Question

Current (annualised) US Treasury spot rates are as follows:

6 months	1 year	18 months	2 years
0.4%	0.5%	0.6%	0.7%

Bond Cashflows:

Maturity: 2 years semi annual

Par value: 100

Coupon: 1.625/2 = 0.8125

6 months from now = 0.8125

1 year from now = 0.8125

1.5 year from now= 0.8125

2 years from now = 100+0.8125

From the US treasury spot rates above and assuming Z-spread of 35 basis points, calculate appropriate discount rates (implied spot rates) for this bond’s cash flows. Show calculations.

Answer 1

6 month discount rate = 6 month treasury spot rate + Z-spread

6 month discount rate = 0.4% + 0.35%

6 month discount rate = 0.75%

1 year discount rate = 1 year treasury spot rate + Z-spread

1 year discount rate = 0.5% + 0.35%

1 year discount rate = 0.85%

1.5 year discount rate = 1.5 year treasury spot rate + Z-spread

1.5 year discount rate = 0.6% + 0.35%

1.5 year discount rate = 0.95%

2 year discount rate = 1 year treasury spot rate + Z-spread

2 year discount rate = 0.7% + 0.35%

2 year discount rate = 1.05%

Illustrating the usage of the discount rates in Bond pricing

Bond price = Cashflow / (1 + 6 month discount rate / 2 ) + Cashflow / (1 + 1 year discount rate / 2)² + Cashflow / (1 + 1.5 year discount rate / 2)³ + Cashflow / (1 + 2 year discount rate / 2)⁴

Bond price = 0.8125 / (1 + 0.75% / 2)¹ + 0.8125 / (1 + 0.85% / 2)² + 0.8125 / (1 + 0.95% / 2)³ + 100.8125 / (1 + 1.05% / 2)⁴

Bond price = 101.1391