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Eurodollar Futures



Introduction
Eurodollars are time deposits denominated in U.S. dollars at banks outside the United States, and thus are not under the jurisdiction of the Federal Reserve. Initially, this term was used for dollar deposits in European banks, but now it refers to dollar deposits not just in European banks but any banks. For example, a U.S. dollar deposited in Japan or China would qualify as a Eurodollar. The prefix “Euro” here does not refer to the European Union. Instead, it just means that the dollars are deposited outside of the United States.

This concept can be extended to other currencies as well. For example, Euro-yen refers to Yen time deposits in banks outside of Japan. Similarly, Euro-rupee refers to rupee time deposits in banks outside of India. Euro-euro refers to Euro currency time deposits in banks outside of Eurozone countries.


History
After the World War II a significant quantity of U.S. dollars remained outside of the United States, particularly in Europe, as a result of the Marshall Plan. To rebuild Europe after the war devastation, imports were needed and most of the imports came from U.S. Moreover, with local currencies becoming worthless and redundant, the rebuild of Europe require payments to be made in a strong and acceptable currency, which incidentally happened to be U.S. dollars.


Eurodollar Rate
Eurodollars are dollar time deposits in banks outside of the United States. The deposit can be made in any country whose banks accept such time deposit. Most of the European banks accept such dollar time deposit and the rate of interest offered by them differ. Thus, there is no single time deposit rate that we can refer to. However, we can use the USD-LIBOR rate as a reference for two reasons - first, the rate is obtained through data submissions provided by major banks in London for bulk deposits of US dollars, which serve as a good and reliable estimate of the rate; second, London being an international financial center and its banks playing an important role in the European financial sector means that the rate is very close representation of the actual demand and supply of dollars within Europe, where the bulk of the Eurodollar deposits are present.

Thus, USD-LIBOR rate can be referred to as the Eurodollar rate.

The, USD LIBOR rates are quoted for maturities upto 1 year. The following table shows the rates on 4th January 2019.

Currency Overnight 1 Week 1 Month 2 Month 3 Month 6 Month 1 Year
USD 2.39400 2.40975 2.52056 2.62313 2.80388 2.85575 2.96488
CHF -0.79240 -0.81060 -0.78260 -0.72880 -0.71160 -0.63740 -0.49920
EUR -0.46429 -0.44029 -0.41943 -0.37743 -0.34457 -0.29857 -0.17700
GBP 0.67763 0.70425 0.73013 0.79413 0.90538 1.03069 1.17175
JPY -0.0893 -0.09667 -0.09400 -0.08000 -0.07450 0.00733 0.10267

As you can see, the rates for USD LIBOR are quoted for overnight to one year maturities. This represents the rate offered by one bank to another bank on a dollar deposit or lent. These rates represent the wholesale rates (for deposits of a few hundred million dollars). The retail rates are different.


Eurodollar Futures
The Eurodollar futures contract refers to the financial futures contracts based on USD-LIBOR deposit rates, traded at the Chicago Mercantile Exchange (CME). In other words, the “Eurodollar Futures” are derivative instruments whose underlying is the USD-LIBOR. The following are the features of these futures contracts. The following are the contract specifications.

Features Details
Contract Unit $2,500 x contract grade IMM Index ($25 per basis point per annum)
Product Symbol CME Globex: GE
CME Clearport: ED
Clearing: ED
Contract Months March (H), June (M), September (U) and December (Z), and nearest four “serial” months (excluding the March Quarterly cycle)
Trading hours around the clock Electronic: 5:00pm - 4:00pm (Sunday - Friday) (Central Times)
Minimum Tick Nearest expiry contract months: 1/4th of one basis point
All other contract months: ½ of one basis point
Dollar value of one tick Nearest expiry contract months: $6.25
All other contract months: $12.50

As discussed above, at any point in time there are about 44 different futures contracts on the USD-LIBOR rate (40 quarterly contracts + 4 serial month contracts). The following are the contracts as on 8th January 2019.

SL No Contract Month Closing Price Implied Yield
1 January 2019 97.24 2.76
2 February 2019 97.28 2.72
3 March 2019 97.29 2.71
4 April 2019 97.295 2.705
5 May 2019 97.29 2.71
6 June 2019 97.27 2.73
7 September 2019 97.285 2.715
8 December 2019 97.295 2.705
9 March 2020 97.37 2.063
10 June 2020 97.41 2.59
11 September 2020 97.435 2.565
12 December 2020 97.425 2.575
13 March 2021 97.465 2.535
14 June 2021 97.475 2.525
15 September 2021 97.47 2.53
16 December 2021 97.43 2.57
17 March 2022
18 June 2022 97.405 2.595
19 September 2022 97.39 2.61
20 December 2022 97.36 2.64
21 March 2023 97.34 2.66
22 June 2023 97.31 2.69
23 September 2023 97.285 2.715
24 December 2023 97.245 2.755
25 March 2024 97.22 2.78
26 June 2024 97.19 2.81
27 September 2024 97.155 2.845
28 December 2024 97.11 2.89
29 March 2025 97.085 2.915
30 June 2025 97.06 2.94
31 September 2025 97.03 2.97
32 December 2025 97.005 2.995
33 March 2026 97.00 3
34 June 2026 96.985 3.015
35 September 2026 96.945 3.055
36 December 2026 96.945 3.055
37 March 2027 96.935 3.065
38 June 2027 96.925 3.075
39 September 2027 96.92 3.08
40 December 2027 96.875 3.125
41 March 2028 96.865 3.135
42 June 2028 96.85 3.15
43 September 2028 96.845 3.155
44 December 2028 96.84 3.16

The implied yields can be used to construct a yield curve, which is very helpful for understanding, hedging, speculating and valuing other financial instruments, including derivatives.

The below is an implied yield curve for 10 years into the future based on the closing prices given in the above table.

Implied Yield Curve

We will discuss more about the yield curve later. For the moment, let's try to understand how to use or trade Eurodollar futures.

We are on 8th January 2019 and the spot rates of USD-LIBOR are as follows.

Currency Overnight 1 Week 1 Month 2 Month 3 Month 6 Month 1 Year
USD 2.39275 2.40513 2.51113 2.63388 2.79681 2.84875 2.99474

We are interested to borrow USD 1 million sometime in 3rd week of March 2019 for a period of 3 months. Our bank usually provides us short term loans at LIBOR+2%. If we were to borrow currently for a period of 3 months then we can use the current LIBOR rates; accordingly, our borrowing cost would be 4.79681% (LIBOR+2% or 2.79681+2%). However, we are not interested to borrow money now. Our requirement of money is 3 months from now. If we go to our bank then they may either offer us a forward borrowing interest rate or may ask us to come back in March 2019 so that they can offer a rate based on the LIBOR at that point in time.

We could go back to our bank in March 2019 and borrow at the LIBOR rate prevailing at that time. However, such a case exposes us to the risk that interest rates may increase by then. If the interest rates increase then our borrowing costs would increase. It is also possible that the interest rates may decrease by then. In such a case, our borrowing costs would decrease. We are, however, bothered about the increase in interest rate as it affects us adversely.

If we strongly believe that the interest rates may increase in 3 months’ time from now, can we do something about it?

We can use interest rate derivatives to manage this future interest rate risk. For managing short term interest rate risk, we can use either a Forward Rate Agreement (FRA) or Eurodollar Futures. In this example. We will use Eurodollar futures as that’s the subject we are trying to understand.

Eurodollars are traded as per contract months (please refer the Eurodollar contract table above). Contracts are settled on the 2nd business day prior to the 3rd Wednesday of the contract month. That means, a January 2019 contract would settle on 14th January 2019 (as 3rd Wednesday of January 2019 is 16th); a February 2019 contract would settle on 18th February 2019 (as 3rd Wednesday of February 2019 is 20th); and a March 2019 contract would settle on 18th March 2019 (as 3rd Wednesday of March 2019 is 20th).

In the Eurodollar contract table above, the closing price of a January 2019 contract as on 8th January 2019 is 97.24. What this means is that the market participants, on an average, think that the price of USD-LIBOR on the settlement day (i.e. on 14th January 2019) would be 97.24 or the expected market rate of USD-LIBOR would be 2.76. The current LIBOR for a 1-month borrowing is 2.51. The market is expecting the LIBOR rates to go up.

We are interested in a borrowing for 3 months, 3 months from now (around last week of March 2019). Currently, a March 2019 contract (3-month-from-now contract) is trading at a price of 97.29 (implied yield being 2.71). This means that the market participants, currently, are expecting the USD-LIBOR interest rates in March (18th March specifically) to be 2.71. We are afraid that this rate may increase; we do not know exactly by how much. But we think that it may possibly be 2.90.

If our fear turns out to be correct then our borrowing cost would be 4.9% (2.9% + 2%). To hedge against this risk, we can use Eurodollar contract. To use it, first we need to select the appropriate contract. For our example, we will select the March 2019 contract as that resembles the expected interest rates in March (the rough time of our actual borrowing). For better results, we should look at the current and possible future shape of the yield curve to determine the appropriate contract month. We will discuss this aspect later.

The March contract is traded at 97.29 (implied interest of 2.71). We can select this contract for our hedge. The next thing we need to figure out is the market side. The March contract can be bought or sold. Which market side should we take? This depends on our expectations of future interest rates. We expect the interest rates to increase. This will result in a fall in bond prices. If we can sell the contract at a higher price and buy it back when the prices are low, we can make a profit. Thus, we should sell the March contract or take a short position in the March contract.

Our idea is that the current yield is 2.71 (price of 97.29) on the March contract. If the yields increase as per our expectations, then the prices will fall, thereby giving us a profit. Let’s assume that on 18th of March 2019 the spot USD-LIBOR rate is 2.90 (as per our expectation). This will result in the fall in the prices of Eurodollar futures, most probably to 9.71 (100-2.90). If we square our position by buying a contract then our profit will be 0.19 per contract.

How many Eurodollar contracts should be buy? Each Eurodollar futures contract is for a notional amount of USD 1 million. Thus, we should sell 1 contract.

Our trades would be: In March 2019, we would be borrowing the money from our bank. The bank would most probably quote an interest rate equal to current LIBOR+2%, i.e. 4.9% (2.9% + 2%). In January 2019, when we had planned our borrowing, the 3-month LIBOR was 2.79. Our borrowing cost increased by 0.11% due to the increase in interest rate. This resulted us in a loss of $275. The calculation is as below.

Interest liability as per spot LIBOR rates in January 2019

$$1,000,000 {4.79\over 100} {90\over 360} = $11,975. $$



Interest liability as per actual borrowing cost in March 2019

$$1,000,000 {4.90\over 100} {90\over 360} = $12,250 $$



The difference between the two (or loss) is $275.

However, we negated the loss due to interest rate increase by trading in the Eurodollar futures markets, where we made a profit of 0.19 per contract. This in dollar terms equates to $475, as below.

$$1,000,000 {0.19\over 100} {90\over 360} = $475 $$



We have thus made a profit of $200 by taking this hedge.

It is quite possible that the interest rates may have decreased. Let’s suppose that the interest rates decreased to 2.56. In this case, we will make a loss on Eurodollars but benefit from our actual borrowing.

Our actual borrowing would be 4.56% (2.56% + 2%). The notional gain due to this decrease in interest would be 0.23% (4.79 - 4.56). This amounts to a dollar amount of $575. The calculation is as below.

$$1,000,000 {0.23\over 100} {90\over 360} = $575 $$



We would have lost in the Eurodollars trades. The loss would be $375. The calculation is as below.

$$1,000,000 {0.15\over 100} {90\over 360} = $375 $$



The net of both the trades is a gain of $200.

By hedging, the loss in one market is cancelled out by the profit in the other market.

Summarily, to trade in Eurodollars we need to decide about the following three aspects.

Eurodollar Futures vs. Interest Rate Swaps


Measuring short term interest rate risk
Interest rate risk can be measured through concepts such as Duration (Modified Duration) and Basis Point Value (BPV).

Duration is a concept that was originated by the British actuary Frederick Macaulay. Mathematically, it is a reference to the weighted average present value of all the cash flows associated with a fixed income security, including coupon income as well as the receipt of the principal or face value upon maturity. Duration reflects the expected percentage change in value given a 1% or 100 basis point change in yield.

For example, a 5-year note may have a duration of 4 years. It means that the note can be expected to decline 4% in value given a 1% increase in yields.

The duration represents a useful and popular measure of risk for medium to long-term coupon bearing securities. For shorter duration instruments (money market instruments), the preferred risk measurement technique is Basis Point Value (BPV).

BPV is a concept that is closely related to duration. It measures the expected monetary change in the price of a security given a 1 basis point (0.01%) yield. It may be measured in dollars and cents based upon a particular face value security, commonly $1 million face value. It is also referred to as the “dollar value of a 01” or simply “DV of a 01”.

Basis point values can be calculated as a function of the face value and the number of days until maturity associated with a money market instrument. The following is the formula for calculation.

\[ BPV = Face value \text{ x } {days\over 360} \text{ x } {0.01\over 100} \]


For example, a $10 million 180-day money market instrument carries a BPV of:

\[ BPV = $10,000,000 \text{ x } {180\over 360} \text{ x } {0.01\over 100} = $500 \]


What this means is that if the yield increases by 0.01% then the price will decrease by $500. Alternatively, if the yield decreases by 0.01% then the price will increase by $500. Thus, we can say that for a 0.01% change in yield, we can expect a $500 movement of the price either way. Using this concept, we can measure the expected loss or profit given a particular movement in interest rates. This concept is extremely useful for understanding the risk in a short term instrument.

The following are a few more examples of the above concept.

For example, a $100 million 60-day money market instrument has a BPV of $1,666.67, as shown below.

\[ BPV = $100,000,000 \text{ x } {60\over 360} \text{ x } {0.01\over 100} = $1,666.67 \]


For example, a $1 million 90 day money market instrument has a BPV of $25, as shown below

\[ BPV = $1,000,000 \text{ x } {90\over 360} \text{ x } {0.01\over 100} = $25 \]


As a ready reference, we can create a grid of the BPV values for various maturities and principal or notional amounts. The following is an example of the grid.

Days $500,000 $1 million $10 million $100 million $1 billion
1 $0.14 $0.27 $2.78 $27.8 $278
7 $0.97 $1.94 $19.45 $194.5 $1945
30 $4.17 $8.33 $83.33 $833.3 $8333
60 $8.33 $16.67 $166.7 $1667 $16670
90 $12.5 $25 $250 $2500 $25000
180 $25 $50 $500 $5000 $50000
270 $37.5 $75 $750 $7500 $75000
360 $50 $100 $1000 $10000 $100000


Hedging short term rate exposure using Eurodollar futures
The essence of any hedging or risk management is to match up any change in risk exposure to be hedged (Value at risk) with an offsetting change in the value of a futures contract (Value of futures) or other derivative instruments.

\[ \Delta Value_{risk} = \Delta Value_{futures} \]


The appropriate “hedge ratio (HR)” may be calculated as the expected change in the value of the risk exposure relative to the expected change in the value of the futures contract that it utilized to hedge such risk.

\[ HR = \Delta Value_{risk} \div \Delta Value_{futures} \]


Change in value is a rather abstract concept. But it may be measured by reference to the BPV as discussed above. Thus, we may use the equation by substituting BPV for this abstract concept of change as follows.

\[ \Delta Value_{risk} \sim BPV \]


The BPV of one Eurodollar futures contract is unchanging at $25. We may, thus, identify a generalized Eurodollar futures hedge ratio as follows:

\[ HR = BPV_{risk} \div BPV_{futures} = BPV_{risk} \div $25 \]


Let’s now use this concept to find out a hedge ratio.

Let’s assume that a corporation anticipates that it will require a $100 million loan for a 90-day period beginning in six months’ time that will be based on a 3-month LIBOR rate plus some fixed premium. The BPV of this loan may be calculated as $2,500.

\[ BPV = $100,000,000 \text { x } \frac {90} {360} \text { x } \frac {0.01} {100} = $2,500 \]
The corporation is concerned that rates may rise before the loan is needed and that it will, therefore, be required to pay higher interest rates. This exposure may be hedged by selling 100 Eurodollar futures that mature six months from the current date.

\[ Hedge Ratio \ (H) = $2,500 \div $25 = 100 \]
Similarly, the asset manager planning to purchase the $100 million loan may be concerned that rates will decrease. Thus, the asset manager might buy 100 Eurodollar futures as a hedge.

Sell Eurodollar futures = Hedge risk of rising interest rates
Buy Eurodollar futures = Hedge risk of declining interest rates
In these examples, we assumed that the loan is tied to a 3-month LIBOR rate. However, commercial loans are often based on alternative rates including prime rates, commercial paper, etc. Those rates may not precisely parallel LIBOR movements i.e. there may be some “basis risk” between the instruments to be hedged and the Eurodollar futures contract that is employed to execute the hedge.

It is important to establish a high degree of correlation between LIBOR rates, as reflected in Eurodollar future prices, and the specific rate exposure to be hedged. In particular, use of a BPV hedge ratio implies an expectation that yields on both instruments fluctuate in parallel i.e. by the same number of basis points. Such correlation is central to the effectiveness of the hedge and for qualification for hedge accounting under FASB No. 133.


Using Eurodollar futures to value Interest Rate Swaps (IRS)
The volumes of the Eurodollar futures have grown on a parallel path along with over-the-counter swaps, particularly Interest Rate Swaps. The Eurodollar futures are interwined with the IRS market as a source for pricing and a tool to hedge the risks associated with the swaps. In particular, banks and broker-dealers making a market in over-the-counter(OTC) swaps represents primarily Eurodollar market participants.

Interest rate swaps are typically quoted by reference to a fixed rate. That rate is calculated such that the present value of the cash flows of the fixed rate is equal to the present value of the floating rate.

\[PV_{Fixed} = PV_{Floating} \]
The floating rate payments are also unknown. However, they may be estimated by examining the shape of the yield curve, or more practically, by referencing the rates associated with Eurodollar future prices which reflect the shape of the yield curve.

When an IRS is transacted such that the present value of the estimated floating rate payments equals the present value of the fixed rate payments, no monetary consideration is passed on the basis of this initial transaction. This is also referred to as the "Par Swap". In our example, we will consider our swap to be a "Par Swap".

Let's consider the following.
We are required to find the fixed price and value of a 2-year swap where the floating rate is determined by reference to a USD-LIBOR rate. We are in December 2018 currently.

To calculate the fixed rate, we need to calculate the present value of the floating rate, as the PV of the floating rate should be equal to the PV of the fixed rate. The floating rates are unknown but we can use the Eurodollar futures rates for our calculation as they represent the best guess about what the future floating rates of USD-LIBOR would be.

Let's assume that the following are the Eurodollar futures rates.

Instrument Expiration Date Price Implied Yield
3-Months LIBOR 0.3125
June 2019 Eurodollars 13-June-2019 99.6350 0.3650
September 2019 Eurodollars 19-Sep-2019 99.5450 0.4550
December 2019 Eurodollars 19-Dec-2019 99.3950 0.6050
March 2020 Eurodollars 19-Mar-2020 99.1550 0.8450
June 2020 Eurodollars 18-June-2020 98.8250 1.1750
September 2020 Eurodollars 17-Sep-2020 98.4650 1.5350
December 2020 Eurodollars 17-Dec-2020 98.1300 1.8700
18-Mar-2021


We can use these rates as the indicative future floating rates for our swap and also as the discounting rates. The following is the calculation of the discounting factor based on these rates.

Instrument Expiry Date Days Day Span Price Rate Compound Value (CV) Discount Factor (PV) (1/CV)
3-Months LIBOR 96 0.3125 1.0008 0.9992
June-2019 Eurodollars 13-June-2019 96 98 99.6350 0.3650 1.0018 0.9982
September-2019 Eurodollars 19-Sep-2019 194 91 99.5450 0.4550 1.0030 0.9970
December-2019 Eurodollars 19-Dec-2019 285 91 99.3950 0.6050 1.0045 0.9955
March-2020 Eurodollars 19-Mar-2020 376 91 99.1550 0.8450 1.0067 0.9934
June-2020 Eurodollars 18-June-2020 467 91 98.8250 1.1750 1.0096 0.9904
September-2020 Eurodollars 17-Sep-2020 558 91 98.4650 1.5350 1.0136 0.9866
December-2020 Eurodollars 17-Dec-2020 649 91 98.1300 1.8700 1.0184 0.9820
18-Mar-2021 740


The fixed rate of the swap can be calculated by using the following formula.

\[ R_{Fixed} = \frac { 4 \text { x } \sum_{i=1}^n [PV_i \text { x } R_i \text { x } \frac {(days_i)} {360} ] } { \sum_{i=1}^n PV_i} \]

\[ R_{Fixed} = \frac { 4 \text { x } ([0.9992 \text { x } 0.003125 \text { x } \frac {96} {360} ]) + ([0.9982 \text { x } 0.003650 \text { x } \frac {98} {360} ]) + ([0.9970 \text { x } 0.004550 \text { x } \frac {91} {360} ]) + ([0.9955 \text { x } 0.006050 \text { x } \frac {91} {360} ]) + ([0.9934 \text { x } 0.008450 \text { x } \frac {91} {360} ]) + ([0.9904 \text { x } 0.011750 \text { x } \frac {91} {360} ]) + ([0.9866 \text { x } 0.015350 \text { x } \frac {91} {360} ]) + ([0.9820 \text { x } 0.01870 \text { x } \frac {91} {360} ]) } {0.9992 + 0.9982 + 0.9970 + 0.9955 + 0.9934 + 0.9904 + 0.9866 + 0.9820} \]

\[R_{Fixed} = 0.9079 \text {%} \]

Using the above fixed rate and discounting rates, we can find the present value of both the fixed rate cash flows and the floating rate cash flows. The below is the calculation.

Payment Date Fixed Payments Discount Factor PV of Fixed Payments Floating Payments Discount Factor PV of Floating Payments
13-06-2019 $22,697.63 0.9992 $22,656.22 $8,333.33 0.9992 $8,326.39
19-09-2019 $22,697.63 0.9982 $22,656.22 $9,936.11 0.9982 $9,917.98
19-12-2019 $22,697.63 0.9970 $22,630.19 $11,501.39 0.9970 $11,467.22
19-03-2020 $22,697.63 0.9955 $22,595.63 $15,293.06 0.9955 $15,224.33
18-06-2020 $22,697.63 0.9934 $22,547.47 $21,359.72 0.9934 $21,218.42
17-09-2020 $22,697.63 0.9904 $22,480.70 $29,701.39 0.9904 $29.417.53
17-12-2020 $22,697.63 0.9866 $22,393.81 $38,801.39 0.9866 $38,282.02
18-03-2021 $22,697.63 0.9820 $22,288.45 $47,269.44 0.9820 $46,417.31
$1,80,271.20 $1,80,271.20


As we can see that the IRS rate can be calculated using the rates from the Eurodollar futures. Similarly, the Eurodollar future rates can also be used for valuation of an IRS.


END OF NOTES

Updation History
First updated on 12.01.2019