Question

You are given the following information

Bond A has a price of $ 123.78, it matures on Jan-2030, its coupon rate is 3.78%, and it's AAA-rated

Bond B has a price of $ 117.34, it matures on Jan-2030, its coupon rate is3.65%and it's AA-rated

Bond C has a price of $ 119.22, it matures on Jan-2030, its coupon rate is 3.96%, and it's BBB-rated.

Bond D has a price of $ 129.3, it matures on Jan-2030, its coupon rate is 7.2%, and it's BB-rated.

US Bond X has a price of $ 110.25, it matures on June-2029, and its coupon rate is 1.78%

US Bond Y has a price of $ 111.27, it matures on July-2030, and its coupon rate is1.95%

a) Calculate the credit risk premium of each of the given rated bonds.

b)Let's say that you have to price a 10-year AAA-rated bond that is issued on Nov 30, 2020 – Calculate the coupon for the bond if you are given that the risk-free rate on that day will be 0.69% and that the credit premiums remained the same.

Note: all coupon rates are per annum with semi-annual compounding

Answer 1

Let's calculate the yield of each of the bonds given using the Rate function of excel. Recall that all coupon rates are per annum with semi-annual compounding. Hence, Nper = 2 x years to maturity; PMT = Annual coupon / 2

Please see the table below:

Bond	year to maturity	Annual Coupon rate	Nper	PMT	PV	FV	Semi annual Yield	Annual yield
	n	C	2 x n	100 x C/2	-Price		Rate (Nper, PMT, PV, FV)	2 x Semi annual yield
A	9.5	3.78%	19	1.89	-123.78	100	0.5663%	1.1327%
B	9.5	3.65%	19	1.825	-117.34	100	0.8343%	1.6687%
C	9.5	3.96%	19	1.98	-119.22	100	0.8773%	1.7547%
D	9.5	7.20%	19	3.6	-129.3	100	1.7705%	3.5410%
X	9	1.78%	18	0.89	-110.25	100	0.3040%	0.6079%
Y	10	1.95%	20	0.975	-111.27	100	0.3882%	0.7765%

Part (a)

US bond yield for 9.5 year maturity, y = Average of (9 years maturity bond, 10 year maturity bond) = (Yield of bond X + Yield of bond Y) / 2 = (0.6079% + 0.7765%) / 2 = 0.6922%

Hence, the credit risk premium of any of the given rated bonds = Annual yield of that bond - y = Annual yield - 0.6922%

Hence, the final answer is as shown in the last column below:

Bond	Annual yield	Credit risk premium
A	1.1327%	0.4405%
B	1.6687%	0.9764%
C	1.7547%	1.0625%
D	3.5410%	2.8488%

Part (b)

Yield for this bond = Risk free rate + credit risk premium for AAA rated bond = 0.69% + 0.4405% = 1.1305%

Hence, the Coupon rate of a par bond = yield = 1.1305%