Reading 43, Pracitice problem 2

CFA Level II Fixed Income
#1

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.

#2

Is this a semi-annual pay bond?

#3

Bonds pay coupons semiannually.

#4

Nope. I tried to add a picture but it is only visible in Preview

#5

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?

#6

not an error. it’s bootstrapping YTM (par rates) to compute spot rates, which are used to discount CFs (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 CFs (CPN 3, CPN 3, CPN + face 103) using these spot rates.

#7

^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.

#8

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.

#9

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. _

#10

Hi All, having same issue with this problem. I calculated z2 as 1.5019%. Calculating for z3, I came up with 1.667% but the answer is saying z3 should be 1.7049%. Is the book wrong?

#11

Never mind, missed a zero in the second fraction 3 different times