Using Eurodollar Futures to Hedge Future Borrowing Rates
Summary
The note explains how a short Eurodollar futures position can hedge the cost of borrowing at a future three-month LIBOR rate. It corrects the initial claim that a short position loses when rates rise: Eurodollar futures are quoted as 100 minus the implied rate, so rising rates lower the contract price and benefit the short. The example compares a futures gain with the higher interest expense on a one-million-dollar loan, showing how the position can offset the rate increase.
The hedge effectively converts a future floating-rate borrowing cost into a rate fixed when the futures position is opened, though the contract does not exchange interim loan cash flows. The note distinguishes this practical hedge from pure cash-and-carry arbitrage, which it says is more complicated because future rates are stochastic. It also mentions arbitrage relationships among futures, swaps, and deposits but gives no detailed valuation framework or evidence about executable opportunities.
Key ideas
- A short Eurodollar futures position can hedge a borrower exposed to rising LIBOR.
- The contract price moves inversely to its implied interest rate.
- The example illustrates how the futures gain can offset added loan interest expense.
- The futures hedge fixes the effective borrowing rate without exchanging loan cash flows during the contract.
- Pure arbitrage valuation is more complex, and the note does not establish a general cash-and-carry trade.
Tags
Full text
# Forward parity in fixed income
# Forward parity in fixed income
In stock and index we have a beautiful forward-spot parity $$ F(t,T) = S(t)\cdot B(t,T) \tag{1} $$ which tells us that to price a forward contract at time $t$ with expiry $T$ we can just borrow money using the bond $B$ and buy a stock now to deliver it at expiry. If the parity does not hold, given that all securities involved are very liquid, we can make free money by going short one leg and long another. One can even say that all risk-neutral/martingale pricing idea arises from an elaborate version of $(1)$.
I wonder whether similar relations do exist in Fixed Income world. For example, I was thinking of Eurodollar futures: if I short the futures, at expiry I'll lose if 3 months LIBOR goes higher than the initial forward price. Thus, to find an opposing leg as a hedge, I need to somehow gain from LIBOR going up. Intuitively thinking, I shall benefit from future upward movements of LIBOR in case I borrow money at this rate. However, I am not sure how to translate it into a valid strategy. In general, I'd be interested in valuation techniques for Eurodollar futures.
## Answer by meh (score 1)
https://quant.stackexchange.com/a/19213
> if I short the futures, at expiry I'll lose if 3 months LIBOR goes higher than the initial forward price
If you short the future and LIBOR rate goes up you will actually make money, not lose money.
If you short a Eurodollar contract you are effectively locking in that interest rate. Here's an example.
Say it's December 2015 and you need to borrow 1M in March 2016. The GEH6 is currently trading at 99.27. This corresponds to an interest rate of 0.73%. This seems like a perfectly reasonable rate to you so you sell the GEH6 future. Now at expiration you are able to borrow at the current LIBOR rate, which is also where your Eurodollar future is going to settle. Let's say that the LIBOR rate at settlement was 1.1%. So rates went up quite a bit and that sucks because you need to borrow 1M dollars. However, your Eurodollar contract settled at 98.9. (100 - 1.1). That means you that you made 925 dollars on your hedge.
Now if you check what your interest on a 1M 3 month loan @ 1.1% vs @ 0.73% is you'll notice it's about 925. Or the exact amount you made on the hedge.
The reason I say that the Eurodollar future here is a proxy for a swap is because you are effectively turning a floating rate (LIBOR) into a fixed rate. The difference is that there is no exchange of cash flow throughout the life of the contract.
As for arbitraging Eurodollar future, it's a bit more complicated. I'm not sure if a pure arbitrage(Cash-Carry type trade) actually exists because the rate at time T is a stochastic process. I would take a look at this paper for some arbitrage ideas anyways.
http://www.jamesgoulding.com/Research_II/Eurodallar/Eurodollar%20(Study%20-%20Contract%20Design).pdf
There do of course exist arbitrage opportunities between the Eurodollar contracts, swaps, and deposits.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.