AIM 1: Calculate, using the Merton model, the value of a firm’s debt and equity and the volatility of firm value.

1、Suppose a fixed income portfolio manager buys a risky bond issue with a face amount of $100 million that matures in one year. To hedge the credit risk that the issuer of the debt will not pay the full amount, the debt holder buys a credit default put on the value of the issuing firm. What are the payoffs for holding a risky bond and the credit default put, if the 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) $80 million and the credit default put payoff is $20 million. 

D) $100 million and the credit default put payoff is $20 million.

The correct answer is C

If the firm value is only $80 million, then the holder of risky debt will experience a $20 million loss unless they also have 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

2、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.

The correct answer is C

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

3、Suppose a firm has two debt issues outstanding. One is a senior debt issue that matures in three years with a principal amount of $100 million. The other is a subordinate debt issue that also matures in three years with a principal amount of $50 million. The annual interest rate is 5 percent and the volatility of the firm value is estimated to be 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 to expiration of three years. 

A) III only. 

B) I only.

C) II and IV only. 

D) I and II only. 

The correct answer is A

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

4、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 at time m, which of the following equations represents the payoffs to debt holders at maturity?

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

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

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

D) max(Vm - Dm, 0). 

The correct answer is C

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 into default. The resulting payment to debt holders is Dm- max(Dm- Vm,0). The payment to the firm’s stock holders is max(Vm- Dm,0).

5、In the Merton model, with only debt and equity in the capital structure, the value of debt will decrease and the value of 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.

The correct answer is A

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

6、The Merton model is:

A) a structural model and a value-based model.

B) a structural model but not a value-based model.

C) a value-based model but not a structural model.

D) neither a structural model nor a value-based model.

The correct answer is A

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

7、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 and II.

B) I only.

C) I, II, and IV.

D) III and IV.

The correct answer is A

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

8、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.

I.           Equity = 0; Debt = $20.

II.         Equity = $10; Debt = $35.

III.        Equity = $10; Debt = $20.

IV.      Equity = 0; Debt = $35.

A) III only.

B) II only.

C) I only.

The correct answer is A

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

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

I.           interest rate declines.

II.         volatility of firm value increases.

III.        value of the firm increases.

IV.      volatility of firm value decreases.

A) I only.

B) III and IV only.

C) I, III, and IV only.

D) I and II only.

The correct answer is C

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

AIM 5: Explain how interest rate dynamics and the interaction with firm value affect the price of debt.

Suppose a levered firm (with only one debt issue) is experiencing financial distress and that the firm’s value of debt is affected by unanticipated changes in interest rates. Which of the following statements is/are consistent with the models that include variables that measure interest rate dynamics?

 I. The value of debt will increase if the volatility of interest rates declines.

 II. The value of debt will increase if the correlation between the firm value and changes in interest rates increases.

 III. The value of debt will increase if the speed of mean reversion of interest rates increases.

 IV. The value of debt will increase if the long-term mean increases.

A) I and III.

B) I and IV.

C) II and IV.

D) I and II.

The correct answer is B

Statements I and IV are true. In the Shimko, Tejima, and van Deventer (1993) model, an increase in the volatility of interest rates will result in lower values for debt and higher values for equity; therefore, statement I is true. Likewise, a higher correlation between firm values and changes in interest rates will result in lower debt values and higher values for equity; therefore, statement II is false. The Vasicek model includes a speed to reversion term that is also included in the model presented by Shimko, Tejima, and van Deventer. In this model, a higher value for the speed term reduces the value of debt and a increases the value of equity; therefore, statement III is false. The long-term mean in the Shimko, Tejima and van Deventer model is directly related to debt values and inversely related to equity values; therefore, statement IV is true.

AIM 8: Compute the probability of default, PD, and loss given default, LGD.

1、Which of the following is/are TRUE statements that make predicting the probability of default more difficult for debt that 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) III only.

B) I, II, and IV.

C) I, II, III, and IV.

D) I and IV.

The correct answer is D

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 make estimating 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 amount plus 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.

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

   PD                          LGD

A) 6.51%                  $1,086,000

B) 0.78%                  $780,000

C) 56.50%                 $16,629,000

D) 2.21%                  $252,000

The correct answer is A

Merton model of probability of default (PD) is:

where:

F     = face value of the zero-coupon bond,

V     = value of the firm

T     = maturity date on bond

σ     = 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.

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

      I. firm value.

     II. firm value volatility.

    III. the expected return on the firm.

    IV. the time to maturity of the debt claim.

A) I, III, and IV.

B) II, III, and IV.

C) III and IV.

D) I, II, III, and IV.

The correct answer is A

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

AIM 2: Explain the relationship of credit spreads, time to maturity, and interest rates.

When determining credit risk spread, the benchmark security is most likely a(n):

A) Treasury bond.

B) high-yield corporate bond.

C) low-yield corporate bond.

D) AA rated bond.

The correct answer is A

The credit risk spread is measured in relation to a default-free security. Of the choices above, the security with the least chance of default is the Treasury bond. The AA rated bond is high quality, but not the highest quality (which would have an AAA rating). The high-yield corporate bond is an unlikely candidate for the benchmark security because high yield usually denotes high risk. The low-yield corporate bond is a possibility, but it is not likely that this bond is as default-free as the Treasury security.

AIM 10: Discuss the fundamental differences between various credit portfolio models.

1、With respect to computing correlations, one of the three major drivers of portfolio credit risk, CreditMetrics uses:

A) the beta distribution.

B) a linear factor model.

C) the Poisson distribution.

D) a VAR approach.

The correct answer is B

CreditMetrics uses the standard approach of estimating the sensitivity of the returns of the assets to a set of factors using a linear model and then computing the correlations of the returns using the correlation matrix of the factors, the sensitivities, and the asset-specific risks of the assets.

2、The first step of CreditMetrics would include all of the following EXCEPT:

A) gathering yield curve data.

B) calculating the probability of default.

C) none of these.

The correct answer is D

The Poisson distribution is not part of CreditMetrics. The first step consists of the gathering of inputs. The gathering includes calculating many measures such as probability of default, recovery rate statistics, factor correlations and their relationships to the obligors, yield curve data, and individual exposures that are distinct from the other inputs.

3、Which of the following is (are) a characteristic of the KMV model?

I.           Each obligor has its own sensitivity to each of the common risk factors.

II.         The model produces a VAR measure.

III.        It includes current economic conditions.

IV.      It includes an estimate of correlation between firm values based on the correlation between observed equity values.

A) I only.

B) II and IV only.

C) II only.

D) I, II, III, and IV.

The correct answer is B

Statements II and IV are true. Statement I is only true for CreditRisk+. Statement II is a characteristic of CreditMetrics and the KMV models. Statement III is a weakness of all portfolio credit models. Statement IV is a characteristic and major advantage of the KMV model.

AIM 9: Assess the credit risks of derivatives.

1、ADC Inc. enters into a plain vanilla interest rate swap contract with Betax Inc. At the 3rd settlement date, ADC is owed $2.5 million but is unable to enforce the contract due to a technicality. This is an example of:

A) contract risk.

B) legal risk.

C) business risk.

D) credit risk.

The correct answer is B

Legal risk is the risk of loss due to legal or regulatory issues. Most legal risk issues are a direct result of being unable to enforce contracts.

2、A credit default swap does NOT hedge against which of the following risks?

A) Default risk.

B) Market.

C) Credit Deterioration.

D) Operations risk.

The correct answer is B

Credit default swaps hedge default risk as well as credit deterioration risk if the swaps are marked-to-market. They don’t, however, hedge market risk because the value of the swap is defined by the credit event. In addition, with regard to operations risk, the credit default swap will provide a hedge if the operational problem is serious enough.

3、An investor purchases 300,000 of ABC Corps bonds with an annual coupon of 8% and maturity of 5 years. The yield is 8% so the bonds are selling at par. The total notional amount of the bonds is $10,000,000. The investor hedges 80% of the position by becoming a total rate of return swap (TROR) payer. ABC’s computer system is hacked and the firm’s bonds decrease in price from $100 to $90. What is the payoff to the TROR total rate of return swap due to the increase in operations risk?

A) $3,000,000.

B) $2,100,000.

C) $2,400,000.

D) $1,700,000.

The correct answer is C

The loss on the investor’s bond position is $3,000,000. The investor has hedged 80% of the position, so they will receive 80% of $3,000,000 or $2,400,000.

($90-$100) x 300,000 = $3,000,000 x 80% =$2,400,000

4、The buyer of a credit default swap (CDS):

A) receives periodic payments after default equal to the promised payments on the defaulted bond. 

B) assigns the coupon payments from the loan to the issuer of the swap in exchange for a stated (but somewhat lower) string of guaranteed payments. 

C) makes periodic payments to the seller of the swap until a default occurs. 

D) makes a single payment to the seller of the swap at inception of the swap. 

The correct answer is C

The buyer of the CDS makes periodic payments to the seller until a credit event such as a default occurs.

5、Commercial Finance has lent $5 million to Barely, Inc. for one year at 7%, and entered into a credit default swap with Credit Insurers for 130 basis points. If the swap calls for semi-annual payments, what is due on the first payment assuming that no default has occurred?

A) Commercial Finance will pay Credit Insurers $32,500.

B) Credit Insurers will pay Commercial Finance $32,500.

C) Commercial Finance will pay Credit Insurers $207,500.

D) Commercial Finance will pay Credit Insurers $142,500.

The correct answer is A

Commercial Finance will pay Credit Insurers the sum equal to: ($5 million) (0.013 / 2) = $32,500.

6、From the swap seller’s perspective, a default swap creates a:

A) short position in the reference obligation. 

B) call position in the reference obligation. 

C) long position in the reference obligation. 

D) put position in the reference obligation. 

The correct answer is C

From the swap seller’s perspective, a default swap creates a long position in the reference obligation. If the reference obligation increases in value or credit quality, the default swap decreases in value below the price at which it was originally sold.

7、The buyer of a credit-default swap (CDS):

A) has no risk exposure to the combined holdings of the CDS and reference obligation.

B) must place collateral with the seller of the CDS to ensure performance. 

C) is subject to the credit risk of the seller.

D) can surrender the CDS for the value of the accumulated payments.

The correct answer is C

The buyer of the CDS faces the risk that the seller may not be able to make the required payment if the reference obligation defaults. Two factors impact this risk: (1) if the probability of the reference obligation default increases with time, then so, too, may the probability of seller default, and (2) economic and operational factors may cause an increase in the correlation between the default of the reference obligation and the seller’s default.

8、A default swap acts like a:

A) call option on the reference obligation for the buyer of the swap.

B) look back option on the reference obligation for the buyer of the swap.

C) up-and-out option on the reference obligation for the buyer of the swap.

D) put option on the reference obligation for the buyer of the swap.

The correct answer is D

A default swap acts like a put option on the reference obligation for the buyer of the swap. If there is a default, the buyer receives a payment, which limits the buyer’s downside risk.

9、Which of the following would most likely be settled with one party requiring the other to purchase the underlying asset?

A) A total return swap.

B) Senior basket default swap.

C) Subordinate basket default swap. 

D) A credit default swap. 

The correct answer is D

In a credit default swap, one party makes payments to the other until the default (if it occurs), the terms of the swap may require the receiver of the payments prior to the default to purchase the underlying asset. All of the other choices usually only involve a cash settlement.

10、Which of the following is/are a credit event?

 I. Failure to make a required payment.

 II. Restructuring that makes the creditor worse off.

 III. Bankruptcy.

 IV. Invocation of a cross-default clause.

A) II and III.

B) I, II, and III.

C) I, II, III, and IV.

D) I, II, and IV.

The correct answer is C

All statements are true. Credit events include:

  ? Failure to make required payments.

    ? Restructuring that harms the creditor.

    ? Invocation of cross-default clause.

    ? Bankruptcy.

11、A seller must make a payment to the credit protection buyer based on a trigger event. According to the International Swaps and Derivatives Association (ISDA), all of the following are trigger events EXCEPT a:

A) restructuring.

B) obligation acceleration.

C) repudiation/moratorium. 

D) stock split.

The correct answer is D

ISDA identified six trigger events which trigger a payment from a credit protection seller to a credit protection buyer:

Bankruptcy

Failure to pay

Restructuring

Obligation acceleration

Obligation default

Repudiation/moratorium

12、The most that the buyer of a credit default swap can expect to receive in the event of a default is:

A) interest and principal payments as originally scheduled.

B) the par value of the instrument.

C) a premium price for the instrument.

D) 85% of the originally scheduled payments.

The correct answer is B

In the event of default, the most that the buyer of a credit default swap can receive is the par value of the instrument.

13、For a Nth-to-default swap, the credit protection it offers would most likely equal a:

A) senior basket default swap if N = 1.

B) subordinate basket default swap if N = 1. 

C) subordinate basket default swap if N = 0.

D) senior basket default swap if N = 0.

The correct answer is B

Of all the possible answers, this is the best one because a subordinate basket default swap makes a payment on the first default as will a Nth-to-default swap if N=1. A senior basket default swap does not make a payment until some threshold is reached, which is usually set so more than one reference entity must default before there is a payout. There is no such thing as a Nth-to-default swap where N=0.

14、The type of basket default swap that usually makes a payment on the default of a single reference entity and then terminates is the:

A) inverted swap.

B) Nth-to-default swap. 

C) senior basket default swap.

D) subordinate basket default swap.

The correct answer is B

The Nth-to-default swap makes no payments on the 1, 2, …N-1 defaults nor on the N+1, N+2 defaults. Payments are only made on the Nth default, and then the swap terminates.

15、Which of the following credit derivatives would hedge market-wide interest rate risk?

A) A TROR.

B) Credit spread put.

C) Credit spread swap.

D) Credit spread forward.

The correct answer is A

In a total rate of return swap (TROR), the TROR receiver will pay the TROR payer if the reference obligation experiences a price decline that is greater than the coupon. The price decline could be due to an increase in credit risk or an increase in interest rates. Thus the TROR protects the TROR payer against interest rate risk. In the credit spread derivatives mentioned, the contracts’ values depend on a credit spread that is the difference between the reference obligation’s yield and a risk-free bond. The credit spread and the contracts’ values will thus be unaffected by changes in market-wide interest rates, all else equal.

16、Which of the following CORRECTLY describes the total return receiver in a total return credit swap? The total return receiver will:

A) hedge credit exposure.

B) hedge interest rate risk.

C) diversify default risk.

D) increase credit exposure.

The correct answer is D

A total return credit swap transfers all of the economic exposure of a reference asset or a basket of referenced assets to the total return receiver in the total return credit swap.

17、The credit derivative that can hedge the most types of risk is most likely the:

A) basket default swap.

B) total return swap.

C) credit default option.

D) credit spread forward.

The total return swap provides the protection buyer with a payoff for a decline in the value of the underlying regardless of the reason for the decline. A default or spread product specifies a particular condition that must occur. In the case of a credit default option being used to hedge a bond, for example, the spread could widen from macroeconomic factors, which would cause the bond’s value to decline. Since the decline was not caused by a default, however, the option would not provide a payoff.

18、An investor can gain the exposure and return of an underlying loan by:

A) being the credit risk seller in a total return swap.

B) being the credit risk buyer in a total return swap.

C) entering into an interest-rate swap with a BB credit.

D) pledging compensating balances with the lender bank.

The correct answer is B

The credit-risk seller pays to the credit-risk buyer the total return of the underlying instrument. An investor can gain the exposure and return by being the buyer in a total return swap.

19、In a total return swap, the:

A) total return payer bears the risk of holding the reference asset.

B) total return payer transfers the risk of holding the reference asset to the total return receiver.

C) total return receiver transfers the risk of holding the reference asset to the total return payer. 

D) credit risk of the buyer and seller cancel each other out.

The correct answer is B

In a total return swap, the total return payer transfers the capital gains and losses of the reference asset to the total return receiver.

20、The total return payer in a total return swap (TRS) must pay the total return buyer:

A) the total bond return minus the coupon payments.

B) the total bond return.

C) only the coupon payments and any principal received from the bond.

D) a floating rate payment usually based on the London Interbank Offered Rate (LIBOR). 

The correct answer is B

The credit risk seller pays to the credit risk buyer the total return of the underlying bond which is equal to the coupon payments plus price appreciation or minus price depreciation.

21、The total return payer (credit risk seller) in a total return swap (TRS) is exposed to:

A) the interest-rate risk of the debt obligation.

B) paying floating rate payments.

C) the credit risk of the issuer of the debt obligation.

D) the credit risk of the credit risk buyer. 

The correct answer is D

The seller of credit risk in a TRS is exposed to the credit risk of the buyer. If the value of the underlying obligation depreciates, the credit risk buyer must compensate the credit risk seller. The amount of depreciation could be substantial—as in the case of default—and the credit risk buyer may not have the resources to pay the credit risk seller. The seller often requires the buyer to pledge collateral to support this potential payment.

22、Credit risk in a swap can be reduced by:

I.           requiring a margin.

II.         netting payments between parties.

III.        full two-way payment covenant.

IV.      limited two-way payment covenant.

A) I and IV only.

B) I, II, and III only.

C) II and III only.

D) II and IV only.

The correct answer is B

A limited two-way payment covenant abolishes obligations if either party is in default.

23、Which of the following is least likely a characteristic of credit default swaps? Credit default swaps:

A) are similar to a credit put option.

B) transfer credit risk exposure.

C) trade on an exchange.

D) Payoff if a credit event occurs.

The correct answer is C

Credit default swaps can be compared to a credit put option or an insurance contract. Credit default swaps are not traded on an exchange; rather they are traded over the counter.

24、Which of the following statements concerning a credit default swap is FALSE?

A) The contract size is established by the International Swaps and Derivatives Association (ISDA).

B) It is comparable to a credit put option.

C) It acts as an insurance policy for the buyer against a company defaulting on its bonds. 

D) It is a private contract between a buyer and seller.

The correct answer is A

Buyers and sellers determine the size and maturity of a credit default swap.

25、Credit derivatives have their own unique risks. All of the following are risks associated with credit derivatives EXCEPT:

A) counterparty risk.

B) default risk.

C) operational risk.

D) liquidity risk.

The correct answer is B

Default risk is associated with reference assets. Risks specially associated with credit derivatives include: liquidity risk, operational risk, counterparty risk, and pricing/model risk. Liquidity risk is the result of a contract’s uniqueness. The potential of traders or investors to improperly use credit derivatives is operational risk. The risk that one party may not live up to their end of the contract is counterparty risk. Finally, the complexity of pricing credit derivatives can result in pricing/model risk.

26、What risk describes a credit derivative buyer or seller NOT fulfilling their agreement?

A) Pricing risk.

B) Counterparty risk.

C) Liquidity risk.

D) Operational risk.

The correct answer is B

Counterparty risk describes the risk that one party does not fulfill their credit derivative agreement. Pricing risk describes the problems associated with the accuracy of complex models that price credit derivatives. Liquidity risk occurs as a result of the lack of interest in the secondary market for credit derivative contracts customized for other entities. Operational risk is the result of off-balance sheet treatment of credit derivatives, which can create excessive credit risk exposure for the firm.

27、It has been 90 days since the last coupon payment on a default swap. The notional principal is $10,000,000, and the reference price is 100%. The final price is estimated at 40%, and the annual coupon rate was 8%. What is the cash amount to settle the swap?

A) $5,800,000.

B) $9,040,000.

C) $5,200,000.

D) $4,600,000.

The correct answer is A

The settlement of the default swap is the notional principal times the reference amount minus the final and accrued interest.

28、Which of the following is NOT listed as an International Swaps and Derivatives Association default trigger for payment under a credit default swap?

A) A downgrade from a ratings agency.

B) Bankruptcy.

C) Obligation default.

D) Failure to Pay.

The correct answer is A

Bankruptcy, obligation default, and failure to pay are listed as default triggers by the International Swaps and Derivatives Association. A downgrade from a ratings agency is not.