Using Spot Rates and Forward Rates to value a Bond

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Hi all
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
 
Without a 1½-year spot rate, you cannot answer this question.
Neither approach is correct.
 
Hi Magician,
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:
1) P(0.5) = 100/(1 + 0.10) ^0.5 = 100 / (1.10)^0.5 = $95.35 OR
2) Half year rate : [1 + (0.10/2) ] ^ 2 - 1 = 0.1025 , P(0.5) = 100/(1.1025)^1 = $90.70 OR
3) We would still need a 0.5-year spot rate? (If yes, would this spot rate be a on a compound interest basis or simple interest?)
 
Iampossible wrote: Hi Magician,
Click to expand...
Howdy.
Iampossible wrote: 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)
Click to expand...
My pleasure.
Iampossible wrote: 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:
1) P(0.5) = 100/(1 + 0.10) ^0.5 = 100 / (1.10)^0.5 = $95.35
Click to expand...
Yes, if the 10% yield is an effective annual yield (EAY).
Iampossible wrote: 2) Half year rate : [1 + (0.10/2) ] ^ 2 - 1 = 0.1025 , P(0.5) = 100/(1.1025)^1 = $90.70
Click to expand...
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.
Iampossible wrote: 3) We would still need a 0.5-year spot rate? (If yes, would this spot rate be a on a compound interest basis or simple interest?)
Click to expand...
Yes. However, with a flat yield curve, the par rates, spot rates, and forward rates for all maturities are all 10%.
 
Thanks again Magician - I now have a much better understanding. You are awesome !!
 
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