Suppose XYZ Corp. has two bonds paying semiannually according to the following table.
 
The recovery rate for each in the event of default is 50%. For simplicity, assume that each bond will default only at the end of a coupon period. The market-implied risk-neutral
probability of default for XYZ Corp. is
A. Greater in the first six-month period than in the second
B. Equal between the two coupon periods
C. Greater in the second six-month period than in the first
D. Cannot be determined from the information provided
Answer:A
First, we compute the current yield on the six-month bond, which is selling at a discount. We solve for y∗ such that 99 = 104/(1 + y∗/2) and find y∗ = 10.10%. Thus, the yield spread for the first bond is 10.1 - 5.5 = 4.6%. The second bond is at par, so the yield is y∗ = 9%. The spread for the second bond is 9 - 6 = 3%. The default rate for the first period must be greater. The recovery rate is the same for the two periods, so it does not matter for this problem.