Question

The following table summarizes the yields to maturity on several​ one-year, zero-coupon​ securities: Security Yield ​(%) Treasury 3.063.06 AAA corporate 3.183.18 BBB corporate 4.184.18 B corporate 4.844.84 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

a]

Price of 1-year zero-coupon bond = par value / (1 + yield)

Price of 1-year zero-coupon bond = $1,000 / (1 + 3.183%)

Price of 1-year zero-coupon bond = $969.15

b]

Credit spread = yield on bond - yield on Treasury security

Credit spread = 3.183% - 3.063% = 0.120%

c]

Credit spread = yield on bond - yield on Treasury security

Credit spread = 4.844% - 3.063% = 1.781%

d]

Lower the credit rating, higher the credit spread and higher the credit rating, lower the credit spread.

Lower rated bonds are more risky for the bond investor. Hence, bonds investors require a higher return on these bonds to compensate them for the additional risk. Therefore lower rated bonds have higher yields.