I need help with "Bootstrapping". Thanks

CAIA
#1

A six-month zero-coupon bond has a price of USD 97, while a 12-month 7.00 Percent annual coupon bond (paid semiannually) has a price of USD 100.50. Both bonds have a face value of USD 100. Find the 12-month spot rate based on annual compounding, semiannual compounding, and continuous compounding:

Step 1: 6 month cashflows are worth 97 Percent of face value --> first coupon = 0.97 x USD 3.5 = USD 3.395 Step 2: 12 month coupon bond is worth USD 100.5 - USD 3.395 = USD 97.105 Step 3: face value including semiannual coupon = USD 100 + USD 3.5 = USD 103.5 Step 4: 12 month cash flows are worth USD 97.205 / USD 103.5 = 0.93821 of face value Step 5: How do I calculate the Spot Rates based on annual compounding, semiannual compounding, and continuous compounding given the discount factor of 0.93821?

Solution: The one-year spot rate can be expressed as 3.98 Percent annually compounded, 3.94 Percent compounded semiannually, or 3.90 Percent compounded continuously. How do I get these values?

#2

If I assume the EAR is 3.98%, then the semi-annual rate is 2 *[(1.0398)^(1/2)-1] and the continuous rate is ln(1.0398). However, I have no idea how they get 3.98% as the annual compounded rate. :roll_eyes:

Based on what you provided above, I would have calculated the 1 year spot rate as 1/0.93821 - 1 = 6.59%.

1 Like
#3

Thank you for helping with the semi-annual and continuous compounded rate. I am still puzzled how to get the annual rate of 3.98%. The exercise is from the official CAIA lvl 1 September 2020 exam book. I will send them an e-mail.

#4

What is the official exam book? Is that the mock exams on the CAIA website?

#5

I think the solution should be 6,47% and the one that provides Caia is not right.

#6

A late reply but I thought I would still give a note because it took me ages to figure this out too, hope this can help others

The solution u stated obviously got mixed up with the 1st question in the alternative investments level 1 text book in chapter 5.

The 3.98% u did above is chapter 5 question 1

For question 2 as u have listed most of the work, in order to find:

  1. continuous compounding

y= T[Ln Face Value/ Bond Price]

  1. compounded annually (Compound Annual Growth Rate) = [(Ending Value / Begin Value)^1/n]-1

  2. compounded semi annually

(Compounded Semi-annual Growth Rate) = 2[(Ending Value / Begin Value)^1/2]-1

So in this case the answers should be 6.38%, 6.59%, and 6.48% respectively

#7

Thanks for sharing.