I have a fundamental question which I need to get cleared.
Suppose we have this bond: 10% Annual Coupon Par =$100 Term to maturity =2 years and we are given Zero (Spot) Rates: 1-year = 5% 2- year = 6% If I wanted to value the bond at t = 1.5 yrs (that is, remaining term 0.5 yrs), would the below make sense ? one-year forward rate, one year from now -> [(1.06)^2 / (1.05)^1] - 1 =7% Cash Flows : t= 1 , 10 t= 2 , (10+100) =110 Approach 1: Bond Price at t=1.5 yrs = 110/(1.07) ^0.5 = $106.34 Approach 2: Need a half yearly rate = [(1 + 0.07/2)] ^ 2 - 1 = 0.071225 Bond Price at t=1.5 yrs = 110 / (1.071225)^1 = $102.69 Could you please advise which approach is correct ? Thanks in Advance
Thank you so much for confirming this (And yes,the question wasn’t from a proper study guide or text - it just sprung to mind while studying a different example)
I have another doubt I’d like to clear.
If say instead we are given that the Yield curve is flat at 10%. To value a zero-bond that will pay $100 in 1-year, at t= 0.5 yrs, would you do:
Yes, if the 10% yield is an effective annual yield (EAY).
No, because this _ isn’t _ a half-year rate; it’s an effective annual rate if the 10% yield is a bond equivalent yield (BEY). Notice that your calculation is 10.25%; in this situation the half-year yield should be about 5%, not about 10%.
If the 10% yield is a BEY, then the half-year effective rate is 10% / 2 = 5%, and the price is $100 / 1.05 = $95.24.
Yes. However, with a flat yield curve, the par rates, spot rates, and forward rates for all maturities are all 10%.