Question

The following table summarizes the yields to maturity on several​ one-year, zero-coupon​ securities: Security Yield ​(%) Treasury 3.08 AAA corporate 3.15 BBB corporate 4.17 B corporate 4.91

a. What is the price​ (expressed as a percentage of the face​ value) of a​ one-year, zero-coupon corporate bond with a AAA​ rating? b. What is the credit spread on​ AAA-rated corporate​ bonds? c. What is the credit spread on​ B-rated corporate​ bonds? d. How does the credit spread change with the bond​ rating? Why?

Answer 1

Answer(a): Computation of price​ (expressed as a percentage of the face​ value) of a​ one-year, zero-coupon corporate bond with a AAA​ rating-

Given: YTM(r) = 3.15%, n = 1, Assume the face value is $1000

Price of Zero coupon bond = Face vaue / (1+r)ⁿ

Price of Zero coupon bond = 1000 / (1+.0315)¹

Price of Zero coupon bond = $969.46

Expressed as a percentage of the face​ value: (969.46 / 1000) * 100 = 96.946%

Answer(b): Credit spread on​ AAA-rated corporate​ bonds:

Credit spread = YTM of AAA rate corprate bond - YTM of treasury bond (risk free)

Credit spread = 3.15% - 3.08%

Credit spread = .07%

Answer(c): Credit spread on​ B-rated corporate​ bonds:

Credit spread = YTM of B rate bond - YTM of treasury bond

Credit spread = 4.91% - 3.08%

Credit spread = 1.83%

Answer(d): Credit rating of bond changes due to change in credit risk related to bond. Bonds that have lower ratings, provide higher return with high risk so investors purchase high risk bonds to get the high returns that is why the credit spread changes.