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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.

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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.

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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

aianjie

 

The correct answer is A

Merton model of probability of default (PD) is:

 

 [attach]13935[/attach]

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:

 

 [attach]13936[/attach]

 [attach]13939[/attach]

What is the amount of the expected LGD?

 

 [attach]13940[/attach]

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

aianjie

 

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.

aianjie

 

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.

aianjie

 

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.

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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.

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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.

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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.