Question

​The thirty-year US Treasury bond has a 2.5% coupon and yields 3.3%. What is its price?

​A thirty-year corporate bond with a 4% coupon is priced at par. Is it possible for the corporate bond to have a higher price than the Treasury? How is the corporate bond’s “spread” quoted?

​Both bonds are 100 face and semi-annual.

Answer 1

T-Bond Tenure = 30 years or 60 half-years, T-Bond Coupon = 2.5 % paid semi-annually, T-Bond Yield = 3.3 %, T-Bond Face Value = $ 100

Semi-Annual Coupon = 0.025 x 0.5 x 100 = $ 1.25

Market Price of T-Bond = 1.25 x (1/0.0165) x [1-{1/(1.0165)^(60)}] + 100/(1.0165)^(60) = $ 84.84

A 30 year corporate bond with a coupon of 4 % selling at par implies a yield to maturity equal to the coupon of 4 % for the corporate bond. Hence, the yield = 4 %.

It is not possible for a US Corporate Bond (US being the keyword here) to have a price higher than (or yield lower than) a US Treasury bond of similar maturity as the latter on account of being guaranteed by the US Government is free of default risk and quite close to being riskless. The former, on the other hand always has a default risk which manifests itself in it possessing a higher yield to maturity as compared to the corresponding maturity US Treasury bond. The difference between the two bond's yield is known as the yield spread or sometimes the risk-premium. Corporate Bond spreads are usually quoted in basis points relative to the benchmark (treasury yield of equal maturity) yield rate. In this context, for example, the corporate bond yield is 4 % whereas that of the treasury bond is 3.3 %, thereby implying a yield spread of 0.7 % or 70 basis points.