Hedging Interest Rate Risk withFinancial Futures: Some BasicPrinciplesMichael T. Belongia and G. J. Santoni

011 much of the postwar period, stable rates ofinflation — 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 facing

deposito~ 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 and 0. J. Santoni is a senioreconomist at the Federal Reserve Bank of St. Louis. John 0. Schulteprovided research assistance.‘For a general description of events that have introduced or in-creased interest rate risk, see Carrington and Hertzberg (1984) andKoch, of al. (1982).

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

DURATION GAP AND INTEREST BATERISK

In the mid-1970s, when lat-ge fluctuations in interestrates began to occur-, it became increasingly evidentthat depository institutions needed some measure ofthe relative risks associated with various portfolio

holdings. 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 ofassets or liabilities. “Gap” refers to the differencebetween the durations of an institution’s assets and itsliabilities.’

‘Legal restrictions and guidelines on the use of financial futures bydifferent types of financial institutions are summarized in Lower(1982). A comparison of statutes on the use of futures by insurancecompanies is made in Gottlieb (1984).

‘For more detailed discussions of duration analysis and its applica-tion to financial institution portfolios, see Kaufman (1984): Bierwag,Kaufman and Toevs (1983): Toevs (1983); Santoni (1984): Samuel-son (1944); and Hicks (1939), pp. 184—88.

15

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 duratron 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 plans tofirms planned life is assumed to bc only one year. It pay liv borrowing this amount for another- 90 dass.has xtended a loan with a face value of 51.000 to be Because the firm’s proceeds from the new loan and itsrepaid in a single payment at the end ofthe veat at an payment ofthe old loan cancel, its net r-cceipts at thisinterest rate of 10 percent. The present value of the time are zero. The firm anticipate being able to toll

loan, and, thus the amount paid out by the firm to the the loan ovcr every 90 days at the same interest rate.horr 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 paytwo percentage-point spread is the return eat-ncd by with new borrowings. At the end oftheyeat, the fun

16

FEDERAL RESERVE SANK OF ST. LOUIS OCTOBER 1984

/

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 difference betwcen the pr escnt~alu of the asset S909.09 SI 000/1 101 and the

present 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~en40 dais.In this example, the gap between the durations of the

asset and liability is 270 days I = 360 — 90).~As apractical matter, the asset’s 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 firm’s equity.

Panel B of table I shows the effect of an unexpected200 basis-point rise in interest rates. The increaser-aises the firm’s 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 abalance sheet summarof the effect of the change on the present values of theasset, liability and owner equity. The increase in

interest 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 higher

interest 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 ofthe firm’s equity wouldhave risen to $29.49 Isee panel C of table 1), an increaseof about 78 percent.

This extreme volatility in the fin’ns equitx’ is due tothe mismatch of the durations of the asset and liabilitythat r’nake up the firm’s 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 ofthe 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 of single-payment financial instruments are equal tothe maturities of the instruments. In other cases, calculation ofduration is not as straightforward. See footnote 3.

‘Savings and loan associations are required to maintain a significantshare of their portfolios in long-term home mortgages in order toobtain federal insurance of deposits. See Federal Home Loan BankAct of 1932, sec. 4(a).

17

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 to

seek out methods to reduce their exposure to interestrate risk. Among other things, these firms have madegreater use of floating rate loans and interest rate swap

agreements. Recent regulatory changes have allowedthem to allocate more of their loan portfolios to short-term consumerloans. In addition, a number ofinstitu-

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 employing the futures market, it seems that accountingrequirements have discouraged the use of futures to hedge interestrate risk. Until recently, regulators and accountants feared thatlosses from futures transactions could be hidden in financial reports.Therefore, they would not permit a hedge to count as one transac-tion with spot gains or losses offsetting futures markets losses orgains. Instead, they required futures losses to be marked to themarket while spot gains could be deferred. This asymmetric treat-ment of gains and losses on the two sides of a hedge distortedearnings estimates and, therefore, discouraged the use of tutures.

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- short

positions in futures contracts. Such speculative betson future price movements, however, are not uniqueto futures market trading. The nature of most types ofbusinesses requires a speculative bet about the futurecourse of a pat-ticular price.

Growing crops, for example, gives farmers long

positions 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, thefarmer’s 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 aprice 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 ofdelivery.

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, thespread between the spot and futures prices is largely

determined by the interest cost.

See Morris (1984) for more detail on changes in accounting stan-dards. Asay, et al. (1981) provide examples of how former account-ing standards discouraged the use of futures by banks and thriffinstitutions.

18

FEDERAL RESERVE BANK øF ST. LOUIS OCTOBER 1984

The Relationship Between Spot andFutures Markets for Treasury Bills: AnIllustration

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

delivery 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 of10.49 per-cent on August 7, 1984. Any person tradingthis contract obtained the right to buy lselll aTreasury

bill 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 B

can he used to illustrate this point. l”or- 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 this

discount rate, the price he pays for the bill is $96.41 per$100 of face value!

‘Futures contracts in other types of financial instruments, such asGNMA passthrough certificate contracts, 90-day CDs, Treasurybonds and Treasury notes, also are available at the Chicago Boardof Trade.

‘The information in table 3 is taken from pages 38 and 39 of theAugust 8, 1984, Wall Street Journal. The actual tables in the WallStreet Journal contain more information than is presented here, Forour purposes, however, the additional information is extraneous.

‘$96.41 $l00/(1.1039)”. The discount factor is raised to thepower of 134/360 = .37. This calculation is slightly different from thediscount calculation used in determining actual trading prices, but

N

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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. Ihis alternative gives him a discount rate of10.49 percent. Buying the treasurybill in September atthis discount would require apayment 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 wer’eto 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 ‘l’reasury bill thatmaturcd the third week in March on the spot market.

numertcal drfferences between the two formulas are small. See

Stigum (1981) for the markets discount formula.$9754 = $100!(1 1049)2.

“$9644 — $97.54/(1 .0991) The rnterest rate used in the calcula-tion is the rate on August 7 for a security maturing on September20(43 days in the future)

19

FEDERAL RESERVE DANK OP ST. LOUIS OCTOSER 1964

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 firm’s assets and liabilities. Considerableconfusion appears to exist as to what the finn’s hedg-ing objective should be and how hedges should be

constructed. 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 net

wealth (present value of the firm’s equity). This focuson net wealth is crucial because, as the examplesshow, reducing cash flow mismatches to zero doesnot minimize the exposure of the firm’s 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)” =

“Small differences are due to the existence of transaction costs. If thedifferences were large, profitable arbitrage opportunities wouldexist. These, of course, would vanish quickly as traders tookadvantage of the situation.

“There is, of course, the problem that the spot instrument beinghedged may not be identical to the futures market instrument. If so,the price of one may diverge from the other because of a change in afactor that affects the price of one but not the other. This is called“basis risk” and is ignored in the following examples.

‘4A flat yield curve is assumed for ease of exposition. The examplesbecome more complicated if the yield curve slopes up or down and/or the spread between borrowing and lending rates changes.

Table 5The Relationship Between Treasury BillSpot and Futures Prices: August 7,1984, Per $100 of Face ValueCase 1: Purchase of a I roasury hrll that matures the th’ru week

in December 1984

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20

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FEDERAL RESERVE BANK OF ST. LOUIS OCTOBER 1984

the finn’s September 15 tn’ansactions. As in panel B of

table 1, the increase in interest i-ates raises the firm’srefunding 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 ofthis 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 ofthe 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 and

timing, 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 firm’s balance sheetposition in terms of present values. The futures con-tracts are enter’ed 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 ofinterest rates on September’ 15. Panels B and C illus-

“Strictly speaking, futures contracts entered into by member banks ofthe Federal Reserve System are treated as balance sheet memo-randa items. These are reported on Schedule L, Commitments andContingencies, of the Call Report. Hence, for accounting purposes,futures contracts do not affect the assets and liabilities of the firmuntil the contracts are exercised.

tn-ate the effect on the present values of the firm’s

assets, liabilities and equity iii immediately followingthe above tr’ansactions, interest rates n-ise unexpect-

edly panel B) or fall unexpectedly panel Cl by 200basis points.

An unexpected increase in interest rates causes tirepresent value of the loan to fall relative to the present’value of the liability. By itself this would cause areduction in the firm’s equity. At the same time,however, the increase in interest rates genen’ates apositive expected net cash flow from the futurescontracts, which, of course, has a positive net presentvalue. Other things the same, this causes equity to rise.The net effect of both changes is that equity remainsunchanged. The reverse occurs if interest rates de-

cline by 200 basis points.

This hedge has eliminated the fin-ms exposure to

interest rate risk. In contrast, recall that a 200 basis-point change in the interest rate causes the equity of

the unhedged firm in table 2 to change by about 75percent.

Hedging as a “Profit Center”

The purpose of hedging is to reduce the variance of

a firm owner’s wealth. In a textbook example of aperfect hedge, the gain or loss from a short position in

the futun’es market will offset exactly the compensat-ing loss or gain on the spot assets and liabilities heldby the fiim. A hedge is constructed because — in thepnesence of an uncertain future — wealth is greater if

the institution foregoes a profit stream that is higheron average I if it goes unhedgedl in exchange for aprofit stream that is lower on average f by the cost ofthe hedging open’ations I but more certain.

Some portfolio managers, however, lose sight of thisfact and assume speculative positions in the futuresmarket with the objective of earning profits from theposition 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 use offutures 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’, itspurpose is to establish futures positions so that theowner’s wealth is held constant; this will occur if theincrease Idecreasel in the value of the firm’s spotholdings of assets and liabilities is offset exactly by theloss lgainl in the futures market.

22

FEDIRAI. RUIRYE BANK OF ST. LOUIS OCTOBER 1914

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23

FEOIRAL RESERVE BAtIK OF ST. LOUIS OCTOSER 1994

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SUMMARY

Higher and more variable interest rates have in-creased the risk faced by financial institutions associ-ated with attracting deposit funds and extendingcredit.’rhis article presented some simple examples oftechniques that can isolate and quantih’ sources of afinancial institution’s exposure to interest rate risk.The discussion also described how financial futurescan be used to reduce this risk. A simple hedgingexample indicated that relatively conservative use of

futures markets can have a potentially large impact onreducing risk exposure. The use offutures trading is athreat to the long-run performance of a financial firmonly if applied in a manner inconsistent with hedging.

REFERENCES

Asay, Michael R., Gisela A. Gonzalez. and Beniamin Wolko-witz. “Financial Futures, Bank Portfolio Risk, and Account-ing,” ,JournalofFutures Markets (Winter 1981). pp. 607—la.

Bierwag, G. 0., George G. Kaufman and Alden Toevs. “BondPortfolio Immunization and Stochastic Process Risk,” JournalofBank Research (Winter 1983), pp. 282—91.

Booth, James R, , Richard L. Smith, and Richard W. Stolz. “Useof Interest Rate Futures by Financial Institutions,” Journal ofBank Research (Spring 1 984), pp. 1 5—20.

Carringlon, Tim, and Daniel Hertzberg. “Financial InstitutionsAre Showing the Strain of a Decade of Turmoil,” Wall StreetJournal (September 5, 1984).

Federal Home Loan Bank Act of 1932. Public No. 304, 72 Cong.,HR 12280.

Gay, G. D., and R. W. KoIb. “The Management of Interest RateRisk,” Journal ofPortfolio Management (Winter 1 983), pp. 65—70.

Gottlieb, Paul M. “New York and Connecticut Permit Insurers toUse Futures and Dptions: A Comparison,” Chicago MercantileExchange MarketPerspechves (Mayljune 1984). pp. 1—S.

Hicks. J. R. Value and Capital (Oxford: Clarendon Press, 1939).Kaufman, George G. “Measuring and Managing Interest Rate

Risk: A Primer,” Federal Reserve Bank ot Chicago EconomicPerspectives (January-February 1984), pp. 16—29.

Koch, Donald L., Delores W. Steinhauser and PamelaWhigham. “Financial Futures as a Risk Management Toolfor Banks and S&Ls,” Federal Reserve Bank of Atlanta Eco-nornic Review (September 1982). pp. 4—14.

Koib, R. W. Interest Rate Futures: A Comprehensive Introduction(Robert F. Dame, Inc., 1982).

Kolb, Robert W., Stephen G. Timme and Gerald D. Gay. “MacroVersus Micro Futures Hedges at Commercial Banks, ‘‘ JournalofFutures Markets (Spring 1984), pp. 47—54.

‘IAC’ C,

FEDERAL RESERVE BANK OF ST. LOUIS OCTOBER 1984

Lower, Robert C. Futures Trading and Financial Institutions: TheRegulatoiy Environment (Chicago Mercantile Exchange,1982).

Morris. John. “FASB Issues Rules for Futures Accounting,”American Banker (August 24, 1984).

Olson. Ronald L. and Donald G. Simonson. “Gap Managementand Market Rate Sensitivity in Banks,” Journal ot Bank Re-search (Spring 1982), pp. 53—SB.

Samuelson, P. A. “The Effect of Interest Rate Increases on theBanking System,” American Economic Review (March 1944).pp. 16—27.

Santoni, G. J. “Interest Rate Risk and the Stock Prices ofFinancial Institutions,” this Review (August/September 1984).

Simonson, Donald G., and George H. Hempel. “Improving GapManagement for Controlling Interest Rate Risk,” Journal otBank Research (Summer 1982). pp. 109—15.

Stigum, Marcia. Money Market Calculations: Yields, Break-Evensand Arbitrage (Dow Jones-Irwin, 1981).

Toevs, Alden. “Gap Management: Managing Interest Rate Risk inBanks and Thrifts,” Federal Reserve Bank of San FranciscoEconomic Review (Spring 1983), pp. 20—35.

Wardrep, Bruce N. and James F. Buch. “The Efficacy of Hedg-ing with Financial Futures: A Historical Perspective,” JournalofFutures Markets (Fall 1982), pp. 243—54.

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