Question

1yr Tnote at par with 8.63% ytm p.a.

1.5yr Tnote with a 5% coupon rate and 9.62% ytm p.a

Compute the zero yields. Please report per annum semi-annual compounding yields.

Answer 1

S1 = zero yield for year 1 = YTM of the 1 year note = 8.63%

For 1.5 year T Note: Coupon per half year = 5% / 2 = 5% / 2 x 1000 = 25

Price = PV of future cash flows using zero yields = 25 / (1 + S1/2) + 25 / (1 + S1 / 2)² + (25 + 1000) / (1 + S_1.5 / 2)³

= 25 / (1 + 8.63%/2) + 25 / (1 + 8.63% / 2)² + (25 + 1000) / (1 + S_1.5 / 2)³ = 46.94 + 1,025 / (1 + S_1.5 / 2)³

Alos, Price = Present value of future cash flows at the YTM = 25 / (1 + YTM / 2 ) + 25 / (1 + YTM / 2)² + (25 + 1000) / (1 + YTM / 2)³ = 25 / (1 + 9.62% / 2) + 25 / (1 + 9.62% / 2)² + (25 + 1,000) / (1 + 9.62% / 2)³ =  936.87

Hence, 46.94 + 1,025 / (1 + S_1.5 / 2)³ = 936.87

Hence, (1 + S_1.5 / 2)³ = 1,025 / (936.87 - 46.94) = 1.15

Hence, S_1.5 = (1.15^1/3 - 1) x 2 = 9.65%

Hence, zero yield for year 1 = S1 = 8.63% and that for year 1.5 = S_1.5 = 9.65%