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A COMMENT ONA HEDGING DEFICIENCYIN EURODOLLAR FUTURES

IRA G. KAWALLER

Professor Chances analysis shows that hedge results from eurodollarfutures are imperfect; and he credits the futures contract design as beingthe source of the error. This comment argues that the unanticipated out-comes that Professor Chance evidences stem not from the design of thecontract, but rather from improperly sizing hedge transactions. If appro-priately sized hedges are used, perfect hedge outcomes in fact, will follow. 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:187193, 2007

In his article that appeared in the February 2006 issue of this Journal,Professor Don Chance postulates that the design of the eurodollarfutures contract is deficient, in that the futures price does not convergeto the spot price. The consequence of this design is that hedge resultswill necessarily be imperfect. I tend to look at the issue with a distinctlydifferent perspective resulting in a contrary conclusion.

The eurodollar futures contract is commonly thought to be a price-fixing mechanism that locks in offered rates on 3-month eurodollar

For correspondence, Kawaller & Co., 162 State Street, Brooklyn, NY 11201; e-mail: [email protected]

Received February 2006; Accepted May 2006

Ira G. Kawaller is the founder of Kawaller & Company, LLC and the managing partner of the Kawaller Fund. The former is a consulting company that specializes in assistingcommercial hedgers in their use of derivatives; the latter is a derivatives-based hedgefund.

The Journal of Futures Markets, Vol. 27, No. 2, 187193 (2007) 2007 Wiley Periodicals, Inc.Published online in Wiley InterScience (www.interscience.wiley.com).DOI: 10.1002/fut.20253

188 Kawaller

Journal of Futures Markets DOI: 10.1002/fut

1Forty quarterly expiration months are available, along with the four most-imminent nonquarterlymonths. The nonquarterly expirations are known as serial months.

time deposits. The value dates of the underlying deposits are thirdWednesdays of the expiration month (e.g., the third Wednesday ofMarch, June, September, or December).1 The precise rate that thefutures contract secures is found simply by subtracting the futures pricefrom 100. For example, a futures price of 95.00 reflects the capacity tolock up a 5% offered rate on the underlying 3-month deposit. Given thisconvention, it should be clear that as interest rates rise, futures pricesfall, and vice versa.

Presumably, Professor Chance would argue that the hedger wouldlikely end up with a different resulti.e., somewhat different from 5% inthe above example. I hope to demonstrate that the perfect result is, infact, obtainable; however, to realize that perfect result, the hedge has to beimplemented properly. Professor Chances imperfect result is a functionof an improperly sized hedge, not the fault of the contract design.

THE EURODOLLAR FUTURES CONTRACT DESIGN

Eurodollar futures expire two London business days before the thirdWednesday of the contract month (i.e., on the trade date for a spoteurodollar deposit with a settlement date of the third Wednesday).Following expiration, any participant who had an open position as of theexpiration would be required to make a final mark-to-market adjustment;then no further obligations or responsibilities would remain. The finalsettlement price is set equal to 100 minus the spot 3-month LondonInterbank Offered Rate (LIBOR) on the expiration day, as reportedby the British Bankers Association (BBA). That is, contrary to ProfessorChances assertion, the final settlement price perfectly reflects spot 3-month LIBOR. The Chicago Mercantile Exchange (CME) capturesthe BBA LIBOR quotation on the expiration date and then settles thecontract to the final price that reflects exactly this yield. You cant getbetter convergence than that!

This comment argues that if the exposure to be hedged is identicalto the underlying of the associated futures contract, the hedged outcomeshould be perfect. If, however, these two components of the hedgingrelationship are not identical, then some degree of imprecision of thehedge will prevail. This seeming ineffectiveness, however, is simplythe traditional basis risk issue that affects any hedge where the expo-sure and the instrument that underlies the futures contract exhibit any

Comment 189


2The value of $25 per 0.01 price change is reflective of the basis point value of a $1 million depositwith a 90-day maturity.3This convention is overridden if the next business day would bring the maturity day into the follow-ing calendar month. In that case, the maturity date would be made earlier, rather than later.

differenceswhether in connection with timing or with regard to thequality of the underlying instrument or commodity. In any case, if theexposure being hedged were a 3-month security priced at LIBOR (orLIBOR a known and constant spread) as of two London business daysbefore the third Wednesday of the month, the issue of basis risk wouldseem to be mootbut it may not be if the day counts associated withthe hedged item and the eurodollar futures are not identical. A discrep-ancy of this type is typical as the futures contract design imposes theassumption of a 90-day quarter,2 but most calendar quarters are either91 or 92 days.

Consider the case where a hedger intends to issue 3-montheurodollar deposits with a value date equal to the third Wednesday ofthe March (priced two London business days earlier). In this case, adifficulty arises because the 3-month maturity associated with the cashdeposit will typically have a different day count from the 3 months asso-ciated with the futures contract. That is, by convention, interest oneurodollar deposits accrues on the basis of the actual-over-360 daycount convention, where maturity dates are set to be the same calendarday as the deposits start date, or the next business day following.3 Inour example, given an issue date of, say, March 15th, the maturitywould be June 15th, and thus the deposit would happen to have a 92-day maturity. Meanwhile, the design of the eurodollar futures contractimposes the presumption of a 90-day maturityconsistent with thedesign feature that assigns a $25 basis point value to price changes inthe futures contract, i.e., $25 $1 million 0.0001 (90360).

This design feature canand shouldbe accommodated for, byproperly sizing the hedge to reflect the differences between the tworespective interest rate sensitivities. The appropriate number of futuresto use is simply found by dividing the basis point value of the exposureby the basis point value of the contract. Mathematically, the hedge ratio(or the number of futures contracts required) to hedge a $1 milliondeposit exposure would be found as follows:

N $1 million 0.0001 aDaysEXP

360b

$1 million 0.0001 a 90360

b

DaysEXP90

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4This perfect hedge outcome does ignore the incremental earnings associated with the potential toinvest variation margin gains or the costs associated with financing variation margin losses.Professor Chance recognized that same concern. He (and I) effectively brush aside this concern byassuming that rate changes occur only on the last day of the hedgeeffectively causing the value ofthese incremental effects to become zero.

where N is the hedge ratio and DaysEXP is day count from the start dateof the exposure to the maturity.

In the above example, DaysEXP would equal 92, and thus the requirednumber of futures contracts would be 9290 1.022222 . . . per million.Clearly, if one were only hedging a million dollars of exposure, this preci-sion would be lost in the rounding, and a one-for-one hedge would be theappropriate practical solution; but, in fact, this hedge (or any one-to-onehedge) would be too small by more than 2%. Put another way, the one-for-one hedge only covers 97.8% of the risk. The remaining portion of riskwould not be hedged. Thus, the risk would be largely mitigated, but notfully offset. This conclusion, however, only holds for the one-for-onehedge construction. Assuming if the magnitude of the exposure allowedfor perfect hedge sizing, the risk could be entirely offset.

An Example

This point can be demonstrated using an example that assumes that frac-tional contracts could be transacted. Extending the above case, wherethe DaysEXP is 92 and thus the required number of futures contracts are9290 per million, suppose the futures are originally sold at a price of95.00. Here, the perfect result would be to realize an ex post LIBOR of5% for the prospective liability subject to risk. In fact, as long as the spotLIBOR and the final futures price reflect the same yieldwhich theywill by contract design this outcome is assured.4 This result is demon-strated for two cases. In the first case, LIBOR is assumed to have movedto 4% as of the common date when the futures expire and the rate isdetermined for the exposure; in the second case LIBOR is assumed tohave moved to 6%.

The interest expense is simply Principal ($1 million) times the ter-minal spot LIBOR times Time ( 92360); the futures result reflectsthe 200 basis point moves in either direction times the $25 value of abasis point, times the hedge ratio; and the combined results simplyadd futures losses to (or deduct futures gains from) the interest paid.The effective yield derives from dividing the combined results by the$1 million principal and then annualizing this simple interest rate bymultiplying by 36092.

Comment 191


This example illustrates two critical points:

1. As long as the final futures price perfectly corresponds to the cashLIBOR paid (or received) on the deposit being hedged, if the hedgeratio properly reflects the correct value of a basis point for the expo-sure, the ex post hedge result will perfectly reflect the price of thefutures contract as of the date that the hedge is initiated.

2. Spot LIBOR as of the date the hedge is initiated is irrelevant. Putanother way, the effective rate that will be realized from a properlyconstructed futures hedge is the rate that corresponds to the startingfutures priceirrespective of the spot LIBOR as of the hedges startdate.

The above presentation begs the question: What happens in thecase where perfect convergence does not occur? That is, either becauseof differences in timing for the proposed exposure versus the periodassociated with the 3 months underlying the futures contract (i.e., start-ing on the third Wednesday of the contract month), or because thedeposit being hedged might be priced at a non-zero spread over/underLIBOR? These circumstances are illustrated in Tables I and II.

In these two cases, the example is constructed where the rate usedfor the interest accrual on the exposure differs from the rate reflected bythe final futures price by 10 basis points. This non-convergence effectfeeds directly to the bottom line, basis point for basis point, such thatinstead of realizing the 5% outcome consistent with trading the futuresat 95.00, the hedger realizes this 5% adjusted by the basis effect as of thedate the hedge is terminatedin these cases, 5.10%. Thus, to the extentthat hedgers can accurately anticipate the ending basis conditions, the

TABLE I

Alternative Hedge OutcomesPerfect Convergence

Case 1 Case 2

Futures price at hedge inception 95.00 95.00LIBOR at hedge termination 4.00% 6.00%Futures price at hedge termination 96.00 94.00Rate used for interest accrual on the exposure 4.00% 6.00%DaysEXP 92 92Hedge ratio 1.02222 1.02222

Interest paid on the liability 10,222.22 15,333.33Futures results (2,555.56) 2,555.56Combined results 12,777.78 12,777.78Effective yield 5.00% 5.00%

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TABLE II

Alternative Hedge OutcomesImperfect Convergence

Case 1 Case 2

Futures price at hedge inception 95.00 95.00LIBOR at hedge termination 4.00% 6.00%Futures price at hedge termination 96.00 94.00Rate used for interest accrual on the exposure 4.10% 6.10%DaysEXP 92 92Hedge ratio 1.02222 1.02222

Interest paid on the liability 10,477.78 15,588.89Futures results (2,555.56) 2,555.56Combined results 13,033.33 13,033.33Effective yield 5.10% 5.10%

ex post results may still be anticipated, preciselybut only if the hedge isimplemented with the appropriate hedge ratio.

Critically, these results are perfect only in an accounting sense.That is, the above examples demonstrated that except for rounding error,it is possible to construct a hedge where the ex post accounting resultwill match ex ante expectations. This result, however, is contingent uponfutures gains or losses being recognized in earnings concurrently withthe recognition of the cash interest expenses or revenues associated withthe exposure; and, importantly, this treatment is precisely the treatmentprescribed by under cash flow hedge accounting rules.

One could argue that being perfect in an accounting sense is differentfrom being perfect in an economic sense; and I would agree. But this criti-cism applies to all futures contractsnot just eurodollars. That is, becausefutureshedge results are generated daily through the process of daily mark-to-market variation settlement adjustments, the perfect economic hedge(as opposed to the perfect accounting hedge) would be one that offsets thepresent value of the forthcoming price effects of the exposure, whereas thehedge devised in the above example only addresses the nominal amount ofthe price effect without taking into account any timing differences.

Though conceptually elegant, hedges constructed to offset thesepresent value effects (commonly referred to as tailed hedges) are problem-atic, in that they require making dynamic adjustments as interest rateschange and/or as time goes by. Ultimately, however, as the hedge periodreaches its end and the present value factor approaches unity, the size ofthe tailed hedge position will approach that of the untailed hedge.5

5See Kawaller (1994) for a more complete discussion of the issues relating to tailed and untailedEurodollar futures hedges.

Comment 193


As a practical matter, tailed hedges tend to be preferred by firmsthat operate in a mark-to-market accounting environment (such as trad-ing or investment companies), but other enterprises that seek to deferthe recognition of hedge results will tend not to tail their hedges andseek hedge accounting treatment; and for these firms, the perfectaccounting result is the primary objectivean objective that can be real-ized with eurodollar futures.

CONCLUSION

The source of the difference between the perspective of the originalarticle by Don Chance and that of this comment is that different method-ologies are being applied to determine the size of the hedge. I propose amethod for sizing a eurodollar futures hedge that equates the dollar valuesof the basis points for the hedged item and the futures position, respec-tively; and I show that with such a hedge construction, hedgers shouldrealize perfect hedging results. Professor Chance demonstrates imperfecthedge results in his analysis, and he attributes the seemingly deficientoutcomes to flaws in the design of the futures contracts. I believe the faultlies with the methodology for sizing the hedge positions. With an appro-priately sized hedge, there should be no surprises.

BIBLIOGRAPHY

Chance, D. M. (2006). A hedging deficiency in eurodollar futures. Journal ofFutures Markets, 26(2), 186207.

Kawaller, I. G. (1992). Choosing the best interest rate hedge ratio. FinancialAnalysts Journal, 48(5), 7477.

Kawaller, I. G. (1994). Comparing eurodollar strips to interest rate swaps.Journal of Derivatives, 2, 6779.

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