Given the following information about Treasury securities, what’s the 18 month spot rate? Maturity and Yield of Treasury Securities: Maturity (years) Coupon Rate Price 0.5 0 96.78 1.0 0 94.36 1.5 6% 97.55 For 6months: (1+r)= 100/96.78 r=0.033 For 12months: (1+r/2)^2=100/94.36 r=0.029 Therefore, bootstrapping: 97.55 = Present value of 3 + 3 + 103 97.55 =3 / 1.033 + 3 / (1 + 0.029)^2 +103 / (1 + r)^3 (1 + r)^3 = 1.1218 r = 0.03905 On a BEY basis = 0.03905 x2 = 7.8% Do you guys get the same results?
a) spot rate for 6 months = YTM for the first bond. 100/96.78 - 1 b) sport rate for 12 months = YTM for the second bond, but discounted at the rate from a 100/(1.033)^2 c) 3/(1.033) + 3/(1. + rate from b)^2 + 103 / (1 + X)^3 = 97.55 now solve for X.
coupons come from the 6% right, you just divide by 2 to get $3.
daj, makes sense.