Hull - Eurodollar futures

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David,

I have two questions on this topic. It always haunts me.

1) Suppose the future quote is 90 for delivery in 60 days. What does it mean? Does it mean that the expected forward LIBOR rate for 60-150 day period is 10% (quart. compounding, actual/360)? Suppose after 60 days the quote of the contract is still 90 i.e. a price of 975,000. So, what next? Does the long get to invest this 975,000 for 90 days to get 1,000,000 after 90 days. And in that case, the rate is 25,000/975,000*4=10.26% (quart. comp actual/360) which is higher than the prevailing LIBOR of 10%.

Not very sure if I have explained myself.

2) Hull Exercise 6.23 - Assume a bank can borrow or lend in the same interest rate in LIBOR mkt. 90 day rate is 10% p.a. and 180 day rate is 10.2% p.a. continuously compunded and actual/actual. Eurodollar future price maturing in 91 days is quoted at 89.5. What arbitrage opportunities are open.

Regards,

Alan

 

[David Harper CFA FRM]

Hi Alan,

Eurodollars aren't natural for me either (I don't trade them). I think it's easy to forget: they are just a derivative with a price and they cash settle (so there is no lending functionality embedded in the derivative itself). Here are the CME specs:
http://www.cmegroup.com/trading/interest-rates/stir/eurodollar_contract_specifications.html
... From delivery: "Expiring contracts are cash settled to 100 minus the British Bankers’ Association survey of 3-month U.S. Dollar LIBOR on the last trading day. Final settlement price will be rounded to four decimal places, equal to 1/10,000 of a percent, or $0.25 per contract"

In this way, the design of the ED futures contract is to be a derivative that pays $25 for each basis point gain/loss

I input the example of a 90 quote into the Hull 6.3 table (one of the sheets in learning 3.b.5 XLS. Candidly, for myself, I typically need to open this sheet to remind myself how ED works!).
Very simple XLS is here @ http://db.tt/DGnRdcB

so (eg) in January the quote = 90, which implies a forward rate of 100 - 90 = 10% (exactly as you say). This is just a futures contract on an 60-day forward LIBOR rate; i.e., "the 60-day implied forward--implied by the ED contract--is 10%. By taking a long/short position in the ED futures, I promise to pay/receive the difference between 10% and the future realized 90-day LIBOR. If the realized (in the future LIBOR is 9%, i gain; if it is 11%, I lose."

so (eg) as in the XLS, if the future 90-day spot LIBOR goes down to 9% (i.e., the realized future spot rate is less than the original forward rate in the contract), then the quote goes up to 91 and the long is paid (gains) by $25 * 100 basis points = $2,500 (i.e., quote +100 bps --> price +$2,500).

In regard to 2):
The Eurodollar contains (pays based on) an implied forward 90-day LIBOR of 10.5% (100 - 89.5).
On the other hand, the two spot rates (I am going to ignore the 1 day difference between 90 & 91 days) imply that we can lock in a 90-day forward rate = (10.2%*180) - (10%*90)/(180-90) = 10.4%. Since there is a difference, we want to buy the cheap thing and sell the expensive thing: borrow forward @ 10.4% and lend forward at 10.5% for an arbitrage of +0.1%.

To borrow forward at 10.4%, we borrow for 180 days at 10.2% and immediately lend those proceeds for 10.0% at 90 days. This locks in our "borrow forward at 10.4%"
To lend forward at 10.5%, we lend forward at LIBOR but hedge out the interest rate by buying ED futures contract: locking in our "lend forward at 10.5%"

I think that's the transaction, i feel like it could be simpler but don't see how to do it. Hope that is helpful! ... David

 

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Thanks David,

Grt explanation.... I wont say I have completely gripped the topic, but I'm much more comfortable now...

Alan