Replicating Interest Rate Swaps with Eurodollar Strips - MemoFin.fr

INTEREST RATESReplicating Interest Rate Swapswith Eurodollar StripsMAY 16, 2013John W. Labuszewski David Boberski Daniel GrombacherManaging Director Managing Director Senior DirectorResearch & Product Development312-466-7469jlab@cmegroup.comResearch & Product Development212-299-2542david.boberski@cmegroup.comResearch & Product Development312-634-1583Daniel.grombacher@cmegroup.com

eceiver) is generally referred to simply as the“payer” while the fixed rate receiver (floating ratepayer) may be referred to simply as the “receiver.”Interest Rate Swap (IRS)For example, one may swap a quarterly paymentbased upon a specified fixed rate of interest, such as1%, applied to a principal value of $10 million forthe next 5 years; for a quarterly payment basedupon 3-month LIBOR rates applied to a principalvalue of $10 million for the next 5 years. Theseperiodic fixed vs. floating rate payments are typicallynetted such that only the net amount due is passedbetween payer and receiver.Clearly, the fixed rate payer hopes that floatingrates rise such that his future receipts are increased.The floating rate payer, or fixed rate receiver, hopesthat floating rates decline such that his futurepayments are diminished.ED Volume (Mill Cnts)FixedRatePayer1,0009008007006005004003002001000FixedPaymentsFloatingPaymentsEurodollar & IRS Growth1981198319851987198919911993199519971999200120032005200720092011EurodollarsDealerFixedPaymentsFloatingPaymentsIRSFixedRateReceiver$450$400$350$300$250$200$150$100$50The seminal interest rate swap transaction wasconcluded in 1980 while Eurodollar futures wereoriginally introduced in 1981. Since that time the$0Outstanding IRS (Trillions)IRS market has grown to some $379.4 trillion inoutstanding notional value as of June 2012. 1Volume in CME Eurodollar products have grown on astrikingly parallel path along with over-the-counterswaps. This underscores the fact that Eurodollarfutures and inextricably intertwined with the IRSmarket as a source for pricing and a tool to hedgethe risks associated with swaps. In particular, banksand broker-dealers making a market in over-thecounter(OTC) swaps represent primary Eurodollarmarket participants.BBA LIBOR SwapThe British Banker’s Association (BBA) LIBOR fixingsrepresent a benchmark against which many interestrate products including CME Eurodollar futures andinterest rate swaps routinely are pegged. Becauseof this focus on the BBA LIBOR fixing rate and theliquidity associated with Eurodollar futures, aparticular type of IRS – a “BBA LIBOR Swap” – isfrequently traded in the over-the-counter (OTC)markets.A BBA LIBOR Swap may be constructed to referencethe 3-month BBA LIBOR fixing as the basis for thefloating rate payments, frequently on the samedates as standard CME Eurodollar futures are settled(so-called “IMM dates”).As such, there is a closely compatible relationshipbetween BBA LIBOR Swaps and CME Eurodollarfutures that facilitates use of futures as a referencefor pricing, and a tool for hedging, swaps. Further,this implies that futures may be used as a proxy tomimic the performance of a BBA LIBOR Swap, albeitwith some qualifications. 21 As reported by the Bank of International Settlements(BIS) in its semi-annual survey of the over-the-counter(OTC) derivatives marketplace.2 Note that, unlike OTC swaps, CME Eurodollar futures donot exhibit convexity, or a non-linear relationshipbetween price and yield. Rather, futures exhibit a linearrelationship such that a one basis point (0.01%) changein yield uniformly represents a monetary change of$25.00 in the value of a single futures contract. Thislack of convexity implies that one must adjust one’sEurodollar position periodically in order to achieve asimilar effect.3 Replicating IRS with Eurodollar Strips | May 16, 2013 | © CME GROUP

Pricing SwapsInterest rate swaps are typically quoted (on anopening basis) by reference to the fixed rate ofinterest. That fixed rate is calculated as the ratethat renders equivalent the present value of theanticipated periodic fixed rate payments (PV fixed );with the present value of the anticipated periodicfloating rate payments (PV floating ).Those floating rate payments may be estimated byexamining the shape of the yield curve, or morepractically, by referencing the rates associated withEurodollar futures prices which reflect the shape ofthe curve.PV Fixed = PV FloatingWhen an IRS is transacted such that the presentvalue of the estimated floating rate payments equalsthe present value of the fixed rate payments, nomonetary consideration is passed on the basis ofthis initial transaction. This is also referred to as a“par swap.” In other words, the “non-par payment”(NPP) is set at zero ($0).NPP = 0 = PV Floating − PV FixedThe fixed rate (R fixed ) associated with a swap may becalculated by reference to the following formula.R fixed = 4 ∙ ∑ni=1PV i ∙ R i ∙ days i∑ni=1PV i360 Where PV i = present value discounting factor; R i =rate associated with each successively deferredperiod; days i = number of days in each successivelydeferred period. Note that those rates may bedetermined by reference to Eurodollar futurespricing.For example, find the value of a 2-year swap wherethe floating rate is estimated by reference to theBBA 3-month Eurodollar time deposit rate as ofJanuary 30, 2013. Table 4, found in the appendixbelow, provides details regarding the calculations.The fixed rate of interest associated with the swapmay be calculated as 0.3861%.The present value of the fixed and floating ratepayments given a fixed rate of 0.3861% may becalculated as $76,934.49. The equivalence of thesetwo cash flow streams may be established byreference to Table 5 found in the appendix. As such,this is a par swap that may be transacted with noup-front monetary consideration.R fixed = 4 ∙ 0.9997 ∙ 0.002265 ∙ 47360 + 0.9989 ∙ 0.003000 ∙ 91360 + 0.9981 ∙ 0.003300 ∙ 91360 + 0.9972 ∙ 0.003650 ∙ 91360 + 0.9962 ∙ 0.004050 ∙ 91360 + 0.9950 ∙ 0.004500 ∙ 91360 + 0.9938 ∙ 0.005100 ∙ 91360 + 0.9923 ∙ 0.005800 ∙ 91360 ÷ (0.9997 + 0.9989 + 0.9981 + 0.9972+ 0.9962 + 0.9950 + 0.9938 + 0.9923)= 0.3861%Note that, once transacted, an IRS might be ratherunique to the extent that there are a plethora ofvariables associated with the transaction. Theseinclude features such as the specific floatingreference rate, the periodic reset dates, the dateconventions, etc. Because there are a large numberof variable features associated with an IRS, themarket for swaps is fragmented amongst manyoutstanding swaps with divergent contract termsand conditions.Because the swap market is rather fragmented, bilateralcounterparties who wish to close or retire anoutstanding swap transaction frequently mustnegotiate such a “close-out” or “tear-up” directlywith the original counterparty. These closingtransactions are typically quoted by reference to thenon-par value of the swap at the time of such closeout.For example, interest rates may have advancedsince the original transaction was concluded at aNPP=0. As such, the fixed rate payer is advantagedwhile the floating rate payer is disadvantaged.Thus, the floating rate payer may be required tocompensate the fixed rate payer with a NPP thatreflects the difference between the PV floating andPV fixed per current market conditions.4 Replicating IRS with Eurodollar Strips | May 16, 2013 | © CME GROUP

yields, the difference now becomes PV floating – PV fixed= $9,451.73 - $9,623.57 = -$171.84. This suggeststhat the floating rate payer is exposed to a risk inDecember 2013 that may be quantified with a BPV =$252.08 (=-$423.92 less -$171.84). This furthersuggests that the floating rate payer may hedge thatparticular reset date by selling 10 Dec-13 Eurodollarfutures.HR = $252.08 ÷ $25 = 10.1Similarly, the floating rate payer might sell variousamounts of Eurodollar futures in successivelydeferred months to hedge the risk of rising rates andfalling prices as calculated in Table 7 below.ActionSell 10 Mar-13 futuresSell 10 Jun-13 futuresSell 10 Sep-13 futuresSell 10 Dec-13 futuresSell 10 Mar-14 futuresSell 10 Jun-14 futuresSell 10 Sep-14 futuresTotal 70 ContractsThis hedge is “self-liquidating” in the sense thatevery 3 months as the rate over the subsequent 3-month period is established, the Eurodollar futuressold to hedge that specific risk are cash-settled.However, this does not imply that the hedgerequires no maintenance.ConvexityThe BPV associated with Eurodollar futures isunchanging at $25/contract. However, like couponbearing fixed income instruments, swaps experience“convexity.” For example, the responsiveness or BPVof the swap’s value fluctuates as yields rise and fall.Convexity generally increases as a function of thetenor of the swap.Thus, it is advisable periodically to quantify the swapstructure and determine if the recommended hedgestructure might have changed as a function offluctuating rates and swap convexity. 4Margins per Dodd-FrankThe Dodd-Frank Wall Street Reform and ConsumerProduction Act was endorsed by President Obama onJuly 21, 2010 (“Dodd-Frank bill” or “the Bill”). TheBill enacts sweeping reforms affecting the over-thecounter(“OTC”) derivatives markets and reversesthe portion of the Commodity Futures ModernizationAct (“CFMA”) of 2000 that had largely exemptedOTC derivatives from significant regulatoryoversight.The broad provisions of the Bill will be supportedand implemented by myriad specific and detailedregulations currently under development by the twoprimary agencies, the Commodity Futures TradingCommission (“CFTC”) and the Securities ExchangeCommission (“SEC”). It remains unclear exactlywhat will eventually emerge as the regulatoryframework per which OTC derivatives will beregulated. But the picture is starting to come moreclearly into focus.On November 8, 2011, the CFTC issued final rulespertaining to the general provisions and coreprinciples of a Derivative Clearing Organization(“DCO”). In particular, these rules stipulate theperformance bond (or “margin”) requirements forfinancial futures, centrally cleared swaps, and swapsthat are not centrally cleared.According to Part 39, Subpart B, Section39.13(2)(ii), which governs risk margin methodologyand coverage, a derivatives clearing organization:“…shall use models that generate initial marginrequirements sufficient to cover the derivatives clearingorganization’s potential future exposures to clearingmembers based on price movements in the intervalbetween the last collection of variation margin and thetime within which the derivatives clearing organizationestimates that it would be able to liquidate a defaultingclearing member’s positions (liquidation time); provided,however, that a derivatives clearing organization shalluse:(A) A minimum liquidation time that is one day for futuresand options;4The convexity associated with a strip of Eurodollarfutures may be assessed using various electroniccalculation tools. Please refer to the “EDS” functionalityon the Bloomberg system. Note CME Group has alsolaunched a new “Eurodollar Futures E-quivalents” toolwhich may be used to identify how one may construct aEurodollar strip in replication of an IRS instrument. Youcan access this tool atwww.cmegroup.com/edequivalents6 Replicating IRS with Eurodollar Strips | May 16, 2013 | © CME GROUP

(B) A minimum liquidation time that is one day for swapson agricultural commodities, energy commodities, andmetals;(C) A minimum liquidation time that is five days for allother swaps; or(D) Such longer liquidation time as is appropriate basedon the specific characteristics of a particular productor portfolio; provided further that the Commission, byorder, may establish shorter or longer liquidationtimes for particular products or portfolios.”In short, under the new rules, market participantsmust post initial performance bonds to cover a onedayliquidation timetable for financial futurestransactions, a 5-day liquidation timetable forcentrally cleared financial swaps, and a 10-dayliquidation timetable for non-centrally clearedfinancial swaps.With respect to non-cleared financial swaps, the 10-day liquidation timetable is only proposed. Theserules will mandate that previously uncleared,bilaterally executed, plain-vanilla financial swaps becleared by a qualified central counterparty (“QCCP”)and become subject to a 5-day liquidation timetable.Margin requirements for standardized, liquid futurescontracts, such as Eurodollars, will generally be lessonerous than margins required for an analogousposition in a cleared, plain vanilla interest rate swap.This is intuitive to the extent that IRS instrumentsare customized transactions which typically cannotbe liquidated in times of market stress with equalfacility to futures.For example, the margin requirements for astructured 5-year Eurodollar futures strip thatmimics a 5-year IRS results in 50% margin savings.The margin on a 10-year structured Eurodollarfutures strip is estimated at 42% less than that of acomparable 10-year IRS.Concluding NoteBusiness practices in the OTC derivatives andexchange traded futures markets are converging ina process often referred to as “futurization.” Asevidence, consider that the Dodd-Frank financialreform bill mandated centralized counterpartyclearing of standardized IRS instruments.Similarly, Eurodollar futures may be utilized to priceand hedge and, to a degree, replicate theperformance of IRS instruments. But futures offersignificant capital efficiencies vis-à-vis comparablecleared over-the-counter IRS instruments.To learn more about this product, visitwww.cmegroup.com/eurodollar.Estimated Margin Requirementsas % of Notional Value(As of December 2012)TenorCleared Equivalent MarginIRS ED Strip Savings2-Year 0.420% 0.255% 39%5-Year 1.580% 0.795% 50%10-Year 3.250% 1.895% 42%For example, the margin requirements for astructured 2-year Eurodollar futures strip thatmimics a 2-year interest rate swap may beestimated as of December 2012 as 0.255% ofnotional value. By contrast, the marginrequirements associated with a cleared 2-yearinterest rate swap are estimated at 0.420%. Thus,one may use Eurodollar strips to replicate a riskexposure that is similar to an IRS instrument with39% margin savings.7 Replicating IRS with Eurodollar Strips | May 16, 2013 | © CME GROUP

Table 1: Find Value of Strip(As of 1/30/13)InstrumentExpirationDayCompoundDaysPrice Rate (R)DateSpanValue (CV)Strip YieldStub Investment 47 0.2265% 1.0003 0.226%Mar-13 Eurodollars 3/18/13 47 91 99.7000 0.3000% 1.0011 0.275%Jun-13 Eurodollars 6/17/13 138 91 99.6700 0.3300% 1.0019 0.297%Sep-13 Eurodollars 9/16/13 229 91 99.6350 0.3650% 1.0028 0.317%Dec-13 Eurodollars 12/16/13 320 91 99.5950 0.4050% 1.0038 0.336%Mar-14 Eurodollars 3/17/14 411 91 99.5500 0.4500% 1.0050 0.357%Jun-14 Eurodollars 6/16/14 502 91 99.4900 0.5100% 1.0063 0.381%Sep-14 Eurodollars 9/15/14 593 91 99.4200 0.5800% 1.0078 0.408%12/15/14 684Table 2: Find Swap Value(As of 1/30/13)InstrumentExpirationDateDaysDaySpanPriceRate (R)CompoundValue (CV)DiscountFactor (PV)(= 1/CV)Stub Investment 47 0.2265% 1.0003 0.9997Mar-13 Eurodollars 3/18/13 47 91 99.7000 0.3000% 1.0011 0.9989Jun-13 Eurodollars 6/17/13 138 91 99.6700 0.3300% 1.0019 0.9981Sep-13 Eurodollars 9/16/13 229 91 99.6350 0.3650% 1.0028 0.9972Dec-13 Eurodollars 12/16/13 320 91 99.5950 0.4050% 1.0038 0.9962Mar-14 Eurodollars 3/17/14 411 91 99.5500 0.4500% 1.0050 0.9950Jun-14 Eurodollars 6/16/14 502 91 99.4900 0.5100% 1.0063 0.9938Sep-14 Eurodollars 9/15/14 593 91 99.4200 0.5800% 1.0078 0.992312/15/14 6848 Replicating IRS with Eurodollar Strips | May 16, 2013 | © CME GROUP

Table 3: Confirm Par Value(As of 1/30/13)PaymentDateFixedPaymentsDiscountFactorPV of FixedPaymentsFloatingPaymentsDiscountFactorPV ofFloatingPayments3/18/13 $9,651.50 0.9997 $9,648.65 $2,957.08 0.9997 $2,956.216/17/13 $9,651.50 0.9989 $9,641.34 $7,583.33 0.9989 $7,575.359/16/13 $9,651.50 0.9981 $9,633.30 $8,341.67 0.9981 $8,325.9412/16/13 $9,651.50 0.9972 $9,624.42 $9,226.39 0.9972 $9,200.503/17/14 $9,651.50 0.9962 $9,614.58 $10,237.50 0.9962 $10,198.346/16/14 $9,651.50 0.9950 $9,603.66 $11,375.00 0.9950 $11,318.619/15/14 $9,651.50 0.9938 $9,591.29 $12,891.67 0.9938 $12,811.2412/15/14 $9,651.50 0.9923 $9,577.25 $14,661.11 0.9923 $14,548.32$76,934.49 $76,934.49Table 4: Find BPV of Swap(As of 1/30/13)PaymentDateFixedPaymentsDiscountFactorPV of FixedPaymentsFloatingPaymentsDiscountFactorPV ofFloatingPayments3/18/13 $9,651.50 0.9997 $9,648.52 $2,957.08 0.9997 $2,956.176/17/13 $9,651.50 0.9989 $9,640.97 $7,836.11 0.9989 $7,827.569/16/13 $9,651.50 0.9981 $9,632.69 $8,594.44 0.9981 $8,577.6912/16/13 $9,651.50 0.9971 $9,623.57 $9,479.17 0.9971 $9,451.733/17/14 $9,651.50 0.9961 $9,613.48 $10,490.28 0.9961 $10,448.956/16/14 $9,651.50 0.9949 $9,602.32 $11,627.78 0.9949 $11,568.529/15/14 $9,651.50 0.9936 $9,589.71 $13,144.44 0.9936 $13,060.2912/15/14 $9,651.50 0.9921 $9,575.43 $14,913.89 0.9921 $14,796.34$76,926.70 $78,687.269 Replicating IRS with Eurodollar Strips | May 16, 2013 | © CME GROUP