Convexity Adjustment questions (p63)

[ajsa]

Hi David,

1. You mentioned Convexity Adjustment assumes continuous compounding. And I noticed that in your example on p63 you converted the future rate implied by eurodollar futures price to be continous compounding rate. Will we be required to do that in the exam?

2. In that example, on the left column you noted ACT/360, but on the right column you used ACT/365 in the calcuation. Could you advise?

Thanks.

 

[David Harper CFA FRM]

Hi ajsa,

This is just a re-creation of Hull's example 6.4
(if you like my underlying XLS is the sixth sheet in the learning XLS:
http://www.bionicturtle.com/premium/spreadsheet/3.a.9_interest_rate_futures_set/)

1. Possibly but i would say unlikely. More likely you'd be given the inputs and asked to apply the convexity adjustment formula in one pass.

2. The label "futures rate (actual/360)" means that the Eurodollar futures rate is quoted according to an actual/360 day count convention. Then Hull performs a day conversion to actual/365 (I am not entirely sure why this is necessary. I must miss something, he assumes the FRA rate is actual/365 for some reason....). So, the conversion here has two parts: (i) from quarterly to continuous (to meet the criteria of the Ho & Lee convexity adjustment) and (ii) day count from actual/360 to actual/365 (for a reason I don't understand).

Thanks, David

 

[ravenmaster]

Following Hull:

on actual/365 basis with quarterly compounding:
(act/365)×s = (act/360)×6%
s = (365/act)×(act/360)×6% = (365/360)×6% = 6,0833%

on actual/365 basis with continuous compounding:
exp{t} = (1 + 6,0833%/4)^4
t = 4×ln(1 + 6,0833%/4) = 6,0375%


However, doing things the other way around:

on actual/360 basis with continuous compounding:
exp{s} = (1 + 6%/4)^4
s = 4×ln(1 + 6%/4) = 5,9554%

on actual/365 basis with continuous compounding:
exp{(act/360)×5,9554%/4} = exp{(act/365)×t/4}
t = (365/act)×(act/360)×5,9554% = (365/360)×4×ln(1 + 6%/4) = (365/90)×ln(1 + 6%/4) = 6,0382%

How come I get different answers?