Eurodollar Future Vs LIBOR Interest Rate

[rahul.goyl]

Hi David,
I am back....
Could you please help me on the below FRM Question.

The three-month Eurodollar futures price for a contract maturing in six years is quoted as 95.20. The standard deviation of the change in the short-term interest rate in one year is 1.1%. Estimate the forward LIBOR interest rate for the period between 6.0 and 6.25 years in the future.
Choose one answer.
a. 4.83%

b. 4.61%

c. 1.46%

d. 2.92%

Rahul

 

[rahul.goyl]

Hi David,
I manage to found somehow the solution for the same... This is a Gr8 Question to practice for FRM - I see three concept mixed up in this question
A. Convexity Adjustment
B. Day count convention for Eurodollar & LIBOR
C. Compounding Methods

But need to make it more clearer need you help.. why the convexity is multiplied by 6 * 6.25


The correct answer is 4,61%. The convexity adjustment is (1/2) * 0.011^2 * 6 * 6.25 = 0.002269 or about 23 basis points. The future rate is 4.8% with quarterly compounding and an actual/360 day count. This becomes 4.8 * 365/360 = 4.867% with an actual/actual day count. It is 4 * ln(1+0.04867/4) = 4.84% with continuous compounding. The forward rate is therefore 4.84 – 0.23 = 4.61% with continuous compounding

Thanks
Rahul

 

[David Harper CFA FRM]

Hi Rahul,

That's a Hull question ... we did this here:
http://forum.bionicturtle.com/viewthread/1508/
(your source really should be attributing Hull for the question...I think that's the third Hull question you've posted from them...we post Hull questions to the forum, too, but if i don't write the question myself, I absolutely attribute per copyright laws) ...

so, in any case, in regard to Hull 06.21 (<<< -- note the credit where credit is due!)
I totally agree, this is a great exercise!

This is called the Ho & Lee adjustment for convexity bias...the derivation is out of scope, frankly, and it's not particularly important (i.e., there are other methods to adj for convexity). My advice is to simply memorize
e.g., some more detail here : http://www.bionicturtle.com/learn/article/eurodollar_future_convexity_adjustment/
free XLS here: http://www.bionicturtle.com/learn/article/eurodollar_futures_convexity_adjustment_practice_question_par_4_difficulty/
free 5-min vid here: http://www.bionicturtle.com/learn/article/convexity_adjustment_for_eurodollar_futures_and_fra_5_min_screencast/

and you want to KNOW WHY an adjustment is needed (hint: daily settlement). Hope that helps!

David