"Interest rate" in an interest rate future

[Alpha9]

Page 15 of chapter 11 states (not core reading):

"If Z is a Eurodollar futures quote, then (100-Z)% is the Eurodollar futures interest rate..."

Given the way that these contracts are priced, isn't (100-Z)% actually a discount rate (compounded quarterly), rather than an interest rate?
If I put $987,500 in such a contract priced at (Z=) $95, I think I would effectively get $1,000,000 three months later - equivalent to annual interest (quarterly compounded) of 5.0633%, not (100-Z)% = 5%.

Have I misunderstood?!

 

[avanbuiten]

I see your point... my guess would be that the rate is based on the contract size of 1,000,000. Then 12,500 as a percentage of 1,000,000 is 1.25% implying i(4) = 5%. Your point is valid, I guess it's just a strange convention to express it as a percentage of standard contract size.

 

[Alpha9]

Question 11.13 (ii)

So surely the answer to 11.13 (ii) (continuously-compounded futures rate on a three-month contract priced at 95) should be:
-ln ((1-(1-0.95)/4)^4) = 5.0315%
rather than the answer given:
ln ((1+0.05/4)^4) = 4.969%
The point being that as far as I can tell, a price of 95 implies a discount rate of 5% compounded quarterly.
In other words, d(4), not i(4), is 5%. i(4) is 5.0633% (see original post).

 

[Simon James]

Re OP: Don't forget this is a futures contract and hence traded on margin. You do not put in $987,500 for a $1m return 3 months later.

Think about it this way....

If I want to borrow $1m over 3 months at some point in the future and interest rates over that period increase by 1% (an i(4)), my borrowing costs will increase by $2,500.

If I sell a corresponding Eurodollar future, and interest rates rise as above, the value of the contract falls, and I make a profit from my Eurodollar contract of $2,500 - so I have hedged against changes in interest rates.

 

[Alpha9]

Chapter 11 pages 14-15

OK, I think I get it: the point is that this is a quirk of how such a contract is priced (i.e 100 - interest rate×100). In particular, the "contract price", i.e.
10,000×(100-0.25×(100-Z)),
is not the same as the principal that the investor is effectively agreeing to lend/borrow some time in the future.

I think I was confused by the sentence in the reading (albeit not core reading): "As a result, the actual (contract) price or principal paid or received differs from the quoted price." This makes "contract price" and "principal" sound interchangeable, which clearly they're not.

And perhaps the previous sentence but one, "Thus by entering into a long/short position involving a single Eurodollar contract, the investor is effectively agreeing to lend/borrow a principal amount equal in value to about $1m," would benefit from the removal of the word "about".

And, while we're at it, the example following states that $987,500 is "the actual price paid", when in fact no such amount is paid by anyone to anyone else.

Thanks, Simon!

 

[Simon James]

Thanks for the feedback on the notes - we'll look at these to clear up any possible confusion.

 

[GraemeC]

I still don't get it

Re OP: Don't forget this is a futures contract and hence traded on margin. You do not put in $987,500 for a $1m return 3 months later.

Think about it this way....

If I want to borrow $1m over 3 months at some point in the future and interest rates over that period increase by 1% (an i(4)), my borrowing costs will increase by $2,500.

If I sell a corresponding Eurodollar future, and interest rates rise as above, the value of the contract falls, and I make a profit from my Eurodollar contract of $2,500 - so I have hedged against changes in interest rates.

Is there not still a timing difference here though? The settlement date on the future will be at the start of the $1m loan and the interest will not be payable until the end of the three months. So, you will have the use of the $2,500 for the three months. It still looks like a d(4) to me.

 

[Simon James]

Remember the future will be cash settled at the start of the 3 month period (ie the loan/interest will never actually change hands)

 

[GraemeC]

Sorry, but that is my point. The extra $2500 is received 3 months before the $2500 liability on the underlying example transaction that you are trying to hedge falls due.

It is the fact that settlement on the future is at the start of the quarterly period for what I see as an i(4) amount rather than a d(4) amount that is causing me the problem.

Still confused!

Remember the future will be cash settled at the start of the 3 month period (ie the loan/interest will never actually change hands)

 

[RobWat]

Isn't it worse than that?

The $2500 will be received through variation margin before the settlement date of the future contract. So shouldn't it be discounted back to when the variation margin is paid?

And what exactly is the relevance of $987,500?