F; 0)


Question 8 - #49708

Which of the following statements about the Merton model for probability of default would decrease the probability ofa firm defaulting on its debt? An increase in:

I. firm value. II. firm value volatility. III. the expected return on the firm.

A) II and III.B) III only.C) I, II, and III.D) I and III.

Your answer: B was incorrect. The correct answer was D) I and III.

Statements I and III are true. Statement II is false because the firm value volatility is directly related to the probabilityof default; therefore, an increase in volatility will increase the probability of default.



The KMV model produces a measure called expected default frequency (EDF). Which of the following statementsabout EDFs is CORRECT?

A) It decreases when the leverage of the firm falls.B) It is the risk neutral probability of default from Merton's model.

C) It tells investors how the default risk of a bond is correlated with the default risk of other bonds in theportfolio.

D) It increases when the stock price of the firm has been rising.

Your answer: C was incorrect. The correct answer was A) It decreases when the leverage of the firm falls.


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The EDF decreases when the stock price rises, when leverage falls, and when volatility goes down.The EDF is alsosimilar to the risk neutral probability of default from Merton’s model.



The KMV model is most sensitive to estimates of:

A) transition matrices.B) recovery factors and default rate standard deviations.C) credit quality of debtors.D) asset return volatility and correlations.

Your answer: D was correct!

The KMV model is most sensitive to asset return volatility and asset return correlation estimates.


Question 11 - #117279

Davis, Inc. has an expected return on assets in one year of $12 million. The default threshold has been determined tobe $7.5 million, and the annual volatility of asset returns (standard deviation) for Davis has been determined to be15%. Davis's distance to default (DD) is closest to:

A) 0.4.B) 1.6.C) 2.5.D) 1.7.

Your answer: A was incorrect. The correct answer was C) 2.5.

The DD is calculated as:

DD = ($12,000,000 – $7,500,000) / [0.15 × ($12,000,000)] = 2.5



The payoff to the writer of a put is similar to the payoff for a(n):

A) issuer of debt.B) debtor firm’s stockholders.C) holder of debt.D) writer of a call on the debtor firm’s equity.

Your answer: B was incorrect. The correct answer was C) holder of debt.

Holders of debt face the same payoff function as the writer of a put, with the value of the debt being equal to the putprice. The greatest payoff to the holder of the debt is equal to the repayment of the debt and interest, while theholder may have to settle for the prorated value of the firm’s assets in the case of failure of the firm.




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In the Merton model, where Dm is the value of the firm’s debt maturing at time m, and Vm is the value of the firm attime m, which of the following equations represents the payoffs to debt holders at maturity?

A) Dm - max(Dm - Vm, 0).

B) Vm - max(Dm - Vm, 0).

C) Dm - max(Vm - Dm, 0).D) max(Vm - Dm, 0).

Your answer: C was incorrect. The correct answer was A) Dm - max(Dm - Vm, 0).

At maturity of the debt, if the value of the firm’s assets is less than the value of the firm’s debt, the firm goes intodefault. The resulting payment to debt holders is Dm- max(Dm- Vm,0). The payment to the firm’s stock holders ismax(Vm- Dm,0).


Question 14 - #124939

A financial firm has short-term liabilities of $700, long-term liabilities of $1,000, and assets of $2,000. The standarddeviation of asset returns is $200. Compute the distance to default (DD) using the KMV model. (Note: All numbers in$million)

A) 4.0.B) 4.5.C) 5.8.D) 6.5.

Your answer: D was incorrect. The correct answer was A) 4.0.

The DD is calculated as:

Default threshold can be calculated as: short-term liabilities + 0.5 × long-term liabilities.

From the formula, DD = [$2,000 − ($700 + $500)] / $200 = 4.0.



In the Merton model, with only debt and equity in the capital structure, the value of debt will decrease and the valueof equity will increase if the:

I. interest rate increases.II. volatility of firm value increases.III. value of the firm increases.IV. value of the firm decreases.

A) I and II.B) II and III.C) I, II, and IV.D) I only.

Your answer: C was incorrect. The correct answer was A) I and II.


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Statements I and II are true. An increase in interest rates or volatility would increase the value of equity becauseequity is valued as a call option. Since the value of the firm is assumed to be constant the value of debt mustdecrease. Statements III and IV are incorrect because of the direct relationship between both equity and debt valuesand firm value.


Question 16 - #125780

Which of the following is the main driver of the probability of default in the KMV model?

A) Bond yields.B) Stock prices.C) Loan prices.D) Bond prices.

Your answer: B was correct!

Stock prices are the main driver of the KMV model’s estimated default frequencies (EDFs), as they drive the value ofequity.


Question 17 - #125327

According to the Merton model, which of the following most accurately describes the value of a firm’s debt?

A) The payoff is the same as buying a Treasury bill with a face value equal to the firm’s only debt issue, andselling a put on the firm value with an exercise price of the firm's debt.

B) The payoff is the same as buying a Treasury bill with a face value equal to one of the firm’s debt issues,and selling a put on the firm value with an exercise price of the firm's debt.

C) The payoff is the same as buying a Treasury bill with a face value equal to the firm’s only debt issue, andselling a call on the firm value with an exercise price of the firm's debt.

D) The payoff is the same as selling a Treasury bill with a face value equal to the firm’s only debt issue, andselling a call on the firm value with an exercise price of the firm's debt.

Your answer: A was correct!

If the debtholder knew with certainty that he would receive the principal amount at the maturity for the zero-couponbond, then the payoff would be F regardless of the firm value. However, the debtholder cannot expect to receive F ifthe total value of the firm, VT, is less than F. Therefore, if F > VT then the amount received by the debtholder will bereduced by F – VT. This payoff is the same as buying a Treasury bill with a face value of F and selling a put on thefirm value with an exercise price of F.


Question 18 - #117278

In the KMV approach, the distance to default (DD) is:

A) estimated based on the value of debt issues.B) the distance between the mean earnings and the debt service payments.C) the multiple of free cash flow divided by interest and principal payments.

D) the number of standard deviations between the mean of the firm's asset value distribution and a specifieddefault point.


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Your answer: B was incorrect. The correct answer was D) the number of standard deviations between the mean ofthe firm's asset value distribution and a specified default point.

In the KMV approach, the DD is the number of standard deviations between the mean of the firm's asset valuedistribution and a specified default threshold.



Suppose a firm has two debt issues outstanding. One is a senior debt issue that matures in three years with aprincipal amount of $100 million. The other is a subordinate debt issue that also matures in three years with aprincipal amount of $50 million. The annual interest rate is 5 percent and the volatility of the firm value is estimated tobe 15 percent. In the Merton model the value of equity is calculated as:

I. the difference between the value of the firm and the value of senior debt.II. a call option with an exercise price of $100 million and time to expiration of three years.

III. a call option with an exercise price of $150 million and time to expiration of three years.

IV. the value of the firm less the value of a call option with an exercise price of $100 million and time toexpiration of three years.

A) III only.B) I only.C) II and IV only.D) I and II only.

Your answer: C was incorrect. The correct answer was A) III only.

Statement III is correct. The value of equity is the difference between the value of the firm less the value of bothsenior and subordinate debt. The value of equity as a call option would have an exercise price equal to the face valueof senior debt plus the face value of subordinate debt ($100 million plus $50 million). The difference between thevalue of the firm and a call option with an exercise price of $150 million would be the value of senior debt.


Question 20 - #117273

Savid, Inc. has an expected market value of assets in one year of $20 million. The annual volatility of asset returns(standard deviation) for Savid has been determined to be $4.2 million. If the distance to default is 2.7, Savid's defaultthreshold is closest to:

A) $8.66 million.B) $4.2 million.C) $6.9 million.D) $9.43 million.

Your answer: D was incorrect. The correct answer was A) $8.66 million.

The default threshold is calculated as:

distance to default = ($20 million – default threshold) / $4.2 million = 2.7default threshold = $8.66 million



All of the following are assumptions of the KMV model EXCEPT:


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A) bondholders and stockholders cannot negotiate.B) default can only occur at maturity.C) there is no need for an adjustment for liquidity.D) there is only one issue of debt, all of which matures on a given date.

Your answer: A was incorrect. The correct answer was D) there is only one issue of debt, all of which matures on agiven date.

All of these are assumptions of the Merton model. One of the features that distinguishes the KMV model is that itallows for there to be two issues of debt: one that is short term and one that is long term.



The Merton model is:

A) a structural model but not a value-based model.B) a structural model and a value-based model.C) a value-based model but not a structural model.D) neither a structural model nor a value-based model.

Your answer: B was correct!

The Merton model is considered both a value-based model and a structural model.



Which of the following is (are) TRUE statements that make predicting the probability of default more difficult for debtthat is not publicly traded?

I. Historical data of debt values is not reliable because of the lack of liquidity for debt instruments. II. The distribution of debt values is normal. III. Debt is usually issued by creditors who have equity that is publicly traded. IV. Debt portfolios are not typically marked to market.

A) I and IV.B) III only.C) I, II, and IV.D) I, II, III, and IV.

Your answer: C was incorrect. The correct answer was A) I and IV.

Statements I and IV are true. Statement II is incorrect because the distribution of debt returns is not normal.Statement III is incorrect because the issuers of most debt instruments do not have stock issues that trade regularly.

In addition to the lack of public trading, there are four differences in measuring the risk of a debt portfolio that makeestimating the probability of default and the loss due to default more challenging:

• If securities are illiquid, then the historical data is not reliable. • The distribution of bond returns is not normal because the debtholder cannot receive more than the face amountplus the sum of the coupons. • Debt is issued by creditors who do not have traded equity. • Debt is not marked-to-market in contrast to traded securities. That is, a loss is recognized only if default occurs.



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In the Merton model, with only debt and equity in the capital structure, the value of equity will increase in value if the:

I. interest rate increases. II. volatility of firm value increases. III. value of the firm decreases. IV. face value of debt increases.

A) I only.B) I, II, and IV.C) III and IV.D) I and II.

Your answer: D was correct!

Statements I and II are correct. In the Merton model, the value of equity is directly related to the value of the firm andthe principal amount. Interest rate and the volatility of the firm are directly related to the value of equity.



In the Merton model, with only debt and equity in the capital structure, the value of debt will increase in value if the:

interest rate declines.I.volatility of firm value increases.II.value of the firm increases.III.volatility of firm value decreases.IV.

A) I only.B) III and IV only.C) I and II only.D) I, III, and IV only.

Your answer: C was incorrect. The correct answer was D) I, III, and IV only.

Statements I, III, and IV are correct. In the Merton model, the value of debt is directly related to the value of the firmand the principal amount. Time to maturity of the debt claim, interest rate, and the volatility of the firm are all inverselyrelated to the value of debt.



Which of the following includes models in which the assigned score can be interpreted as a probability of default?

A) The k-nearest neighbor approach.B) Support vector machines.C) Parametric discrimination.D) None of the above.

Your answer: B was incorrect. The correct answer was C) Parametric discrimination.

Parametric discrimination is the use of an equation to assign a value to firms, and that value would indicate whether itfalls into a default or non-default category. Included in this category of scoring models is the logit model, in which thescore can be interpreted as a probability.


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Default Risk Quantitative Methodologies

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