for the official mock A PM, the question 43 provided par rates and spot rates but we had to bootstrap and calculate new spot rate to identify an arbitrage opportunity.
But for the official topic question in computing the value of 4 year bond, there was no need to boostrap and had to simply use the provided spot rates (the zero-coupon yield curve).
What is the criteria in deciding when to bootstrap or not?
You’re missing something. If you have the spot rates, there no need to bootstrap. You only bootstrap par rates to get the spot rates.
If you were trying to find arbitrage opportunity, then the question may provide forward rates that don’t sync correctly with the spot rates, or any type of situation.
Bolded for truth
Thanks for your response but have you seen/tried the question? That’s what I thought too but apparently many people got it wrong for using the spot rates provided by the problem. The new spot rates, derived from the par rate, differed slightly from the provided spot rates, and that small decimal differences lead to a different answer.
I just looked over Mock A PM, #43.
You do not bootstrap when spots are given.
The problem states “The bond is quoted in the market at $103.50.”
Using the stated spot rates, calculate the bond coupons and final payments to be $103.49
Because the market is too expensive, there is an arbitrate opportunity.
The problem is silly because the spot rates has a rounding error. They cut off the spot rates to two decimal points. If you want to bootstrap then you get more decimal places to show the spot rates at 4 decimals, and the true value of the bond is $103.4816
It’s a difference of a penny. In the real exam, I would expect the test makers not to put that close of a rounding error that could change the output from one choice to another choice.
I know your frustration - they said the bond had an arbitrage opportunity when it was a penny mis priced. Which isn’t a fair question.
Thanks both for sharing your insights. Much appreciated.