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# R19.P1.T3.FIN_PRODS_HULL_Ch6_Topic: EuroDollarFuturesContracts

#### gargi.adhikari

##### Active Member
In reference to R19.P1.T3.FIN_PRODS_HULL_Ch6_Topic: Euro$FuturesContracts_Convexity_Adjustments Hi, I am trying to understand why the Futures Rate is = ( 100 - the Euro$ Futures Price) = (100-95) = 5 % ...?

Why is : Euro$Futures- Quote= ( 100 - The 3-month Euro$ Futures- Interest Rate)
=> Q% = (100% - R%) ...?

Did I miss this caveat /knowledge point in any of the chapters...? :-( :-(

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#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @gargi.adhikari Please notice in the new Hull study note page 93 (emphasis mine)
Calculate the final contract price on a Eurodollar futures contract:
If R is the LIBOR interest rate, the Eurodollar futures price is quoted at 100–R.

The contract is designed so that a one-basis-point (.01%) move in the futures quote corresponds to a gain or loss of $25 per contract. A one-basis-point change in the futures quote corresponds to a 0.01% change in the underlying interest rate such that: 1,000,000 × 0.0001 × 0.25 = 25 The contract price is defined as: 10,000 × [100 – 0.25 × (100 – Quote)] Hull has a good description but I also like to point folks to a realistic source, see "Price Quotation" here http://www.cmegroup.com/trading/interest-rates/stir/eurodollar_contract_specifications.html Notice: Price Quotation: IMM price points: 100 points minus the three-month London interbank offered rate for spot settlement on the 3rd Wednesday of contract month. E.g., a price quote of 97.45 signifies a deposit rate of 2.55 percent per annum. One interest rate basis point = 0.01 price points =$25 per contract.
So a couple of things:
• The Eurodollar futures price ("price quotation"; a.k.a., futures quote) = 100 minus the future rate (R); e.g., the future price (above) of 95 implies 100 - 95 = 5.0% per annum with quarterly compounding. In this way, if the rate goes down, the price goes up (and whoever is long the contract thusly profits, whoever is short has a loss, because the futures quote/price is (100 - rate).
• The future Contract Unit is designed to gain $25.00 per one basis point (0.01%) change in the rate so that the contract price = 10,000 × [100 – 0.25 × (100 – Quote)], where the (100 - Quote) = rate, and the 0.25 is to compute the 90/360 (three month) applicable rate. So this is effectively "scaling" the R = 100 - Q, because Q = 100 - R, up to a$1.0 million contract.
• In this way, we can distinguish between, the interest rate (R) which informs the quote (aka, futures price) which informs the contract unit. I hope that helps!

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#### gargi.adhikari

##### Active Member
@David Harper CFA FRM Have a followup question on this :-
For scaling down the Rate we use the Day Count Convention= Actual/360= 90/360 and therefore scale down the rate by a factor of .25 and get the quarterly rate of .25(6%) = 1.5%
But while converting the Discrete Rate to a continuous rate, we use the Day Count Convention= Actual /365
Is there a reason why we have 2 different Day Count Conventions for some reason i might be missing...? Thanks for sharing your thoughts and insights as usual

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @gargi.adhikari

Sure, the basic reason for the adjustments is so that the convexity adjustment is subtracted on an apples-to-apples basis (This is Hull's example 6.4, and it has caused plenty of confusion!). The reconciliation is required simply because the convexity adjustment presumes to be solved on an ACTUAL day count with continuous compounding, but the Eurodollar contract per contract specification is based on an ACT/360 day count with quarterly compounding. If, for example, the Eurodollar quote informed a rate that were given in ACT/ACT with continuous compounding (which it is not), then the convexity adjustment could simply be subtracted (ie, 6.00% - 0.475%). But if we subtract rate A from rate B, they should be expressed in the same units. So we showed both steps. Although, we could first simply translate from quarterly 6.00% to continuous 5.955% = 4*LN(1+6.0%/4); and then we could make the day count adjustment with 5.955% * 365/360 = 6.038%, to the same effect. I think we previously chatted about the Eurodollar futures quote and how the quote equals 100 - R; in this example, the quote of 94 signifies an interest rate of 6.00% but it further (by specification) is ACT/360 day count with quarterly compounding (because these contracts have a three month maturity; when in doubt assume the compound frequency is equal to the maturity for short term contracts). Here is the underlying (dynamic) XLS for this exhibit in case you want to experiment:
https://www.dropbox.com/s/ct18vpa0k6jvltj/0513-convexity-adjustment.xlsx?dl=0

I hope that helps!

#### flex

##### Member
Hi @gargi.adhikari

...Although, we could first simply translate from quarterly 6.00% to continuous 5.955% = 4*LN(1+6.0%/4); and then we could make the day count adjustment with 5.955% * 365/360 = 6.038%, to the same effect.
...I hope that helps!
hi, @David Harper CFA FRM .sorry, much...

can u clarify one feature (across 'Convention' tasks) for me:
i noticed, that indifferent from task ('direct' for that %rate is derived from quoted price or 'reverse' when quoted price calc is target from %) day-count rescaling performed at last step (both case). and i doubt that 'direct' should hasn't need "backward" steps-order to 'reverse' task.
Great respect, flex