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.
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 + S1.5 / 2)3
= 25 / (1 + 8.63%/2) + 25 / (1 + 8.63% / 2)2 + (25 + 1000) / (1 + S1.5 / 2)3 = 46.94 + 1,025 / (1 + S1.5 / 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 + S1.5 / 2)3 = 936.87
Hence, (1 + S1.5 / 2)3 = 1,025 / (936.87 - 46.94) = 1.15
Hence, S1.5 = (1.151/3 - 1) x 2 = 9.65%
Hence, zero yield for year 1 = S1 = 8.63% and that for year 1.5 = S1.5 = 9.65%
1yr Tnote at par with 8.63% ytm p.a. 1.5yr Tnote with a 5% coupon rate and...
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