Question

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

Security	Yield ​(%)
Treasury	3.063.06
AAA corporate	3.133.13
BBB corporate	4.124.12
B corporate	4.884.88

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?

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?

The price of this bond will be

nothing​%.

​(Round to three decimal​ places.)

Answer 1

a]

price = face value / (1 + yield)^1 (this is the present value formula with for 1 year discounting)

price = $100 / (1 + 3.13313%) ==> $96.962

b]

credit spread on​ AAA-rated corporate​ bonds = yield on AAA bonds - Treasury Yield

credit spread on​ AAA-rated corporate​ bonds = 3.13313% - 3.06306% ==> 0.070%

c]

credit spread on​ B-rated corporate​ bonds = yield on B-rated corporate​ bonds - Treasury Yield

credit spread on​ B-rated corporate​ bonds = 4.12412% - 3.06306% ==>  1.06106%

d]

The credit spread represents the default risk. Treasury bonds are backed by the Treasury and are considered default-risk free. AAA are the highest rated non-Treasury bonds. They have a higher yield than Treasury bonds to compensate for their higher default risk. B-rated corporate bonds have a lower rating than AAA bonds, which means their risk of default is higher than AAA bonds. Hence B-rated bonds have a higher credit spread than AAA bonds