Comparing Eurodollar Strips to Interest Rate Swaps
Publication: Journal of Derivatives
While interest rate swaps and strips of eurodollar futures can serve as substitutes for each other, use of futures necessarily fosters some degree of uncertainty with respect to the ex post results. Specifically, the practicalities of managing a strip of futures contracts designed to replicate an interest rate swap subjects the trader/hedger to 1) basis risk, and 2) an exposure relating to the dynamic transactional requirements of the futures position. Appropriate consideration of these aspects is a prerequisite for making ex ante relative value comparisons between swap rates and futures strip yields.
Those seeking to convert a floating-interest rate exposure to a fixed-rate, or vice versa, have two choices: interest rate swaps or eurodollar strip hedges. Conceptually, each solution will accomplish the same end, but they do so using different institutional market mechanisms. Because the two instruments offer the same ultimate service (i.e., converting fixed to floating rates, or vice versa), the pricing of the two alternative financial vehicles should be closely related.
Put more specifically, for interest rate swap contracts with maturities bounded by the length of the eurodollar futures strip, the quoted swap rate should correspond to the yield associated with the strip of eurodollar futures contracts that extends for the same period. Because the two alternatives are not perfect substitutes, however, some disparity of prices may be expected.
This article has two goals: 1) to provide a methodology for evaluating eurodollar strip yields, and 2) to demonstrate the process for determining the correct hedge ratios for eurodollar strip hedges designed as substitutes for interest rate swaps. Before embarking on these objectives, we describe the respective market mechanisms briefly.
Exhibit 1 summarizes the standard, “plain vanilla,” swap agreement. Here, two counterparties enter into a contract in which A calculates an interest rate expense obligation based on a floating-interest rate benchmark and B calculates an obligation based on a known, fixed rate.
The amount of the interest expense for which A is responsible will clearly rise in a rising rate environment and fall with declining rates. B’s obligation, by contrast, is constant, based on the notional amount specified by the swap agreement and the contractually determined fixed interest rate. The swap requires periodic interest payments equal to the difference between the two interest obligations (the net), paid by the party with the greater obligation to the party with the lesser obligation.1
Suppose A agrees to pay B based on the London Interbank Offered Rate (LIBOR) on three-month eurodollar deposits, and B agrees to pay A based on a fixed money market rate of 6%.2 Assume a notional amount of $100 million for the swap and quarterly interest settlements.
1 A parallel discussion could be offered in connection with interest revenues (an asset swap) as opposed to interest expenses (a liability swap).
2 The swap fixed rate typically is quoted as a spread over the yield on U.S. Treasury instruments (e.g., 20 basis points above five-year U.S. Treasuries). This practice allows quotations to be viable for an extended period.
With each fixing of LIBOR, a subsequent cash obligation is determined. If LIBOR were equal to 6% at the first rate-setting date, for example, no cash adjustment would be made by either party three months hence, on the settlement date. If LIBOR were 7%, counterparty A would pay B $25,000 ($100 million × 0.07 × 1/4 – $100 million × 0.06 × 1/4) on the settlement date. If LIBOR were 5%, counterparty B would pay A $25,000 ($100 million × 0.05 × 1/4 – $100 million × 0.06 × 1/4).3 This process continues for the term of the contract, following each reset of LIBOR.4
3 An alternative structure requires a settlement of the present value of the prospective cash adjustment, immediately following the setting of the variable interest rate.
4 As noted by Smith, Smithson, and Wilford, in Chapter 2 of Smith and Smithson , swaps can be thought of as a series of forward contracts or forward rate agreements, where a series of long forwards would substitute for a long swap and short forwards for a short swap. In the case of a plain vanilla swap, however, all the forward rate benchmarks are equal. In the general case of a series of forward contracts, on the other hand, the respective forward rates would reflect implied forward rates dictated by the spot yield curve; and thus respective forward rates would likely be different for different reset dates.
If both A and B had no exposure to interest rates prior to the swap transaction, the swap would expose A to the risk of higher short-term rates and the opportunity of lower rates; B’s exposure would be the opposite. More likely, however, counterparties will use swaps to offset existing exposures. In the first case, the swap is being used as a speculative trading vehicle; in the second, it is being used as a hedge.
Three additional aspects of swaps warrant mention. First, as a principal-to-principal transaction, swaps can be tailored to meet the individual needs of the counterparties, which may reflect very specific timing and exposure characteristics. At the same time, some degree of standardization has evolved in the swaps market. As a consequence, participants can typically expect better markets (i.e., tighter bid/ask spreads and greater depth) when their transactions are of the more typical constructions, but somewhat less attractive pricing for more customized deals.
Second, swaps require separate settlements and documentation for each counterparty. Thus, the first deal with a new counterparty requires substantial preliminary work and legal attention. Subsequent deals, on the other hand, tend to be readily transacted. And, finally, and perhaps one of the more significant features of swaps, default risk is ever present, and the cost of non-performance may be considerable. With this last consideration in mind, swap counterparties have increasingly come to adopt collateral-adjustment practices designed to cover this exposure.
II. EURODOLLAR STRIPS
The eurodollar futures contract is a price-fixing mechanism that sets offered rates on three-month eurodollar time deposits, with the value date of the underlying deposit scheduled for the third Wednesday of March, June, September, or December. The precise rate in question is found simply by subtracting the futures price from 100. For example, a futures price of 95.00 reflects the capacity to lock up a 5% offered rate on the underlying three-month deposit. Given this convention, it should be clear that as interest rates rise, futures prices fall, and vice versa.
With the face amount of the eurodollar futures contract being $1 million, and with the underlying deposit having a maturity of three months, every basis point move in the futures price (yield) translates to a value of $25 ($1,000,000 × 0.0001 × 90/360). In general, movements in the eurodollar futures market are closely correlated with yield movements in the spot eurodollar time deposit market, although changes are not precisely equal over any given period.
The futures market participant can maintain either a long position, which profits from a rise in price and decline in yield, or a short position, which profits from a decline in price and rise in yield.5 In either case, the participant will be obligated to mark the contract to market on a daily basis and make daily cash settlements for any change in value, valued at $25 per basis point moved. Also, before any trade is initiated, market participants must post collateral or a “performance bond.”
5 Note that the terminology differs for eurodollar futures and off-exchange forward rate agreements. That is, the short futures, which profits from a rise in interest rates, corresponds to a long forward, and vice versa. Put another way, hedgers seeking to cover the risk of an interest rate increase could either short the eurodollar futures contract or execute a long forward contract on the rate.
A key benefit of this mark-to-market requirement and the initial performance bond is that the structure virtually eliminates credit risk or exposure to counterparty default.
The mark-to-market obligation can be terminated at any time by simply trading out of the position (i.e., making the opposite transaction to the initial trade). Upon expiration of the contract, however, any participant still maintaining an open position makes a final mark-to-market adjustment, and then the contract expires.
The final settlement price is based on an average interest rate derived from a survey of London bankers who report their perceptions of the cash market three-month offered rate to the Chicago Mercantile Exchange. This survey is undertaken two London business days before the third Wednesday of the contract month (i.e., on the trade date for a spot eurodollar deposit with a settlement date of the third Wednesday). Thus, the contract is said to be “cash-settled” with no allowance or capacity for a physical delivery process. Strips of eurodollar futures are simply the coordinated purchase or sale of a series of futures contracts with successive expiration dates. The objective is to lock up a yield for a period or term equal to the length of the strip.
For example, a strip consisting of contracts with four successive expirations would lock up a one-year term rate (for a one-year period beginning at the value date of the first contract in the strip); eight successive contracts would fix a two-year rate; and so on. As is the case with swaps, futures strips may be used to take on additional interest rate risk in the hope of making trading profits, or as an offset or hedge to an existing exposure.
III. CALCULATING STRIP YIELDS
The comparison of eurodollar strip rates to interest rate swap rates requires a four-step process, as follows:
1. Identify all prospective swap rate-setting dates and related maturities.
2. For each such rate-setting date, identify the appropriate futures contracts that would be used for hedging that specific exposure.
3. Depending on the relevant futures prices for each rate-setting date, determine the expected cash flow obligation that would result by hedging with appropriately structured futures hedges.
4. Calculate the internal rate of return, reflecting the projected stream of expected cash flow obligations.
Using price data from Exhibit 2, Exhibit 3 shows sample calculations where strips are constructed in an effort to synthesize spot interest rate swaps with an initial value date of 11/5/93. Interest settlements are assumed to be scheduled semiannually, with the first interest rate exposure occurring six months after the origination of the swap.
A spot seven-year swap with semiannual cash adjustments, for instance, has fourteen independent rate-setting dates. The first setting, and thus the initial cash flow obligation, is determined with the onset of the swap, leaving thirteen forthcoming discrete occasions of interest rate exposure.
Note in Exhibit 3, that given an initial spot value date of 11/5/93, the first reset is on the value date of 5/5/94; subsequent value dates fall on the fifth of November and May through the term of the hedge. Futures hedge rates for all exposures are calculated using the futures prices of the two futures contracts that immediately follow the hedge value dates.6
For example, for a hedge value date of 5/5/94, the June-94 and September-94 futures are the appropriate pair. The synthetic coupon (Ri) is the six-month money market yield associated with a given pair of futures, calculated as follows.7
6 Two-quarter strips rates are used because they are expected to correlate more closely with six-month interest rates than rates associated with any single contract.
7 While Equation (1) allocates equal weight to the component futures contracts, some users might prefer differential weighting. Moreover, while this specification compounds the two respective futures rates, an alternative approach might simply use the average. No universal standard appears to be in effect.
To solve for R1, the first synthetic coupon, relating to the 5/5/94 value date, requires the inputs:
Settlement Prices of November 3, 1993; Spot Value Date: November 5, 1993
The fact that the hedge value date and the value date of the first futures contract in each hedge pair (i.e., the “lead” contract) are not generally coincident may cause the hedger to expect that the synthetic coupon rate will differ from spot six-month LIBOR upon the rate-setting date. For instance, differences might be anticipated because of some expectation that yield curves will exhibit a predominant shape (either upward-sloping or inverted) over the term of the hedge, or because of the presence of some expected liquidity premium. This difference — whatever the source — will directly modify the outcome, basis point for basis point.
The hedger, then, must make a best guess as to the magnitude of the average size of this non-convergence difference over the life of the hedge, or, alternatively, make some maximum/minimum estimates to generate best-case/worst-case potential results. The rationale for these adjustments may be best understood by analogy.
Consider the case of a hedger exposed to ninety-day LIBOR, on a $1 million exposure scheduled for a value date on the third Wednesday of a quarterly month. In other words, consider an exposure equal to the precise underlying instrument of a given eurodollar futures contract. Using the eurodollar futures to hedge this exposure results in an ex post effective rate equal to the rate reflected by the futures contract at the onset of the hedge. That is, irrespective of where LIBOR ultimately goes, an initial futures trade of, say, 95.00 will produce a post-hedge outcome of a 5% money market yield. If the timing of this exposure is such that the reset date precedes the futures expiration, however, and therefore the futures rate does not fully converge to the spot LIBOR, the resulting ex post outcome will differ from the initial futures rate by the amount of the non-convergence.
For example, assume the hedger initiates a hedge by selling one futures contract at a price of 95.00. Then, when the rate-setting date arrives, suppose LIBOR is 3% while the futures price is 96.90. In this case, the futures contract reflects an interest rate for the futures contract that is 10 basis points higher than spot (3.10% versus 3%). The interest on the ninety-day deposit (based on the 3% spot rate) is $7,500, while the futures generates a 190-basis point move, or a loss of $4,750.
Consolidating the futures loss with the cash interest expense would produce a net interest value of $12,250, equivalent to the ex post money market yield of 4.90% — 10 basis points below the futures rate at the start of the hedge. Again, the ex post result is the initial futures rate adjusted for the basis conditions at the time of the hedge liquidation. A downward adjustment made to the synthetic coupon calculations reflects an implicit assumption that spot six-month LIBOR will be less than the liquidation value of Ri on the rate-setting dates. This condition will typically hold when upward-sloping yield curves are present. When inverted yield curves are expected, upward adjustments of the original Ri calculations would be justified.