Question

The following table summarizes yields to maturity on several​ 1-year, zero-coupon​ securities:

Security	Yield
Treasury	2.900%
AAA Corporate1	2.991%
BBB Corporate	3.614%
B Corporate	4.379%

a. What is the price​ (expressed as a percentage of the face​ value) of a​ 1-year, zero-coupon corporate bond with a​ AAA-rating and a face value of $1,000​?

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?

Note: Assume annual compounding.

Answer 1

a) Value of a zero coupon bond value is mathematically represented as:

V = $970.96

b) Credit Spread on a bond = Yield on bond - Yield on Treasury Bond

Credit spread on AAA Bond = 2.991% - 2.900% = 0.091%

c) Credit spread on B-Bond = 4.379% - 2.900% = 1.479%

d) As the credit rating on a bond declines, the risk associated with the bond increases. Higher risk implies requiring higher return and hence, yield on bond also increases. As yield increases, so does the credit spread on bond with lower credit rating.