Question 173.1

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David/

I have a couple questions regarding question 173.1. First unlike in question 172.6, there is no convexity adjustment in 173.1 where we take the future rate and convert it back to a forward rate. Is there a reason why we didn’t need a convexity adjustment here, even though we are using a futures rate?

My bigger question, however, is on the computation of the 390 day libor zero rate equation: [(.03(300) + .04035(90))/ 390 = 3.2389] I went back over the Hull readings, but I never saw an equation whereby you solve for a zero rate by weighting two separate zero rates by their times and then dividing by the time of the second rate. Can you clarify this equation or point me to where in the readings I can get an explanation. I’m very clear on the bootstrapping method to solve for zero rates but this approach eludes me.

Thanks again for all of the outstanding help/ contact from Bionic Turtle

 

[David Harper CFA FRM]

Hi Chris,

No, the only reason is to keep the question relatively simpler (per the caveat in the question: "Please assume that the convexity adjustment is effectively zero here, due to the short maturities involved; i.e., assume the forward rate is equal to the futures rate." You are otherwise quite correct: if there is not a liquid Eurodollar future contract for the rate in question (I haven't checked but that's a decent assumption if we are bootstrapping/extending LIBOR zero curve to find it), then presumably we would require an OTC FRA and we should include the convexity adjustment.

See Hull 4.5 or 6.4. The above uses Hull 6.4

It follows from assuming continuous compounding:
exp(R1*T1) *exp(F1*[T2-T1]) = exp(R2*T2);
i.e., spot at R1 rolling over into forward at F1 should equal spot at R2
exp(R1*T1 + F1*[T2-T1]) = exp(R2*T2); take LN() both sides:
R1*T1 + F1*[T2-T1] = R2*T2;
either F1 = (R2*T2 - R1*T1)/[T2-T1] for the forward rate, but in this case the zero rate:
R2 = R1*T1 + F1*[T2-T1]/ T2

Thanks, David

 

[[email protected]]

David, thank you. And my apologies for not reading the question closely. I really try and find answers to my questions before I take up your valuable time. But I greatly appreciate your help. Bionic Turtle is a tremendous resource. Thanks again

 

[David Harper CFA FRM]

Hi Chris, thank you that is very gracious of you ... but as long as I have the time, I am here to help and I really don't mind chatting about the material because it keeps me fresh in it, too, David