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# Eurodollar Futures contract - how to think about short/long gaining/losing in a coherent way? SOS

#### alexwallace

##### Member
Subscriber
@David Harper CFA FRM ,

Dear David,

Once again, your extremely helpful insights are needed. When Eurodollar futures price changes from 94.555 to 94.715, the answer is that short contract loses $400. Now my question is: is it conceptually/logically correct to think about this case under the general umbrella of short futures position incurring a loss when the price of the underlying asset increases? That way, in this particular case price of the underlying is just the Eurodollar futures price. By the way, what about thinking this way: price increase from 94.555 to 94.715 means rate decrease from 5.445% to 5.285% and here comes the way I suppose it should be thought about: at Eurodollar futures price of 94.555 I could have locked in a rate of 5.445%, while after decrease to 94.715 I can lock in a 5.285%, but for this to lead my thought process to a loss it must be the case that I am already locked in some initial futures price, so that subsequent favorable/unfavorable price/rate movements are causing either loss or a gain, respectively (just like in standard futures contract on other assets, like I don't know, for example, corn). But here comes the part that has been torturing me for a long time: I am short in Eurodollar futures contract and: * Does this mean I locked in a rate at which I can lend OR borrow? This is what I don't understand from the textbooks ** Does being long in Eurodollar futures mean I am locking in a lending or borrowing rate? Long story short, when I am long in Eurodollar futures contract what does this mean - I need some analogy with other NON-interest-rate related futures/forwards. If you manage to somehow explain this to my completely puzzled brain, I will be extremely thankful to You. #### nc27 ##### Active Member Subscriber Hi, I hope I can help you on this one -> when you buy a eurodollar contract, you gain when rate decreases -> when you sell a eurodollar contract, you gain when rate increases But, as every derivative, you understand its utility if you know what it is used for... that is, what does a eurodollar (ED) contract hedge in the first place ? -> In our case, companies like to use ED contracts to hedge interest payments. In the case of ED contracts, interests are calculated over USD 1 million notional (standard size of one eurodollar contract) , rate taken into account to accrued interests is the 3 months libor swap rate ( act/360 basis and compounded quaterly). So now, an example, -> A company needs to borrow USD 2,000,000 in 5 months. 3-months libor rates is today at 1%, but the company fears that it can go up to (say) 4% and so, in 5 months the borrowing cost might be higher.... what can the company do to mitigate this risk ? Sell 2 eurodollar contracts ! -> If the 3 months libor swap rate goes up within the 5 months period, the buyer of the ED contract will have to pay the seller the accrued interest from the 2 ED contracts => The interest are calculated on the USD 2,000,000 notional. -> How those interests payments help the company ? When receiving the cash from the ED contract the company will go to its bank in order to make its borrowing of USD 2,000,000 as planned... the bank will authorize the borrowing at the higher libor rate as planned... BUT ... the company got the cash from the ED 2 contracts ... the company effectively "locked-in" the libor rate at 1%. -> The company receives the 3% interest difference from its counterparty on the derivative trade, and those interests where calculated on a USD 2,000,000 notional... those interest offset the increasing borrowing cost that the bank is now asking you. The derivative contract effectively plays its role of insurance contract (hedging contract). -> Now, your counterparty (which was long the ED contract) would have gained in the case of a rate decrease, and for this point I personally just look at the reverse of the trade ... if you give me money in the case of an increase in rate, the reverse is true. I will have to deposit cash in your margin account in the case of a rate decrease (long side gains when rate decrease in an ED contract). -> To go on with the long side of the trade... imagine that you have a floating rate bond ... that is, the coupon payment is tied to an index such as a libor rate... your fear is that the rate decrease (your coupon PAYMENT will also decrease).... so in this case being long an ED contract might offset the risk ... if rate goes down you lose on the floating bond but you gain from the ED future.. Hope it helps, Last edited: #### alexwallace ##### Member Subscriber Hi, I hope I can help you on this one -> when you buy a eurodollar contract, you gain when rate decreases -> when you sell a eurodollar contract, you gain when rate increases But, as every derivative, you understand its utility if you know what it is used for... that is, what does a eurodollar (ED) contract hedges in the first place ? -> In our case, companies like to use ED contracts to hedge interest payments. In the case of ED contracts, interests are calculated over USD 1 million notional (standard size of one eurodollar contract) , rate taken into account to accrued interests is the 3 months libor swap rate ( act/360 basis and coumpounded quaterly). So now, an example, -> A company needs to borrow USD 2,000,000 in 5 months. 3-months libor rates is today at 1%, but the company fears that it can go up to (say) 4% and so, in 5 months the borrowing cost might be higher.... what can the company do to mitigate this risk ? Sell 2 eurodollar contracts ! -> If the 3 months libor swap rate goes up within the 5 months period, the buyer of the ED contract will have to pay the seller the accrued interest from the 2 ED contracts => The interest are calculated on the USD 2,000,000 notional. -> How those interests payments help the company ? When receiving the cash from the ED contract the company will go to its bank in order to make its borrowing of USD 2,000,000 as planned... the bank will authorize the borrowing at the higher libor rate as planned... BUT ... the company got the cash from the ED 2 contracts ... the company effectively locked-in the libor rate at 1%. -> The company receives the 3% interest difference from its counterparty on the derivative trade, and those interests where calculated on a USD 2,000,000 notional... those interest offset the increasing borrowing cost that the bank is now asking you. The derivative contract effectively plays its role of insurance contract (hedging contract). -> Now, your counterparty (which was long the ED contract) would have gained in the case of a rate decrease, and for this point I personally just look at the reverse of the trade ... if you give me money in the case of an increase in rate, the reverse is true. I will have to deposit cash in your margin account in the case of a rate decrease (long side gains when rate decrease in an ED contract). -> To go on with the long side of the trade... imagine that you have a floating rate bond ... that is, the coupon payment is tied to an index such as a libor rate... your fear is that the rate decrease (your coupon PAYMENT will also decrease).... so in this case being long an ED contract might offset the risk ... if rate goes down you lose on the floating bond but you gain from the ED future.. Hope it helps, Thank You. @David Harper CFA FRM I would like to ask one more question: could you please help me with intuitively understanding the following: Thank You In advance once more! #### nc27 ##### Active Member Subscriber Hi again, I will not elaborate too much for this one but I think that your doubt is linked to the understanding of the concept of risk neutrality... also called no arbitrage condition. When you learn in the textbook the following equation (assuming continuous compounding as per Hull) : forward rate = (R2 * T2 - R1 * T1)/(T2 - T1) The forward rate obtained is a risk neutral measure that ensure that no profit can ba made from investing and borrowing from different market rates (e.g. swap rates) given for future period T1 and T2. The GARP text explained just that. Hope that helps, #### David Harper CFA FRM ##### David Harper CFA FRM Staff member Subscriber Hi @alexwallace That's a pithy, instructive vignette by GARP, I like it. First, candidates should immediately be able to retrieve the forward rate. As has been discussed on this forum dozens of times, the implied forward rate is based on an indifference idea between: exp(4%*2)*exp(f*1) = exp(5%*3) An investor should expect (we are ignoring the liquidity option) to have the same final wealth (after 3 years) under both scenarios: on the left side, invest for 2 years and roll-over for 1 year at the forward rate, versus invest for 3 years. The implied forward rate renders you indifferent. A bit of practice and we can soon see it's pretty easy to get the forward when the rate is CC : 5%*3 - 4%*2 = 15 - 8 = 7% is the implied forward, per the text. For myself, I can only understand with a numerical example. So building off the text, let's say we are "confident that the rate for the third year will be less than 7%" ... let's say we believe it will be 6%. Thinking along the lines of "buy the cheap thing, sell the expensive thing" in an arbitrage, we want to: borrow at the lower rate (on the left side) plus invest at the higher rate (on the right side) if we have$100, on the left borrowing side: 100*exp(4%*2)*exp(6%*1) = 100*exp(8%+6%) = $115.03 we need to repay at the end of three years. The$100 we borrowed funds our investment (on the right side) which grows to $100*exp(15%) =$116.183. Our future profit is $116.183 -$115.03. In fact our future profit = W*[exp(15%) - exp(8%+f)]. Hope that helps.

P.S. cross posted with @nc27 who makes the essential point (first principle), thank you @nc27 !

#### alexwallace

##### Member
Subscriber
Hi @alexwallace That's a pithy, instructive vignette by GARP, I like it. First, candidates should immediately be able to retrieve the forward rate. As has been discussed on this forum dozens of times, the implied forward rate is based on an indifference idea between:

exp(4%*2)*exp(f*1) = exp(5%*3)

An investor should expect (we are ignoring the liquidity option) to have the same final wealth (after 3 years) under both scenarios: on the left side, invest for 2 years and roll-over for 1 year at the forward rate, versus invest for 3 years. The implied forward rate renders you indifferent. A bit of practice and we can soon see it's pretty easy to get the forward when the rate is CC : 5%*3 - 4%*2 = 15 - 8 = 7% is the implied forward, per the text.

For myself, I can only understand with a numerical example. So building off the text, let's say we are "confident that the rate for the third year will be less than 7%" ... let's say we believe it will be 6%. Thinking along the lines of "buy the cheap thing, sell the expensive thing" in an arbitrage, we want to:

borrow at the lower rate (on the left side) plus invest at the higher rate (on the right side)

if we have $100, on the left borrowing side: 100*exp(4%*2)*exp(6%*1) = 100*exp(8%+6%) =$115.03 we need to repay at the end of three years.

The $100 we borrowed funds our investment (on the right side) which grows to$100*exp(15%) = $116.183. Our future profit is$116.183 - \$115.03. In fact our future profit = W*[exp(15%) - exp(8%+f)]. Hope that helps.

P.S. cross posted with @nc27 who makes the essential point (first principle), thank you @nc27 !
Thank You David,

Could you please check my first question also (the one that started the thread)? Thanks

P.S. Don't get me wrong, I am thankful to nc27, but I would be more confident if you provided your opinion about my thought process described in my question (by the way, I completely understand the example nc27 kindly offered, but the general framework leaves something uncertain for me )

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#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @alexwallace I am also grateful to @nc27 for a terrific answer! About your thought process and ED futures, because I have answered variations on the ED dynamic so many times (is why we beg people to search) that I specifically recorded the following two videos:
1. T3-28: Eurodollar futures contract https://www.bionicturtle.com/forum/threads/t3-28-eurodollar-futures-contract.22442/
2. T3-29: Hedge interest rate exposure with Eurodollar futures contract https://www.bionicturtle.com/forum/...osure-with-eurodollar-futures-contract.22443/
To be honest, I don't have time to validate/debug your process above (some members don't realize that my daily backlog exceeds my capacity. Further, we actually prioritize content. I have to answer quickly or I get burned fast. I read it but i didn't immediately grok what you wrote so i can't get stuck .... ), but I think you will see that these two videos give a very careful treatment of ED and their hedging use. I would just briefly highlight the following facts/features (in no particular order) which have helped me:
• The ED settles in cash (see settlement at https://www.cmegroup.com/trading/interest-rates/stir/eurodollar_contract_specifications.html). The planned borrowing (or planned investment) is the exposure. The ED is a derivative, like other derivatives, it is an additional position. The hedge is its payoff. It's a borderline misnomer to think it "locks in" a borrowing rate. Rather, the hedge adds a position so your net portfolio is "as if" you locked in a rate. If you are going to borrow, and rate goes up, your future borrowing rate goes up. The short ED position merely gives you a cash payout so the net is "as if" you locked in the borrowing rate. (illustrated in my 2nd video above)
• Per my first video, the underlying on the contract is the rate, denoted R. To me the really key idea is Q = 100 - R because it highlights the inverse relationship between the quote and the rate. What do you need to remember here? To me, all you need to really remember is that the contract directionally acts just like a bond! Rate moves up, price goes down. Ergo. to hedge future borrowing (where the risk is a rate increase and you want your derivative to payoff), you need a short position in the ED futures contract, because that's when a short bond pays off. I hope that's helpful, I think you'll find the video sequence helpful,

P.S. for future reference, we have tags and I notice that Nicole helpfully tagged these videos with "eurodollar-futures-contract" (i.e., https://www.bionicturtle.com/forum/tags/eurodollar-futures-contract/) so that's pretty intuitive!

... search tags easily with https://www.bionicturtle.com/forum/tags/

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