Hedging Oct1984

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Hedging Interest Rate Risk withFinancial Futures: Some Basic

Principles Michael T. Belongia and G. J. Santoni

011 much of the postwar period, stable rates of inflation accompanied by stable levels of interestrates created a comforting economic environmentfor managers of depositon institutions. Beginning inthe mid-1970s, however-, mot-e var-iable interest rates,br-ought about in part liv more vat-iable inflation, causeda substantial change in the economic conditions facingdeposito~ institutions. Offering long-ter-m ct-edit atfixed rates became tiskiet as lar-ger and mor-e h-equentunexpected changes in interest r-ates introduced morevar-iation into the mat-ket value of these assets. t

This article describes how variation in intetest ratesaffects the market value of depository institutions. Thediscussion then demonstrates how financial futurescontracts might be used to hedge some of the interestrate risk of a portfolio composed of interest-sensitivedeposit accounts and loans of unmatched maturities.Although some regulatory authorities have denied orstrictly regulated the use of futures contracts by de -

Michael T. Belongia is an economist and0. J. Santoni is a senioreconomistat the FederalReserve Bank of St. Louis. John 0. Schulte providedresearch assistance.For a general descriptionof events that have introduced or in -creased interest raterisk,see Carringtonand Hertzberg (1984)andKoch, ofal. (1982).

positomy institutions in the belief that futures tradingis risky and unduly speculative, we argue that the judicious use of futures can reduce the firms expo -sur-e to interest i-ate fluctuations.2

DURATION GAP AND INTEREST BATE

RISKIn the mid-1970s, when lat-ge fluctuations in interest

rates began to occur-, it became increasingly evidentthat depository institutions needed some measure of the relative risks associated with various portfolioholdings. One appreach to the measur-ement of inter -est rate risk is called Duration Gap analysis. Dura -tion refers to the aver-age life of some group of assets or liabilities. Gap refers to the differencebetween the durations of an institutions assets and itsliabilities.

Legalrestrictionsand guidelineson the use of financialfutures bydifferenttypes offinancial institutionsare summarized in Lower(1982).A comparison of statuteson the useof futures by insurancecompaniesis made in Gottlieb (1984).

Formore detaileddiscussions of duration analysisand its applica-tion tofinancialinstitution portfolios, see Kaufman(1984): Bierwag,Kaufmanand Toevs(1983):Toevs (1983); Santoni (1984):Samuel-son (1944);and Hicks (1939),pp. 18488.

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FEDERAL REMRVI SANK OP ST. LOUIS OCTOBER IS

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V~ V\~ ~ ~ ~ An Example the fit rn for empioving its specialized capital rn inter

- - mcdiatrng het%%een borrowers and lenders.ttte t isk introduced into a portfolio of assets and

liabilities of different dur atron is illustr-ated in tables 1 The amount that the firm will owe in thr ee month,and 2 In this example, fot exposrttonal simplicity, the time is $926.75 { = $909.0911.OSi I, which it plansfirms planned life is assumed to bc only one year. It pay liv borrowing this amount for another- 90 dasshas xtended a loan with a face value of 51.000 to be Because the firms proceeds from the new loan andrepaid in a single payment at the end ofthe veat at an payment ofthe old loan cancel, its net r-cceipts at thinterest rate of 10 percent. The present value of the time are zero. The firm anticipate being able to toloan, and, thus the amount paid out by the firm to the the loan ovcr every 90 days at the same interest ratehorr o~ver, is S91J9.09. I 0 finance this loan, the firm Consequently, at the end of 180 days, the finn xpectsborrot~ s s909.09 for 90 days at S per cent inter est. The to owe $944.76 ( S926.75(1.OSl -I, which it plans to patwo percentage-point spread is the return eat-ncd by with new borrowings. At the end oftheyeat, the fun

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FEDERAL RESERVE SANK OF ST. LOUIS OCTOBER 1984

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anticipates having to pay 981.82 ~909.09 >< 1.081.This amount will he paid out of the SI 000 proceedsfi-om its matured asset. The hrm s expected net receipt

at ear-end is $18.18, as shown in pancl A of table I.

Panel A of tablc 2 is a balance sheet summary of thepresent value of this rnvestment plan. The presentalue of the expected net receipt at year end is Sib 53

and is equal to the differ ence betwcen the pr escnt~alu of the asset S909.09 SI 000/1 101 and thepresent value of the expected liahilits 892.56 I S981.82/1.10I. Both futurc ~alues ate discounted at10 pen-tnt the firms opportunity cost.

TI is packagc of assets and Irahilitie is subject toconsider able inter est rate risk because the 10 percentnterest rate on the firm~ loan is fixed for one \cai

nhile its borrowing must be refunded e~en 40 dais.In this example, the gap between the durations of the

asset and liability is 270 days I= 360 90).~ As apractical matter, the assets longer- duration impliesthat a given change in interest rates will change thepresent value of the asset more than it will affect thepresent value of the liability. This differ-ence, of course,will change the value of the firms equity.

Panel B of table I shows the effect of an unexpected

200 basis-point rise in interest rates. The increaser-aises the firms anticipated refunding costs. As aresult, the amount the firm expects to pay at year-endincreases to $995.42. Net r-eceipts fall to $4.58 and thepresent value of the investment plan falls to $4.09.

panel B of table 2 pt-esents a balance sheet summarof the effect of the change on the present values of theasset, liability and owner equity. The increase ininterest rates reduces the present values of both theasset and liability, but the asset value falls by r-elativelymore because its life is fixed for one year, while theliability must be rolled over in 90 days at a higherinterest rate. The increase in interest rates causesowner equity to fall by $12.44, or about 75 percent. Inconti-ast, had the interest rate declined by 200 basispoints, the net present value of the firms equity wouldhaverisen to $29.49 Isee panel C of table 1), an increaseof about 78 percent.

This extreme volatility in the finns equitx is due tothe mismatch of the durations of the asset and liabilitythat rnake up the firms portfolio. Table 3 illustratesthis point. The only diffetence between this and ear -lier- examples is that, in table 3, the duration of theliability has been lengthened to match the duration of the asset. While a 200 basis-point increase in theinterest i-ate still causes the present value of theportfolio to fall, the change, $0.30 or 1.8 percent, ismuch less than before. Clearly, matching the dura -tions of the asset and liability exposes the value of theportfolio to much lower interest rate risk.

COPING WITH THE GAP

Depositor~ institutions, particularly savings andloan associations, maintain portfolios of assets andliabilities that are similar- to the one shown in theinitial example. That is, the duration of their assets

The durations ofsingle-payment financialinstruments are equal tothe maturitiesof the instruments. Inother cases, calculation ofdurationis notas straightforward.See footnote3.

Savingsand loan associations are required to maintaina significantshare of their portfoliosin long-term homemortgages in order toobtainfederal insurance of deposits.See FederalHomeLoan BankActof 1932, sec. 4(a).

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FEDERAL RESERVE BANK OF ST. LOUIS OCTOBER 1984

typically is longer than the duration of their liabilities.As a result, the market values of these institutions havebeen particularly sensitive to interest i-ate fluctua -tions. This, along with the recent experience of highlyvariable interest rates, has led these institutions toseek out methods to reduce their exposure to interestrate risk. Among other things, these firms have madegreater use of floating rate loans and interest rate swapagreements. Recent regulatory changes have allowedthem to allocate more of their loan portfolios to short-term consumerloans. In addition, a number of institu -tions are using financial futures to reduce their expo -sure to interest rate risk.

See Booth, Smith and Stolz (1984).while a number of financialtirms are employingthe futures market, it seems that accountingrequirementshave discouragedthe useof futures to hedge interestrate risk. Until recently, regulators and accountants feared thatlosses fromfutures transactionscouldbe hiddenin financialreports.Therefore,they wouldnotpermita hedge to countas one transac -tion with spot gains or losses offsettingfutures markets losses orgains. Instead, theyrequired futures losses to be marked tothemarketwhilespot gains couldbe deferred. This asymmetric treat-ment of gains and losses on the two sides ofa hedge distortedearningsestimates and, therefore,discouragedthe use oftutures.

Futures Markets and Risk

It may seem odd that the futures market, which isgenerally thought of as being very risky, can be used toreduce risk. Futures tr-ading is risky for people who beton the future price movements of particular commod -ities or- financial instruments by taking long or- shortpositions in futures contracts. Such speculative betson future price movements, however, are not uniqueto futures market trading. The nature of most types of businesses requires a speculative bet about the futurecourse of a pat-ticular price.

Growing crops, for example, gives farmers longpositions in physical commodities during the growingseason. These long positions expose the farmer to therisk of price declines declines that can reduce theprofits from efficient farming (the activity that thefarmer specializes ml. Judicious use of the futuresmarket allows the farmer- to offset his long position inthe commodity by selling futures contracts. Since thesale reduces his net holdings of the commodity, thefarmers exposure to the risk offuture price declines isreduced. Similarly, futures trading presents deposi -tory institutions with the opportunity to i-educe theirexposure to the risk of interest rate changes.

Futures Contracts

A futures contract is an agreement between a sellerand a buyer to trade some well-defined item wheat,corn, Treasury bills) at some specified future date at a

price agreed upon now but paid in the future at thetime of delivery. The futures price is a pr-edictionabout what the price of the item will he at the time of delivery.

In the case of commodities, the price of the goodtoday (the spot price), on average, will be equal to thefutures price minus the cost of storage, insur-ance andforegone interest associated with holding the goodover the interval of the contract. A similar relationshipexists between the spot and futures pr-ices of financialinstruments. However, since the storage and insur -ance cost of holding these instruments is very low, the

spread between the spot and futures prices is largelydetermined by the interest cost.

See Morris(1984) for more detailon changes in accounting stan-dards. Asay, etal. (1981) provideexamples of how formeraccounting standards discouragedthe use offutures by banks and thrifinstitutions.

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FEDERAL RESERVE BANK F ST. LOUIS OCTOBER 1984

The Relationship Between Spot and Futures Markets for Treasury Bills: An Illustration

In January 1976, the International Monetary Market(1MM), now part of the Chicago Mer-cantile Exchange)CME), began tr-ading futures contracts in 13-week

Treasury hills! The basic contract is for $1 million withcontracts matur-ing once each quarter in the thirdweek of Mar-ch, June., September and December. Sincether-e at-c eight conti-acts outstanding, the most distantdelivery date varies between 21 and 24 months into theftrture.

Panel A of table 4 presents quotations for- Treasurybill futures for the trading day of August 7, 1984. PanelB of table 4 lists spot quotations for Tr-easurv bills forthe same trading day.

Panel A of table 4 is interpreted as follows: Septem -ber Treasury bill futures were trading at a discount of 10.49 per-cent on August 7, 1984. Any person tradingthis contract obtained the right to buy lselll a Treasurybill the third week in September with a remainingmaturity of 13 weeks at a discount rate of 10.49percent. A similar- statement holds fur the other con -tracts listed in panel A.

Panel B lists spot market quotations. For- example,Treasury bills due to mature August 9, 1984, traded at adiscount of 9.91 percent Ibidl to 9.79 percent laskl,while those maturing September 20, 1984, tr-aded at adiscount of 9.95 bid) to 9.91 ask), etc.

We noted earlier- that the spot and futures mat-ketsmust he closely related, and the data in panels A and Bcan he used to illustrate this point. lor- example, onAugust 7, 1984, an investor could purchase aTr-easurvbill due to mature December 20, 1984 i.e., 134 dayslater). Ifhe put-chases the bill on the spot mat-ket, heobtains the asked discount of 10.39 percent. At thisdiscount rate, the price he pays for the bill is $96.41 per$100 of face value!

Futures contracts in other types offinancialinstruments, such asGNMA passthroughcertificatecontracts, 90-dayCDs, Treasurybonds and Treasury notes, also are availableat the ChicagoBoardof Trade.

The informationin table 3 is taken from pages 38 and 39 of theAugust8, 1984, Wall Street Journal. The actual tables in the Wall Street Journalcontain more informationthan ispresented here, Forour purposes, however,the additionalinformationis extraneous.

$96.41 $l00/(1.1039). The discount factor is raised to thepowerof134/360 = .37.Thiscalculationis slightlydifferentfrom thediscountcalculationused in determiningactualtrading prices, but

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Alternatnvely the investor could put-chase a futurescontract that gives him the right to buy a I reasurv billin September that will mature the third week inDecember. I his alternative gives him a discount rate of 10.49 percent. Buying the treasurybill in September atthis discount would require a payment of S97.54. thispayment will be made 43 days into the future roughlySeptcmber 20 and the prescnt value of the paymenton ~ugust 7 is $96 44. Notice that this is vcry near theamount that the investor would pay ($96.41) if he wereto purchase a It easurv bill on the spot market thatmatured during the third week of IJecember -

Of course other ,tlternati es are open to the imixestoras wull. He could for example, buy a lreasury bill thatmaturcd the third week in March on the spot market.

numertcaldrfferences between the two formulas are small. SeeStigum(1981)forthe markets discount formula.$9754 = $100!(11049)2.

$9644 $97.54/(1 .0991) The rnterest rateused inthe calcula-tion is the rate on August7 fora security maturingon September20(43 days in the future)

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FEDERAL RESERVE DANKOP ST. LOUIS OCTOSER 196

The present cost of doing this should be near thepresent cost of buying a futures contract that allowshim to purchase a Treasury bill in December- maturingthe third week in March. Table 5 uses the data in table4 to compare the present costs of this and otheialternatives. In each case, the present costs of employ -ing the spot vs. the futures market are very close.

Because a close relationship between these marketsexists, the Treasury bill futures market can be usedeffectively to hedge interest rate risk-

HEDGING THE GAP

The Streams of Receipts and Payments

The example in table I can be used to illustrate howfutures contracts can be applied to hedge the interestrate risk caused by the mismatch in the lives (dura -tions) of the firms assets and liabilities. Considerableconfusion appears to exist as to what the finns hedg -

ing objective should be and how hedges should beconstructed. One possible hedging strategy is to pro -tect the equity of the firm (in the present value sense)fi-om interest rate fluctuations. Another often-citedstrategy is to minimize discrepancies between cashflows over time. It seems clear, however, that firmowners will choose a hedge that piotects their netwealth (present value of the firms equity). This focuson net wealth is crucial because, as the examplesshow, reducing cash flow mismatches to zero doesnot minimize the exposure of the firms equity tointerest rate changes.

Hedging zvet Wealth: An Example

Suppose it is September 15, 1984, and the firminitiates the transactions summarized earlier in panelA of table 1. In addition, to hedge each of its thieerefunding requirements, the firm sells December,March and June futures contracts at 10 percent dis -counts.The price of each contract is $1,000/(1.10) =

Smalldifferences aredue to the existenceof transactioncosts. If thedifferences were large, profitable arbitrage opportunities wouldexist. These, of course, would vanish quickly as traders tookadvantage ofthe situation.

There is, of course, the problem that the spot instrument beinghedged may notbe identical tothe futures market instrument. If so,the priceofone may divergefrom theother because ofa change in afactorthat affects the priceof one but not the other.This is calledbasis riskand is ignoredin the followingexamples.

4A flatyieldcurve is assumed for ease of exposition. Theexamplesbecome more complicatedifthe yieldcurveslopes up or downand/or the spread between borrowingand lending rates changes.

Table 5

The Relationship Between Treasury BillSpot and Futures Prices: August 7,1984, Per $100 of Face Value

Case 1: Purchase of a I roasuryhrllthat matures the thruweekin December1984

.,976.I.5 Ihese rrrnlruvts rrhligatr clii fir-rn jr rIeIieif3~uekI r-rasun bill,ajlh a I,rrp~afrrprrf si rrrrodirrir~tire third ~~rc-krn Derenihrr \larr-h and mini-e\PIiuiiMr for sri r;

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FEDERAL RESIRVE BAtIKCFIT. LOUIS OCTOBER 196

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the finns September 15 tnansactions. As in panel B of table 1, the increase in interest i-ates raises the firmsrefunding cost and reduces the net year-end receipt to$4.58. In addition, however-, the increase in interestrates reduces the expected cost of acquiring the Trea -sury bill to $972.07. Since the firm will receive $976.45upon delivery of the Treasury bills, the futures con -

tract will generate a net flow of receipts equal to $4.38in December, Majch and June. The present value of this flow added to the present value of the net receiptat year-end $4581 is $16.50, which is nearly identicalto the present value for the case in which interest ratesremained unchanged the small difference is due torounding errors I -

Panel C illustrates the outcome for a 200 basis-pointdecline in interest rates. In this case, the futurescontract generates negative net receipts for the firm inDecember, March and June. The present value of thisnegative flow added to the present value of the higherpositive net receipt at year-end sum to $16.52. As theexamples show, this hedge protects the net wealth of the finn regardless of the direction of the change ininterest rates.

While this hedge protects net wealth from changesin interest rates, it does so by allowing net cashreceipts to vary. Net cash receipts, both in amount andtiming, are considerably different in panels A, B and C.In panel A, net receipts are $18.18 at year-end while inpanel B net receipts are spread out over the year andtotal only $17.72. In panel C, the firm has negative netreceipts during the year and a large positive netreceipt at year--end for a total of $18.38. However, thepresent value of the finn is the same in all three cases.

The Balance Sheet

Panel A of table 7 presents the firms balance sheetposition in terms of present values. The futures con -tracts are entered as both assets and liabilities, leavingequity the same as that shown in panel A of table 2.The futures asset is the present value of the futurereceipt of a fixed amount. The futures liability, on theother hand, is the present value of the expected cost of covering the futures contract given the structure of

interest rates on September 15. Panels B and C illus -

Strictlyspeaking,futurescontracts entered intoby memberbanks ofthe Federal Reserve System are treated as balance sheet memo-randa items. These are reportedon Schedule L,Commitments andContingencies, ofthe Call Report. Hence, foraccountingpurposes,futures contracts do not affect theassets and liabilitiesof the firmuntilthe contracts are exercised.

tn-ate the effect on the present values of the firmassets, liabilities and equity iii immediately followingthe above transactions, interest rates n-ise unexpectedly panel B) or fall unexpectedly panel Cl by 20basis points.

An unexpected increase in interest rates causes tirpresent value of the loan to fall relative to the presentvalue of the liability. By itself this would causereduction in the firms equity. At the same timehowever, the increase in interest rates genenatespositive expected net cash flow from the futurescontracts, which, of course, has a positive net presentvalue. Other things the same, this causes equity to riseThe net effect of both changes is that equity remainsunchanged. The reverse occurs if interest rates decline by 200 basis points.

This hedge has eliminated the fin-ms exposureinterest rate risk. In contrast, recall that a 200 basis-point change in the interest rate causes the equity

the unhedged firm in table 2 to change by aboutpercent.

Hedging as a Profit Center

The purpose of hedging is to reduce the variancea firm owners wealth. In a textbook example of perfect hedge, the gain or loss from a short position ithe futunes market will offset exactly the compensating loss or gain on the spot assets and liabilities heldby the fiim. A hedge is constructed because in thpnesence of an uncertain future wealth is greaterthe institution foregoes a profit stream that is higheron average Iif it goes unhedgedl in exchange forprofit stream that is lower on average f by the costthe hedging openations I but more certain.

Some portfolio managers, however, lose sight of thifact and assume speculative positions in the futuresmarket with the objective of earning profits from thposition if interest rates change in their favor. Whilespeculative positions in futures or spot instrumentslcan increase earnings, they can have the oppositeeffect as well.

One potentially significant danger in the usefutures conti-acts to hedge interest rate risk is that thefirm may misunderstand the natui-e of the hedgingfunction. Trading futures for hedging is not intendedto generate profits from the trading itself. Rather, ipurpose is to establish futures positions so that theowners wealth is held constant; this will occur if thincrease Idecreasel in the value of the firms spotholdings of assets and liabilities is offset exactly by thloss lgainl in the futures market.

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FEDIRAI.RUIRYE BANK OF ST. LOUIS OCTOBER 19

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FEOIRAL RESERVE BAtIK OF ST. LOUIS OCTOSER 199

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Lower, RobertC. Futures Trading and Financial Institutions: The Regulatoiy Environment (Chicago Mercantile Exchange,1982).

Morris. John. FASB Issues Rules for Futures Accounting,American Banker (August24, 1984).

Olson. RonaldL.and DonaldG. Simonson. Gap Managementand MarketRate Sensitivityin Banks, Journal ot Bank Re- search (Spring1982),pp. 53SB.

Samuelson, P. A. The Effectof Interest RateIncreases on theBankingSystem, American Economic Review (March 1944).pp. 1627.

Santoni, G. J. Interest Rate Risk and the Stock Prices ofFinancialInstitutions,thisReview (August/September1984).

Simonson,DonaldG.,and George H. Hempel. ImprovingGapManagement for Controlling InterestRate Risk, Journal ot Bank Research (Summer 1982). pp.10915.

Stigum,Marcia. Money Market Calculations: Yields, Break-Evens and Arbitrage (DowJones-Irwin,1981).

Toevs,Alden.GapManagement: Managing InterestRate RiskinBanks and Thrifts,FederalReserve Bank ofSan FranciscoEconomic Review (Spring1983), pp. 2035.

Wardrep, BruceN. and James F. Buch. TheEfficacy ofHedg-ingwithFinancial Futures:AHistorical Perspective,Journal of Futures Markets (Fall 1982),pp. 24354.

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Hedging Oct1984

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