Deriving Spot Rates via Bootstrapping - Algebra

I’m working through the FI readings, and I’d been thinking that in an exam setting, spot rates would probably be given. But two questions in the Reading 43 EOC practice problems from the separate cases require bootstrapping. So, assuming there is a chance we’d be required to do the same on exam day, is there a trick to the algebra that my brain can’t seem to wrap around? Deriving (1+ the variable) cubed as a divisor (as an example of deriving the year 3 spot rate) in a term is giving me some grief.

Trial and error method usually does the trick when you have options to choose from :slight_smile: PLug the one of the option in the equation and see if it solves to zero.

Don’t plug in _ one of the options_.

Plug in the middle option: if it’s correct, you’re done, and if it’s incorrect, you’ll know which one is correct.

^ Indeed - better way.

I wrote an article on yield curves that describes bootstrapping; it may be of some help:

Thanks for the repsonses guys. The problem is, the questions aren’t asking for a specific spot rate, and giving three choices, they’re giving YTMs for 1-3 year maturities and the questions involve calculating arbitrage-free bond prices to identify mispricing, requring finding the spot rates for year 2 and 3 maturities. Can’t really back into those with a plug and chug.

I guess the big question is, is it likely we’d be required to do this kind of algebra on exam day?

Not very likely; that’s Level I stuff.

i had trouble with bootstrapping and read s2000’s article…cleared the whole process up for me. i printed it out to review once more before exam day should i forget the method

Thanks for that. It helps confirm what my gut kept telling me. I have to remember to pay close attention to what the LOSs actually ask for, regardless of who wrote the EOC practice questions. I spent too much time thinking about this yesterday which is a recipe for disaster lol.

You also reminded me that I’ve been meaning to go through your blog, so thanks again!

My pleasure.