Reading 43, Pracitice problem 2

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basy

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Hi, this drives me crazy. Problem 2 is about a 3% coupon bond. Yet the solution is bootstrapping the spot rate with the following example:
1. Spot rates calculated using bootstrapping; for example: Year 2 spot rate (z2): 100 = 1.5/1.0125 + 101.5/(1+z2)2 = 0.015019.
How did the 3% coupon become a 1,5 cashflow here? I checked the Errata, but nothing there.
 
Nope. I tried to add a picture but it is only visible in Preview
 
Ran into the same issue just now.
It states the bond is a “Three-year $100 par, 3% coupon, Annual pay Option free bond”
Can we assume this is an error?
 
not an error. it’s bootstrapping YTM (par rates) to compute spot rates, which are used to discount CF’s (not YTM/par rates). Once Z2 is known, you use that spot rate and the Z1 spot to derive Z3 spot rate. I.e. 100 = 1.7/(1.0125)^1 + 1.7/(1.015019)^2 + 1.7/(1+Z3)^3. THEN you discount the CF’s (CPN 3, CPN 3, CPN + face 103) using these spot rates.
 
^OP is not talking about the YTM nor the spot rates. He’s talking about the coupon rate. So in the numerator, instead of having 1.5, it should be 3.
 
you are trying to determine what market spot rates are being used on the par bond so you can use them to price the “no-abritrage” value of the 3% bonds in the question. spot rates should be the same every where because they come from the par curve… I looked at the problem, it’s right.
 
You’re bootstrapping it wrong OP. You have to use the par curve in order to get the spot rates.
Par rate at year 1 = Spot rate at year 1 = forward rate at year 1 ; we got this covered.
Now, if you want to get spot rate at year two knowing par rate at year two is 1.5%:
100 = (1.5 / (1+par rate at year 1) ) + (101.5/(1+S2)^2) and you solve for S2.
Now if you want to get spot rate at year 3, knowing par rate at year three is 2%
100 = (2/(1+Par rate year 1)) + (2/(1+S2)^2) + (102/(1+S3)^3) and you solve for S3
Conclusion: when you’re bootstrapping, you have to adjust the cashflows by using the ones implied by the par, curve.
 
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