Question

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

Security	Yield ​(%)
Treasury	3.12
AAA corporate	3.26
BBB corporate	4.26
B corporate	4.96

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

Given,

Security	Yield ​(%)
Treasury	3.12
AAA corporate	3.26
BBB corporate	4.26
B corporate	4.96

a). let the face value of a AAA rated corporate bond be $100,

Yield of this bond = 3.26%

So, price of a AAA rated 1 year bond = FV/(1+Yield) = 100/(1.0326) = $96.84

So, price of the bond = 96.84% of its face value.

b). Credit spread = yield of the bond - Treasury(risk free) rate

So, credit spread of a AAA rated bond = 3.26% - 3.12% = 0.14% or 14 basis points

c). Credit spread of a B rated bond = 4.96% - 3.12% = 1.84% or 184 basis points.

d). When bonds rating decreases, credit spread of the bond increases. This is because, with the decrease in bond rating, bond become more riskier and investor demands more return from the investment.