A Eurodollar future is a cash-settled futures contract on a three-month, $1 million Eurodollar deposit that pays LIBOR. These contracts are traded on the Chicago Mercantile Exchange (CME), the London International Financial Futures Exchange (LIFFE), and the Singapore International Monetary Exchange (SIMEX). Eurodollar futures contracts are traded for March, June, September, and December delivery. Contracts are traded out to three years, with a high degree of liquidity out to two years.
Eurodollar futures act like FRAs in that they help lock in a future interest rate and are settled in cash. However, unlike FRAs, they are marked to market daily. (As in currency futures, this means that gains and losses are settled in cash each day.) The price of a Eurodollar futures contract is quoted as an index number equal to 100 minus the annualized forward interest rate. For example, suppose the current futures price is 91.68. This price implies that the contracted-for LIBOR3 rate is 8.32%, that is, 100 minus 91.68. The value of this contract at inception is found by use of the following formula:
The interest rate is divided by four to convert it into a quarterly rate. At maturity, the cash settlement price is determined by subtracting LIBOR3 on that date from 100. Whether the contract gained or lost money depends on whether cash LIBOR3 at settlement is greater or less than 8.32%. If LIBOR3 at settlement is 7.54%, the Eurodollar future on that date is valued at $981,150:
At this price, the buyer has earned $1,950 ($981,150 − $979,200) on the contract. As can be seen from the formula for valuing the futures contract, each basis point change in the forward rate translates into $25 for each contract ($1 million X 0.0001/4), with increases in the forward rate reducing the contract’s value and decreases raising its value. For example, if the forward rate rose three basis points, a long position in the contract would lose $75. This arithmetic suggests that borrowers looking to lock in a future cost of funds would sell futures contracts because increases in future interest rates would be offset by gains on the short position in the futures contracts. Conversely, investors seeking to lock in a forward interest rate would buy futures contracts because declines in future rates would be offset by gains on the long position in the futures contracts.
Before the settlement date, the forward interest rate embedded in the futures contract is unlikely to equal the prevailing LIBOR3. For example, on October 23, 2008, the March 2009 Eurodollar futures contract closed at an index price of 97.6050, implying a forward rate of 2.3950% (100 − 97.6050). Actual LIBOR3 on October 23 was 3.5350%. The discrepancy between the two rates reflects the fact that the 2.3950% rate represented a three-month implied forward rate as of March 16, 2009, which was 144 days in the future. The forward rate is based on the difference between 144-day LIBOR and LIBOR on a 255-day deposit (which matures on June 15, 2009—91 days after the 144-day deposit).
The actual LIBOR3 used is determined by the respective exchanges. Both the CME and LIFFE conduct a survey of banks to establish the closing value for LIBOR3. Accordingly, contracts traded on the two exchanges can settle at slightly different values. SIMEX uses the CME’s settlement price for its contracts.
Contracts traded on the CME and SIMEX have identical contractual provisions. Those two exchanges have an offset arrangement whereby contracts traded on one exchange can be converted into equivalent contracts on the other exchange. Accordingly, the two contracts are completely fungible. LIFFE does not participate in this arrangement.
Application Using a Futures Contract to Hedge a Forward Borrowing Rate
In late June, a corporate treasurer projects that a shortfall in cash flow will require a $10 million bank loan on September 16. The contractual loan rate will be LIBOR3 + 1%. LIBOR3 is currently at 5.63%. The treasurer can use the September Eurodollar futures, which are currently trading at 94.18, to lock in the forward borrowing rate. This price implies a forward Eurodollar rate of 5.82% (100 − 94.18). By selling 10 September Eurodollar futures contract, the corporate treasurer ensures a borrowing rate of 6.82% for the three-month period beginning September 16. This rate reflects the bank’s 1% spread above the rate locked in through the futures contract.
A lengthier explanation of what is going on is as follows. In June, 10 September Eurodollar contracts will be worth $9,854,500:
Suppose that in September, LIBOR3 is 6%. At that rate, these 10 contracts will be closed out in September at a value of $9,850,000:
The difference in values results in a $4,500 gain on the 10 contracts ($9,854,500 − $9,850,000). At the same time, in September, the company will borrow $10 million for three months, paying LIBOR3 + 1%, or 7%. In December, the company has to pay interest on its debt of $175,000 ($10 million X 0.07/4). This interest payment is offset by the $4,500 gain on the 10 Eurodollar contracts, resulting in a net interest cost of $170,500, which is equivalent to an interest rate of 6.82% (4 × 170,500/10,000,000).5
5 The fact that the $4,500 is received in September and the $175,000 is paid in December does not change matters. If the $4,500 is invested at the company’s opportunity cost of 7% for those three months, the $175,000 would be offset by $4,578.75 in earnings ($4,500 × 1.0175). That would result in effective interest of $170,421.25, or a 6.82% rate annualized.
9.3 Structured Notes
In the past decade, a new breed of financial instrument—the structured note—has become increasingly popular. Structured notes are interest-bearing securities whose interest payments are determined by reference to a formula set in advance and adjusted on specified reset dates. The formula can be tied to a variety of different factors, such as LIBOR, exchange rates, or commodity prices. Sometimes the formula includes multiple factors, such as the difference between three-month dollar LIBOR and three-month Swiss franc LIBOR. The common characteristic is one or more embedded derivative elements, such as swaps, forwards, or options. The purpose of this section is not to describe every type of structured note available because there are literally hundreds, with the design of new ones limited only by the creativity and imagination of the parties involved. Rather, it is to describe the general characteristics of these debt instruments and their uses.
We have already seen one of the earliest types of structured notes—a floating rate note (FRN) whose interest payment is tied to LIBOR (the equivalent of swapping a fixed-rate for a floating-rate coupon). Although the FRN formula is quite simple, the formulas on subsequent structured notes have become more complex to meet the needs of users who want to take more specific positions against interest rates or other prices. Structured notes allow companies and investors to speculate on the direction, range, and volatility of interest rates; the shape of the yield curve, which relates the yield to maturity on bonds to their time to maturity and is typically upward sloping; and the direction of equity, currency, and commodity prices. For example, a borrower who believed that the yield curve would flatten (meaning that the gap between short-term and long-term rates would narrow) might issue a note that pays an interest rate equal to 2% plus three times the difference between the six-month and 20-year interest rates.
Structured notes can also be used for hedging purposes. Consider, for example, a gold mine operator who would like to borrow money but whose cash flow is too volatile (because of fluctuations in the price of gold) to be able to service ordinary fixed-rate debt. One solution for the operator is to issue a structured note whose interest payments are tied to the price of gold. If the price of gold rises, the operators cash flows increase and the operator finds it easier to make the interest payments. When gold prices go down, the interest burden is lower. Not only does the note hedge the operators gold-price risk, but the greater ease of servicing this note lowers the operators risk of default and hence the risk premium to be paid.