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.
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.
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