aianjie

 

AIM 4: Compute the cumulative default probability over a multiyear period given the marginal default probability for each year.

1、What is the probability that a corporate loan will be repaid if the 1-year T-bill rate is 8.0 percent and the rate on 1-year zero-coupon corporate bonds is 14.5 percent?

A) 94.32%.

B) 76.34%.

C) 93.50%.

D) 93.98%.

aianjie

 

The correct answer is

The probability of repayment is:

 

 [attach]13901[/attach]

where:

p = probability of repayment

i = Treasury rates

k = corporate rates

So,

[attach]13902[/attach]

aianjie

 

2、The risk-free rate on a 1-year Treasury bill (T-bill) is 3 percent and the implied probability of default on a 1-year zero-coupon corporate note is 3 percent, the promised rate of return on the corporate note is closest to:

A) 6.25%.

B) 6.50%.

C) 6.19%.

D) 6.77%.

aianjie

 

The correct answer is C

The probability of default is defined as “1 – p”, and can be calculated with the following formula:

 

 

 

[attach]13903[/attach]

aianjie

 

3、Basca, Inc. issued a 1-year zero-coupon note at a yield of 1.6 percent. The corresponding 1-year Treasury bill is yielding 1.04 percent. The implied probability of default on the Basca note is closest to:

A) 5.51%.

B) 5.54%.

C) 5.14%.

D) 0.55%.

aianjie

 

The correct answer is D

The probability of default is defined as “1 – p,” and can be calculated with the following formula:

 

 

 

[attach]13904[/attach]

aianjie

 

4、If the risk-free rate on a 1-year Treasury bill (T-bill) is 2.5 percent and the implied probability of default on a 1-year zero-coupon corporate note is 4.0 percent, the promised rate of return on the corporate note is closest to:

A) 6.50%.

B) 6.77%.

C) 6.25%.

D) 6.11%. 

aianjie

 

The correct answer is B

The probability of default is defined as 1 – p, where p is implied probability of repayment and can be calculated with the following formula:

 

 [attach]13905[/attach]

where:

(1 – p) = probability of default

(1 + r) = the promised return on a risk-free investment

(1 + k) = the promised return on a risky investment

[attach]13906[/attach]

aianjie

 

5、Atca Inc. issued a 1-year zero-coupon note at a yield of 6.8 percent. The corresponding 1-year Treasury bill (T-bill) is yielding 2.8 percent. The implied probability of default on the Atca note is closest to:

A) 3.75%.

B) 3.89%.

C) 3.96%. 

D) 0.37%.

aianjie

 

The correct answer is A

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

 

 

 

[attach]13907[/attach]