Question

A five-year 2.4% defaultable coupon bond is selling to yield 3% (Annual Percent Rate and semi-annual compounding). The bond pays interest semi-annually. The risk-free yield is 2.4%. Therefore, its current credit spread is 3% -2.4% = 0.6%. Two years later its credit spread increases from 0.6% to 1% while the risk-free yield doesn’t change. Assuming the face value of the coupon bond and risk-free bond is 100.a)What is the return of investing in this bond over the two year? (10 marks

Answer 1

a) The bond will pay coupon of 1.2 for every six month. The original yield is 3.00% i.e. 1.50% for every six months. Therefore, the original price of the 5 year bond paying 10 six monthly coupons will be 97.233 calculated as follows:

Time Period	Cash Flow	PV Factor @ 1.5%	PV
1	1.2	0.9852	1.182
2	1.2	0.9707	1.165
3	1.2	0.9563	1.148
4	1.2	0.9422	1.131
5	1.2	0.9283	1.114
6	1.2	0.9145	1.097
7	1.2	0.9010	1.081
8	1.2	0.8877	1.065
9	1.2	0.8746	1.050
10	101.2	0.8617	87.201
		Total Price	97.233

Note that the present value factor is calculated as 1/(1.015)ⁿ where n is the respective time period.

After 2 years the yield of the bond has increased to 3.40% (2.40% + 1%) i.e. 1.7% for every six month. Therefore, the price of this bond after 2 years which will then have 6 coupons remaining will be 97.171 calculated as follows:

Time Period	Cash Flow	PV Factor @ 1.7%	PV
1	1.2	0.9833	1.180
2	1.2	0.9668	1.160
3	1.2	0.9507	1.141
4	1.2	0.9348	1.122
5	1.2	0.9192	1.103
6	101.2	0.9038	91.465
		Total Price	97.171

Therefore, the return of this bond for the holding period of 2 years will be calculated by discounting the 4 coupons received of 1.2 and the investment value of 97.233 and price after two years of 97.171. This calculation is done using a spreadsheets which gives the return for 6 months as 1.218% i.e a Return of 2.437% Per Annum (Compounded Semi Annually)

Time Period	Cash Flow	PV Factor @ 1.218%	PV
0	-97.233	1.0000	-97.233
1	1.2	0.9880	1.186
2	1.2	0.9761	1.171
3	1.2	0.9643	1.157
4	1.2	0.9527	1.143
4	97.171	0.9527	92.576
		Total	0.000