[2008]Topic 49: Credit Risks and Credit Derivatives 相关习题 default, holding, manager, amount, credit

aianjie

 

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.

aianjie

 

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

Value of the Firm  V	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

aianjie

 

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.

aianjie

 

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.

aianjie

 

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. 

aianjie

 

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.

aianjie

 

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). 

aianjie

 

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).

aianjie

 

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.

aianjie

 

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.