aianjie

 

6、Beta Inc. issued a 1-year zero-coupon note at a yield of 8.6 percent. The corresponding 1-year Treasury bill (T-bill) is yielding 8.2 percent. The implied probability of default on the Beta note is closest to:

A) 3.75%.

B) 0.37%. 

C) 3.89%. 

D) 3.96%.

aianjie

The correct answer is Bfficeffice" />

The probability of default is defined as (1 – p) and can be calculated with the following formula:

 

 

[attach]13908[/attach]

aianjie

 

7、Calculate the required risk premium for a one year corporate debt, if the one-year t-bill rate is 4%, the probability of repayment is 98%, and the recovery rate is 60%.

A) 0.85%.

B) 0.98%.

C) 1.17%.

D) 1.43%.

aianjie

 

The correct answer is A

Φ = (1 + i) / (γ + p ? pγ) ? (1 + i) = (1.04) / (0.6 + 0.98 ? 0.588) ? 1.04 = 0.00838

aianjie

 

AIM 5: Compute a marginal default probability using the term structure approach.

1、The cumulative probability of default for a note over two years is 3.8 percent. If the probability of default during the first year is 1.5 percent, the probability of default during the second year is closest to:

A) 2.96%.

B) 2.34%.

C) 3.17%.

D) 3.28%.

aianjie

 

The correct answer is B

The cumulative probability of default is equal to one minus the probability of surviving to the end of the period without default:

 

 

 

[attach]13909[/attach]

aianjie

 

2、The rate on a 1-year Treasury note (T-note) is 3.0 percent, and the rate on a 2-year T-note is 4.5 percent. The rate on a 1-year corporate note is 5 percent, and the rate on a 2-year corporate note is 6.8 percent. The implied probability of default on the corporate note in year two is closest to:

A) 2.34%.

B) 3.43%.

C) 2.40%.

D) 4.11%.

aianjie

 

The correct answer is C

We can solve for the 1-year rate, one year forward for each of the T-notes and corporate bonds. Then we can use these two rates to determine the implied probability of default on the corporate note during the second year.

 

 

 

[attach]13910[/attach]

aianjie

 

3、The marginal probability of default for years one and two is 0.5 percent and 1.1 percent, respectively. If the cumulative probability of default for the 3-year period is 4.45 percent, the marginal probability of default for year three is closest to:

A) 2.8%.

B) 2.9%.

C) 3.2%.

D) 2.7%.

aianjie

 

The correct answer is B

The cumulative probability of default is equal to one minus the probability of surviving to the end of the period without default:

 

[attach]13911[/attach]