The Theory of Forward Exchange and Effects of Government Intervention on the Forward Exchange Market Author(s): S. C. Tsiang Reviewed work(s): Source: Staff Papers - International Monetary Fund, Vol. 7, No. 1 (Apr., 1959), pp. 75-106 Published by: Palgrave Macmillan Journals on behalf of the International Monetary Fund Stable URL: http://www.jstor.org/stable/3866124 . Accessed: 14/11/2012 22:10

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This content downloaded by the authorized user from 192.168.52.68 on Wed, 14 Nov 2012 22:10:02 PM All use subject to JSTOR Terms and Conditions The Theoryof ForwardExchange and Effectsof GovernmentIntervention on the ForwardExchange Market

S.C. Tsiang* THE THEORY OF FORWARD EXCHANGE badly needs a sys- tematicreformulation. Traditionally, the emphasishas always been upon coveredinterest arbitrage, which formsthe basis of the so-called interestparity theory of forwardexchange.1 Modern economists,of course,recognize that operationsother than interestarbitrage, such as hedgingand speculation,also exert a determininginfluence upon the forwardexchange rate,2 but a systematictheory of forwardexchange whichexplains precisely how the interplayof all thesedifferent types of operationjointly determinethe forwardexchange rate and how the forwardexchange market is linked to the spot exchange market still appears to be lacking. The purposeof this paper is to workout a more comprehensiveand systematictheory of forwardexchange, which would enable us betterto understandthe behavior of the forwardexchange rate and to deduce the likely consequences of governmentintervention in the forward exchangemarket. * Mr. Tsiang,economist in the Special Studies Division, is a graduateof the London School of Economics,and was formerlyProfessor of Economicsin the National PekingUniversity and the National Taiwan University.He is the au- thorof The Variationsof Real Wages and ProfitMargins in Relation to Trade Cycles and of severalarticles in economicjournals. 1 See, e.g., HenryDeutsch, Transactions in ForeignExchanges (London, 1914), p. 174,and J.M. Keynes,Tract on MonetaryReform (London, 1923), pp. 122-32. 2 See Keynes,op. cit.; P. Einzig, The Theoryof ForwardExchange (London, 1937); League of Nations, Economic IntelligenceService, MonetaryReviews (Geneva, 1937), Section B, "The Market in Forward Exchanges."pp. 42-51; C.P. Kindleberger,"Speculation and Forward Exchange,"Journal of Political Economy,Vol. XLVII (April 1939), pp. 163-81,and InternationalEconomnics (Homewood,Illinois, 1953), Chap. 3, pp. 39-57; F.A. Southard,Jr., Foreign Ex- changePractice and Policy (New York,1940), Chap. III, pp. 75-111; A.I. Bloom- field,Capital Importsand the AmericanBalance of Payments,1934-1939 (Chi- cago, 1950), Chap. II, pp. 39-85; J.E. Meade, The Theory of International EconomicPolicy, Vol. 1, The Balance of Payments(London, 1951),Chap. XVII; J. Spraos,"The Theoryof ForwardExchange and Recent Practice,"The Man- chesterSchool of Economicand Social Studies,Vol. XXI (May 1953),pp. 87-117; and M.N. Trued, "InterestArbitrage, Exchange Rates, and Dollar Reserves," The Journalof Political Economy,Vol. LXV (October 1957), pp. 403-11. 75

This content downloaded by the authorized user from 192.168.52.68 on Wed, 14 Nov 2012 22:10:02 PM All use subject to JSTOR Terms and Conditions 76 INTERNATIONAL MONETARY FUND STAFF PAPERS

Some Definitions

In this paper, the exchangerate will be expressedas the price of a unit of a given foreigncurrency in termsof local currency.Similarly, the forwardexchange rate will be expressedas the unit price in local currencyof foreignexchange bought or sold for futuredelivery. For- ward premium(or discountwhen negative) is to be understoodas the discrepancybetween the forwardand spot exchange rates as a per- centageof the spot exchangerate. In normal circumstances,the forwardexchange rate is determined by threemain typesof operation: 1. Hedgingin connectionwith foreign trade. This typeof operation arises out of the normal desire of merchantswho trade with foreign countriesto insurethemselves against the risk of exchangefluctuation affectingtheir currenttransactions, which are normally contracted monthsbefore the paymentsor receipts involvingforeign currencies become due. The contractedamount of paymentor receiptin foreign currencycan be transformedimmediately into an obligationor a claim fixedin one's own currencyby means of a purchaseor sale of forward exchangeof the same amount. 2. Speculation. Speculationmay be definedin a narrowsense and a wide sense.In the narrowsense, speculation in forwardexchange means any sale or purchasewhich results in the deliberateincurrence of addi- tional risks of exchangeuncertainty on the part of the operator-i.e., it increases the net open position (long or short)3 of the operator- with a view to profitingfrom the discrepancybetween the currentfor- ward rate and the probablefuture spot rate thatthe operatorexpects to prevail.Speculation in this narrowsense is to be contrastedwith "hedg- ing,"which is definedas a sale or purchaseof forwardexchange calcu- lated to reduce the pre-existingexchange risks of the operator-i.e., it covers (or reduces) his originalopen position.In this narrowsense, a professionalspeculator who closes somewhathis excessive open (long or short) positionbecause of a change in his expectationsas to future spot rates or a change in the currentforward rate must be regarded as a hedgerperforming a hedgingoperation. On the otherhand, a mer- chant who chooses to hedge only a part of his exchangecommitment, because the currentforward rate is too high (or too low) in relationto the futurespot rate whichhe expects,cannot be regardedas speculating

3 As defined by Professor Kindleberger, an excess of uncovered claims over liabilities in foreignexchange is called a "long position"; an excess of debts over assets, a "short position." See Kindleberger, International Economics (cited in footnote 2), p. 40.

This content downloaded by the authorized user from 192.168.52.68 on Wed, 14 Nov 2012 22:10:02 PM All use subject to JSTOR Terms and Conditions THE THEORY OF FORWARD EXCHANGE 77 at all, even thoughhis decisionnot to hedgeis essentiallysimilar to that of a speculatorwho takes a chance in incurringan open position. In a wide sense,speculation may be definedas the deliberateassump- tion or retentionof a net open (long or short) positionin foreignex- changeupon considerationof the currentforward rate and the probable futurespot rate whichthe operatorconcerned expects to prevail. Under this broad definition,a merchantwho fails to hedge to the full extent ofhis net exchangecommitment is, to a certainextent, speculating. This wider definitionis the more convenient,since merchantswho deliber- ately leave parts oftheir commitments unhedged are essentiallymaking the same type of decision as professionalspeculators who deliberately assume risky commitments(open positions); consequently,the two actions can be analyzed in the same way. When speculationis definedin this wide sense, however,we must assume that merchants,acting as hedgers,automatically hedge to the full extentagainst theirexchange commitments by purchasesor sales of forwardexchange unless the exchangerisks are alreadyeliminated by otherarrangements. If some of themdo in fact leave part of theirrisky commitmentsunhedged, we shall treatthem as if they,this time acting as speculators,have reassumednet open positionsby oppositeforward transactions,offsetting part of the forwardpurchases or sales with which they have supposedlyhedged themselvesagainst all exchange risks in their originalcommitments that may arise out of theirtrade transactions. 3. Coveredinterest arbitrage. Short-term funds have a naturaltend- ency to flow fromone countryto another in search of the highest returns.Through the mechanismof the forwardexchange market, such search forthe highestreturns can be divorcedof any speculative ex- change risk; that is, the person (or institution)that transfersfunds fromone countryto anotherin search of higherreturns on investment can coverhis spot exchangetransactions by forwardtransactions in the opposite directionand thus avoid assumingany net open position in foreignexchange. Covered interestarbitrage may thus be definedas an internationaltransfer of spot funds for short-terminvestment pur- poses covered by a simultaneousforward transaction of the same amountin the oppositedirection. Such an operationleaves the net posi- tion and exchangerisk of the operatorunchanged, which is the essen- tial featurethat differentiatesit fromboth hedging and speculation. Normally,these threetypes of operationare likely to be performed by differentgroups of people or institutions;however, not infrequently the same person or institutionmay performmore than one type of operation at the same time. Commercialhedging (in the automatic

This content downloaded by the authorized user from 192.168.52.68 on Wed, 14 Nov 2012 22:10:02 PM All use subject to JSTOR Terms and Conditions 78 INTERNATIONAL MONETARY FUND STAFF PAPERS sense) is, of course,performed chiefly by merchants,and speculation chieflyby professionalor amateurspeculators. However, as we have alreadyseen, speculation in thewide sense is practicedto someextent by merchantswho decide not to hedgeup to the fullamount of their commitments.Interest arbitrage is engagedin chieflyby banks and otherfinancial institutions; but, as we shall see later,merchants and speculatorsmay, in a sense,engage in interestarbitrage in connection withtheir hedging or speculatingoperations. Furthermore, although banksusually profess that they do not,as a rule,take any speculative openpositions in foreignexchange and striveto balancetheir positions in each currencyat theclose of each day,available statistics indicate thattheir net positions (both spot and forward)in each foreigncur- rencyare notalways zero and, therefore, that they are engagedin some speculativeoperations according to ourdefinition in thewide sense. In normalcircumstances, these three types of operationconstitute practicallyall the supplyand demandfor forward exchange. In times of abnormaldisturbance, however, the authorities of the countries con- cernedmay intervene directly in the forwardmarket through forward purchasesof their own currencies in orderto preventthe forwarddis- countsfrom widening too much-sometimesin additionto restrictions on interestarbitrage or speculation.4

Covered Interest Arbitrage

Since the traditionaltheory of forwardexchange as set forthby Keynesin his Tract on MonetaryReform is based mainlyupon the possibilityof interestarbitrage, we shall now considerthis type of operationon the forward exchange market. As pointedout above, short- termfunds tend to flowfrom one centerto another(say, fromNew Yorkto London)if the rate of return in onecenter (London) is higher thanthat in theother (New York), afterthe risk of exchangefluctua- tionsis eliminatedby a forwardexchange transaction in the opposite 4 The centralbanks usuallyreserve the rightto intervenein theirforward ex- changemarkets for the purposeof influencingthe forwardrate forany particular foreigncurrency. In some cases,e.g., in the Danish and Swedishforward markets forU.S. dollars,the centralbanks concerned actually buy and sell forwarddollars at theirrespective official spot buying and sellingrates, with a certaindiscount for forwardpurchases and a certainpremium for forward sales. However,at least one centralbank, namely that of Belgium,has announcedthat it presentlydoes not intervenein the forwardmarkets for U.S. and Canadian dollars.Recently, there has been a debate goingon in the UnitedKingdom with regard to the questionof whetheror not the authoritiesshould intervene in the forwardmarket.

This content downloaded by the authorized user from 192.168.52.68 on Wed, 14 Nov 2012 22:10:02 PM All use subject to JSTOR Terms and Conditions THE THEORY OF FORWARD EXCHANGE 79 direction.This propositionhas been most preciselyformulated by J. Spraos.5His formulation,with our own notation, is as follows: SR=spot exchangerate-say, the sterling-dollarrate, quoted in termsof dollars per unit of sterling; FR = three-monthforward sterling-dollar rate quoted as forthe spot rate; Ia= short-terminterest rate in NewYork per three months; Ib= short-terminterest rate in Londonper three months. The propositioncan thenbe statedthat short-term funds would tend to flowfrom New Yorkto London,if FR > SR (l+1) (+Ia); (1) conversely,funds would tend to be transferredfrom London to New York,if FR FR(1+I)< (1+Ia). (2) For example,$100 investedfor three months in New York wouldbe- come$100 X (1+Ia); and if the same sumin dollarsis convertedinto sterlingat thecurrent spot rate and investedfor three months in Lon- donand then converted back into dollars at thecurrent forward rate for sterlingfor three months' delivery, it wouldbecome $100X SRR(1l+I). If the lattersum is larger,arbitragers would gain a net profitby a temporarytransfer of fundsfrom New York to London;if smaller, the netprofit would be gainedby a transferof fundsfrom London to New York.It is thenargued that, if the arbitrage funds do notrun out, such arbitrageoperations (say, transfers of spotfunds from New York to Londoncoupled with an equal amountof forwardsales of sterlingfor dollars)would tend to eradicatethis inequality through some or all of thefollowing possible effects: raising the spot rate of sterlingin terms of dollars (SR); loweringthe forwardrate (FR); raisingthe short- terminterest rate in New York (Ia) and loweringthat in London(I). Thus,the equilibriumrelationship between the spot and forwardex- changerates on theone hand and the interest rates in thetwo financial centerson theother hand is said to be FR F-( (J+II) = Op. Cit.(J-a)·3) pp. 87-89.(3)

5 Op. cit., pp. 87-89.

This content downloaded by the authorized user from 192.168.52.68 on Wed, 14 Nov 2012 22:10:02 PM All use subject to JSTOR Terms and Conditions 80 INTERNATIONAL MONETARY FUND STAFF PAPERS FR (.e -FR-SR is theforward pre If SR is expressedas 1 +p, wherep i.e. S ) is theforward pre- mium(or forwarddiscount, if negative)on sterlingas definedabove, thenequation (3) becomes

(1+p) (1+±P) = (1+Ia). (4) If theterm pIb in (4) is consideredas ofsecond order of small magni- tudeand thereforeneglected, this equation can be furthersimplified to

p= Ia- Ib. (4') This correspondsto the usual verbal formulationof the so-called interestparity theory of forwardexchange, which maintains that the forwardpremium (or discount)tends to be equal to theinterest differ- ential betweenthe two countriesconcerned.6 The currencyof the countrywith a higherinterest rate tends to be quotedat a discounton theforward exchange market, compared with its currentspot exchange rate.For instance,if the interest rate in London,Ib, is greaterthan the interestrate in New York,Ia, thenp is negative,i.e., forwardsterling is at a discount. Thisequilibrium condition is notmeant to be an exactone. First, the short-termrates of interest in bothcountries are not uniquely definable entities.There are differentkinds of short-term rates in bothcountries. Second,as pointedout by Keynesat thevery beginning, the profit rate on such arbitrageoperations must exceed a certainminimum to be sufficientto inducearbitragers to take thetrouble of arbitraging-i.e., thereis a sortof minimumsensibile on thepart of arbitragers,which Keynesput at 1/ per centper annum.7Thus, given a definiteinterest differentialbetween the two countries,the forwardpremium (or dis- count)on sterlingcould still diverge 1/2 per centper annumin either directionfrom the interest parity without inducing any arbitrage oper- ationsto correctthe divergence. Lastly, the most important shortcom- ing of the interestparity theory is the necessaryproviso that, even whenthere is no officialrestriction of short-termcapital movements,

6 Spraoscontends that the usual verbalformulation of the interestparity theory is consistentwith his more rigorousformulation only if Ib is negligiblysmall (op. cit.,pp. 88-89). In makingthis assertion, however, he is not doingjustice to the usual verbalformulation; for what is neglectedthere is simplythe termpb, whichis a productof p, the forwardpremium (or discount),usually a small per- centage,and Ib, the short-terminterest rate in the foreigncountry per three months,another small percentage.Therefore, plb can be negligiblysmall, even whenIb is not negligiblysmall. 7 Keynes,op. cit., p. 128. Keynes' originalestimate of the minimumsensibile was readilyendorsed by Einzig (op. cit.,p. 172), Bloomfield(op. cit.,pp. 52-53), and Spraos (op. cit.,p. 95).

This content downloaded by the authorized user from 192.168.52.68 on Wed, 14 Nov 2012 22:10:02 PM All use subject to JSTOR Terms and Conditions THE THEORY OF FORWARD EXCHANGE 81 the theoryis applicable only so long as "arbitrage funds do not run out,"8 whereas in fact, as Keynes pointed out, "the floatingcapital normallyavailable, and ready to move fromcenter to centerfor the purpose of taking advantage of moderate arbitrage profitsbetween spot and forwardexchange, is by no means unlimitedin amount,and is not always adequate to the market'srequirements."9 This proviso to the interestparity theoryis often made, e.g., by Spraos, in a way that implies that the theoryholds up to the point wherearbitrage funds are about to run out, but ceases to hold beyond that point. In reality,the availability of arbitragefunds does not stop abruptlyat any given point. What is more likely is that arbitragers (chieflybanks withoverseas operations)will generally,after a certain point, become increasinglyreluctant to transfertheir spot liquid re- sources fromthe domesticcenter to any particularforeign center, say London, if the arbitrageoperations they are induced to performare persistentlyin the formof spot purchasesagainst forwardsales of,e.g., sterling.Similarly, after a certainpoint, they will become increasingly reluctantto transfertheir spot liquid resourcesfrom their foreign cen- ters of operationsback to theirhome marketthrough persistent arbi- trage operationsin the opposite direction.This followsfrom the fact that, for their regular business operations,banks and other financial institutions(or any firmswith overseas operations) must have com- mand overcertain amounts of spot liquid fundsin everymajor overseas financial center; mere forwardclaims would not serve the purpose. That is to say, spot liquid assets yield some intangiblereturns of con- venience or liquidityin addition to their interestyields. Banks (and otherfinancial institutions) would normallybe expectedto distribute their commandover spot liquid assets in various financialcenters in such a way that the marginalyields of interestcum liquidity (con- venience) net of exchangerisks of liquid assets would be approximately equal betweendifferent financial centers. As a bank, say in New York, is inducedto arbitrageon the forwardexchange market in the direction of spot buyingof sterlingagainst forwardsale of sterlingof an equal amount,its spot liquid assets in New York are reduced and those in London increasedby that amount,though with the insurancethat this amount of sterlingcan be transferredback into dollars at a fixedrate on a futuredate. As a result,the marginalyield of convenienceof its fundsin New York would be increased,while that of its fundsin Lon- don would be decreased.To induce it to make furtherarbitrage opera- tions in the same direction,i.e., to purchasemore spot sterlingagainst 8 Spraos,op. cit.,p. 88. 9 Keynes, op. cit., p. 129.

This content downloaded by the authorized user from 192.168.52.68 on Wed, 14 Nov 2012 22:10:02 PM All use subject to JSTOR Terms and Conditions 82 INTERNATIONAL MONETARY FUND STAFF PAPERS forwardsales, the marginof profitrepresented by the gap between interestparity and the currentforward premium (or discount)would have to increase.Thus the equilibriumcondition for each arbitrager (thiscondition has to be statedfor each arbitrager,for the marginal convenienceyields of liquidassets in variouscenters are likelyto be differentfor different arbitragers) should be revisedto FR-SR - SR = (Ia+pa) (Ib+p) (5) where pa is the subjective marginalconvenience (or liquidity) yield to the individualarbitrager, i, of his net short-termliquid assets in New York,and pb thatof his netshort-term liquid assets in London. Obviously,p. and pb are decreasingfunctions of his net short-term liquidassets in New York and in London,respectively. Since an arbi- trager(qua arbitrager,who under our definition does not assumeany exchangerisk) will alwaysmatch his purchaseof forwardexchange (sterlingin the presentcase) withan equal amountof sales of spot sterlingexchange, his spot liquid assets in NewYork would be increased by theamount of his currentnet purchases (purchases minus sales) of forwardsterling exchange less his past contractsof purchases(minus sales) thatfall due currentlyand whichmay be regardedas swapped againstnew contracts. By thesame token, his net liquid assets in Lon- donwould be reducedby the same amount. If we makethe simplifying assumptionthat all forwardexchange contracts are forthree months' (90 days') delivery,then the short-termassets of a typical arbitrager in New York may be representedas

S t= : Dr+A. (6) t-89 whereSat denotesthe total net short-termassets of the arbitrager,i, in New Yorkon day t; Dt is his netpurchase of forwardexchange on day t, whichmay be negativeif he sells morethan he buyson that day; and A. representshis othernet short-termassets in New York unrelatedto his foreignexchange dealings. Similarly, his net short-term assets in London may be representedas

S ,=- Dsi+A (7) t-89 whereSb denoteshis totalnet short-term assets in Londonon day t, and Ab his othernet short-term assets in Londonunrelated to his for- eign exchange dealings. Dit is definedin the same way, but, for the reason explainedabove, it takes an oppositesign here. If the liquidity (convenienceyield) functionsof his net short-term

This content downloaded by the authorized user from 192.168.52.68 on Wed, 14 Nov 2012 22:10:02 PM All use subject to JSTOR Terms and Conditions THE THEORY OF FORWARD EXCHANGE 83 assetsin NewYork and London may be approximatedby the following linear equations

( ) p p=-p Sa + = _-p' DiT+A- +ai (8) t-89

pt=--p bSt+-ip,i ( Dir-A)+- i (9) t-89 wherep a and p'b are positive coefficientsand ai and fi are positive constants,then it can be readilyshown that the demand for (or supply of,if thedemand turns out to be negative)forward sterling exchange on thepart of the arbitragerconcerned is a decreasingfunction of the forwardpremium minus the excess of the domestic interest rate (New Yorkrate) overthe foreigninterest rate (Londonrate). By substitut- ing (8) and (9) in (5), we get

pt- (I -I ) -(p '+p'b) 2 Di-p A +pbA b+i--i, t-89 or

-- 1 t-1 t a +p! b{ [pt-(I -I +p -p-iaA -i- +Pii^A ~- Dir (10) i(p a+p ) t-89 wherept is the forwardpremium on sterling.Given the forwardcon- tractsthat the arbitragerhad alreadyentered into in the past, his currentdemand for forwardsterling exchange, Dit, is a decreasing functionof [pt- (It-I) ]. Dit can,of course,be negativeas wellas positive,that is to say,the arbitragermay be inducedto arbitragein thedirection of sellingfor- wardagainst spot buying as wellas in thedirection of buying forward againstspot selling. It is quiteobvious from (10) that,if his outstand- ing previousforward contracts are predominantlyforward purchases t-i of sterling,i.e., if E Di, is a largepositive magnitude, he wouldbe t-s9 moreinclined to arbitragein the directionof sellingforward against spotbuying of sterling,or morereluctant to arbitragein thedirection ofbuying forward against spot selling of sterling. FRt- SRt? Since pt= SRt and, foran individualarbitrager, SRt as well as ft and Ib maybe regardedas given(unless he has an oligopolistic or oligopsonisticinfluence on the spotexchange rate and the interest ratesin the two centers),equation (10), therefore,also giveshis de- mand forforward exchange as a decreasingfunction of the current forwardrate FRt.

This content downloaded by the authorized user from 192.168.52.68 on Wed, 14 Nov 2012 22:10:02 PM All use subject to JSTOR Terms and Conditions 84 INTERNATIONAL MONETARY FUND STAFF PAPERS The aggregatedemand on thepart of arbitragersas a wholeis ob- tainedby totalingthe individualdemand functions for all the arbi- tragers: -1 t-1 2Dit= , A{[pt-(It-Ib+pA -pbAb-aii}- - 2 D,r (11) i(Pa4Pi)i t-89 The essentialcharacteristics of the aggregatedemand function for forwardexchange on the part of arbitragersas a wholeremain un- changed,compared with the demandfunction for an individualarbi- trager.The aggregatedemand, EDi, is stilla decreasingfunction of [pt- (IJ-Ib)]. Again,if the aggregate outstanding forward contracts, which as a wholehave enteredinto in the past,are pre- arbitragers t-1 dominantlyforward purchases of sterling,i.e., if E E Di, is a large i t-89 positivemagnitude, the arbitragerswould, on the whole,be morein- clinedto arbitragein thedirection of selling forward and buyingspot, or morereluctant to arbitragein the directionof buyingforward and sellingspot. Thereis, however,one importantpoint of difference:for arbitragers as a whole,SRt, I, and Ib maynot be givenbut maybe functionsof theaggregate demand, even though individually none of them may be powerfulenough to affectthese variables. As pointedout above,an arbitrager,qua arbitrager,would match an increasein his forward positionby a correspondingdecrease in his spot position(or vice versa). An increasein his forwardposition implies an excessof his currentnet purchaseof forwardexchange over the previousforward purchasecontracts (net of previousforward sale contracts)that fall due on the currentday. If we makethe simplifyingassumption that all forwardcontracts are for90 days'delivery, then the current change in his netforward position is t t-I : Di, - Di, =Dit - Dit-9o (12) t-89 t-90 The correspondingadjustment in his spot position which he has to make to avoid a net open position (spot and forward)is, therefore, -(Dt -Dit-9o).If his currentnet purchase of forwardsterling exceeds his previousnet forwardpurchases due forsettlement on the current day, i.e., if (Dt -Dt-9o)>0, he wouldsell spot sterlingof an equal amount,and viceversa if (Di,-Dit,o) <0. Therefore,the aggregate net purchase(or sale) of spot sterlingby arbitragersas a wholeon ac- countof their arbitrage operations is equal to - (EDit-Di t-9o).If i i

This content downloaded by the authorized user from 192.168.52.68 on Wed, 14 Nov 2012 22:10:02 PM All use subject to JSTOR Terms and Conditions THE THEORY OF FORWARD EXCHANGE 85 thisis a positivemagnitude, it indicatesan aggregatenet purchase; if negative,it indicatesan aggregatenet sale. UnlessSR and Ia are rigidlypegged by the monetaryauthorities, theytend to be pushedup by the aggregatenet purchaseof spotex- changeby arbitragersas a whole.On the otherhand, Ib tendto be loweredby the transferof spotfunds to Londonby arbitragersas a whole.That is dSRt (2Dit-90-o-Dit)0 i i d Iat >0 a(EDit-go-2Dit) i i and

a((2_Dit-9o-Di t) i i Hence, given EDit-9o as a predeterminedquantity,

aSRtSRot O(2Dit) i

aIJ <0 a(SDit) i and oI\ >0 a(Dit)0 i We shall leave the determinationof the spotrate of exchangefor laterdiscussion, as we shall see that,unless it is pegged,it mustbe determinedjointly with the forwardexchange rate. We shall also re- frainfrom broadening our modelto encompassall the variablesand equationsthat are relevantfor the determinationof theinterest rates bothat homeand in the foreigncenter concerned. We shall merely assumethat the domestic and foreignshort-term interest rates may be approximatedby thefollowing linear equations: Ia = I *- Ilt (Dit-D-O_o) (13) i i and I'= I--*+I'b (sDit---Ds-9o) (14) i i

This content downloaded by the authorized user from 192.168.52.68 on Wed, 14 Nov 2012 22:10:02 PM All use subject to JSTOR Terms and Conditions 86 INTERNATIONAL MONETARY FUND STAFF PAPERS whereI"* and Ib* are determinedby factorsextraneous to our limited model and I'l and I'b are positivecoefficients representing, respectively,

aja( tDZ )anda alj Zd .Substituting (13) and a (D it-,EDit-_o) (ED it- D it-90) i i i i FRt- SRt (14) in (11) and writingp,= , we get SRt

FRt SR A 2Di= -0 (--(II'II'b) (it_90+P A A-p-bA b-ai+i}

t-1 -- z2 D , (15) i t-89 where =E( ,(I b)1+ , ,b) It is obvious that the (pla+p,b)± (p,a+p1b) greaterthe effectsof arbitrageoperations upon the domesticand for- eign interestrates, the smaller (numerically) the elasticity of arbi- tragers'demand forforward exchange. Thus the analysis of the behavior of coveredinterest arbitragers at best providesus merelywith a demand (or supply) curve forforward exchange on the part of arbitragers.To assume that such a demand functionon the part of only one sector of the dealers in the forward exchangemarket would by itselfdetermine the forwardexchange rate is to assume by implicationthat such a demand curveis perfectlyelas- tic over a sufficientlywide range to overwhelmall otherdemands and supplies.We have just seen,however, that this demandis normallyless than perfectlyelastic eitheras a functionof the currentforward rate or as a functionof the divergenceof the forwardpremium (or discount) fromthe interestdifferential.

Speculation in Forward Exchange

We shall next analyze the speculative demand for (or supply of) forwardexchange. We shall adopt the widerdefinition under which we mean by speculationin foreignexchange any deliberateassumption of a net open position (an excess of uncoveredclaims over liabilities,or the otherway around) in a foreigncurrency. Such an openposition can, of course,be createdthrough dealings either in forwardexchange or in

This content downloaded by the authorized user from 192.168.52.68 on Wed, 14 Nov 2012 22:10:02 PM All use subject to JSTOR Terms and Conditions THE THEORY OF FORWARD EXCHANGE 87 spot exchange-in other words, speculation can be either in the for- ward market or in the spot market. We shall, however,first tenta- tively assume that all speculation in foreignexchange is in forward exchange,as this is indeed the most convenientway of speculatingin foreignexchange. This assumptionwill not impairthe generalityof the analysis, since it will presentlybe shown that speculation in spot exchange can always be treated as a combinationof speculation in forwardexchange and an interestarbitrage operation such as that describedabove. Suppose that a speculatorwith no initial net commitments(or net position) in foreignexchange, and hencewith no exchangerisk to begin with,is confrontedwith the currentforward rate. If he believes that the futurespot rate (90 days fromthe currentday) is likely to be higherthan the currentforward rate, he would purchase forwardex- change, and thus assume a long position,until the marginal risk of extendinghis long positionby an extraunit of foreignexchange is only just compensatedby the marginby whichhis expectedfuture spot rate exceedsthe currentforward rate. That is, his equilibriumposition can be representedas

ERit-FRt=rij (16) whereERjt is, in the expectationof the speculatorconcerned (denoted here by the subscriptj), the most probable futurespot rate 90 days fromthe currentday, and rjtis the marginalrisk of extendinghis long positionin foreignexchange. The expectedfuture spot rate of any speculatoris never a definite rate,but a range of possible rates withdifferent degrees of probability. However, as long as a speculator'sexpectation as to the futurespot rate is normallydistributed, it can always be uniquelyrepresented by the most likely expected rate (or the mean expected rate) and the variance (or its square root,the standarddeviation) of the probability distributionof his expectation.Thus wheneverwe speak of the expected rate of a speculator,we always mean the most likely futurespot rate in his expectation,or his modal estimateof the futurerate. Obviously,rjt is an increasingfunction of the speculator's current purchaseof forwardexchange, Djt, and the variance of the probability distributionof his currentexpectation, ojt. Thus ERit- FRt= ri{Dt, oit} (16') Conversely,a speculatorwith no initial net positionwould sell for- ward exchange,and thus assume a shortposition, if he believed that the futurespot rate was likely to be lower than the currentforward rate,until the marginalrisk of extendinghis shortposition by an extra

This content downloaded by the authorized user from 192.168.52.68 on Wed, 14 Nov 2012 22:10:02 PM All use subject to JSTOR Terms and Conditions 88 INTERNATIONAL MONETARY FUND STAFF PAPERS unit of foreignexchange was only just compensatedby the marginby whichthe currentforward rate exceededhis expectedfuture spot rate. The marginalrisk forsuch a speculativeseller of forwardexchange is obviouslyan increasingfunction of his currentsale of forwardexchange, -Dkt (accordingto our convention,sales of forwardexchange are to be treated as negative purchases), and the standard deviation of the probabilitydistribution of his currentexpectation, okt. That is

FRt-ERkt = rk{-Dkt, okt (17) which,put in the same formas (16') above, gives

ERkt- FRt= -rk{ -Dkt, akt} (17') Comparisonbetween (16') and (17') suggeststhat the equilibriumcon- ditions for a speculatorwho purchases forwardexchange and for one who sells are essentiallythe same. When the left-handside of the equation is writtenas ERjt- FRt, the marginalrisk on the right-hand side takes positiveor negativesign accordingto whetherthe speculator concernedis a purchaseror a sellerof forwardexchange, i.e., according to whetherDjt is positive or negative. The standard deviation of his expectation,ujt, whichis always a positivemagnitude, affects only the magnitudeof his marginalrisk but not its sign. Thus the speculator concernedwill be a buyeror a seller of forwardexchange according to whetherhis expectedrate is higheror lower than the currentforward rate. The problembecomes much more complicated,however, when the assumptionis waived that the speculatorhas no initialnet position, and henceno initial exchangerisk, before he makes any purchaseor sale on the currentmarket. If he has already accumulateda large longposition fromhis previouspurchases of forwardexchange, the excess of his cur- rent expectedrate over the currentforward rate has to be quite con- siderable to induce him to make any furtherpurchase of forward exchange.Indeed, he may becomea sellerof forwardexchange to cover his pre-existinglong position,when the excess of his expectedrate over the forwardrate is reducedeven thoughit is still positive.Conversely, if he already has a large shortposition from his previoussales of for- ward exchange,his currentexpected rate would have to fall consider- ably shortof the currentforward rate to induce him to make further sales of forwardexchange; and if the gap is so reducedthat he decides to close his initial overextended(in the light of the new situation) shortposition, he may become a purchaserof forwardexchange even thoughhis expectedrate still falls shortof the currentforward rate. The difficultyof this problemlies in the fact that his initial shortor long positionis an aggregateof his previouspurchases and sales which

This content downloaded by the authorized user from 192.168.52.68 on Wed, 14 Nov 2012 22:10:02 PM All use subject to JSTOR Terms and Conditions THE THEORY OF FORWARD EXCHANGE 89 havebeen contracted during the past 89 daysand whichtherefore have days to maturityvarying from 1 to 89. Purchasesor sales that werecontracted yesterday, though possibly at a differentforward rate, have almostthe same effectupon his willingnessto makefurther pur- chasesor sales todayas purchasesor sales concludedtoday, whereas purchasesor sales contractsthat are to maturein a day's timeare alreadywritten off as realizedprofits or lossesalmost as definitelyas contractsthat have already matured.10 It appears,therefore, that past contractsof purchaseor sale would affectthe speculator's willingness or reluctanceto take on morecom- mitmentsin differentdegrees, varying in directrelation to thenumber ofdays the contracts have to runbefore maturity. If theeffects of past forwardcommitments upon the speculator'scurrent risk position are assumedto diminishexponentially, and his currentmarginal risk to be a linearhomogeneous function of his currentand past commitments,1 hismarginal risk may be representedas rit=yi (Dit+XiDit_i+x Dit2+ +X OD-89) (18) whereyj is a positivecoefficient, Aj a positivefraction measuring the diminishinginfluences of past commitmentssuch that X90 is practically zero,and Djt, Djt-l,etc., are thespeculator's net purchases of forward exchangeon thedays indicated by the second subscripts. Each ofthese D/'smay be eitherpositive or negative. It maybe shown12then that rjt= jiDit+-Xirt- (19)

10For a speculator-and indeed for hedgers as well-the maturity of a forward contract does not mean that the contracted amount of foreign exchange will actually be delivered against full payment in local currency. A matured forward contract is usually settled by the contractingparties taking the profit,or paying the loss, implied in the differencebetween the contracted forward rate and the actual currentspot rate at the moment of maturity. 11An homogeneous function is appropriate here, because equations (16') and (17') indicate that the marginal risk of the speculator takes the sign of his com- mitments. 12 Let us define the shift operator E in such a way that Dt+i= EDt and Dt_-=E-Dt. When E is applied to equation (18), that equation can be rewrittenas 1 - E- rit=yiDit(1+XiE-1+X E-2+ *-...+X 9E-89)=3ajD, )ED'

That is rjt(E-X) =^yjEDit or rjt+l- Xjrt= yiDit+ hence rit-Xrit_i= yDjt or rit-= -Dit+X-jit_l.

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This functionfor the marginalrisk of the speculatorindicates that his currentmarginal risk is not only an increasingfunction of his current purchases of forwardexchange (sales are treated as negative pir- chases), but that the risk freshlyincurred by currentpurchases has to be added algebraically (i.e., allowing for signs) to a remnantof his marginalrisk of the day before.And the marginalrisk of the day before would be positiveor negativeaccording to whetherhis weightedcumu- lative positionon that day is long (positive) or short (negative). Substituting(19) in (16), we get ERit- FRt=yjDit+X\rit-i (20) and hence

Dit=-(ERit-FRt) --rit- (21) 1yi Yi Equation (21) may be regarded as a linear approximationof the demand (or supply) functionfor forwardexchange on the part of a speculator regardlessof whetherhe is initially in a long or a short position. The aggregatedemand (supply) functionof speculatorsas a whole is the aggregationof a set of equations like (21), i.e., 1 ZDt= 2- (ERt- FRt)- -rt-_ i 7j i Yi 1 Xi = -1(ERt- FR1) - (-rit- (22) i 'i i 'Yi where ERt, the weightedaverage expected rate of all speculators,is definedas E-ERit / -. The essential characteristicsof the aggregate speculative demand functionremain the same as the demand functionsof the individual speculators; the aggregatespeculative demand (or supply) is an in- creasing (decreasing) functionof the excess of the weightedaverage of the expectedrates of all the speculatorsover the currentforward rate and a decreasing (increasing) functionof their aggregate weighted cumulativelong positions. Equation (22) gives the aggregatespeculative demand for forward exchangeas a definitefunction of the currentforward rate only when the weightedaverage expectedrate of all the speculatorsis eithergiven independentlyof the currentforward rate by extraneousfactors or is a knownfunction of the currentforward rate (as well as of otherex- traneousfactors). We shall not be able to go intothe details of the dv-

This content downloaded by the authorized user from 192.168.52.68 on Wed, 14 Nov 2012 22:10:02 PM All use subject to JSTOR Terms and Conditions THE THEORY OF FORWARD EXCHANGE 91 namics of the formationof exchange rate expectationhere. Sufficeit only to pointout that if the average currentexpected rate is influenced by the currentforward rate so that it is adjusted upward when the currentforward rate increases,the aggregatespeculative demand for forwardexchange would become much less elastic and might even become an increasingfunction of the currentforward rate. Write

ER t= ER t+FRt whereER* is givenby extraneousfactors and y representsthe influence of FRt upon ERt. Substitutionof this equation in (22) produces

(Dit=22 FRt+2-1ER* - ri_l (22') i i 'Yi i 'Yi i Yi If (X- 1)>0, the aggregatespeculative demand is an increasingfunc- tion of the currentforward rate. If -=1, the aggregatespeculative de- mand is entirelydetermined independently of the currentforward rate by extraneousfactors and lagged variables. Normally,however, the currentforward rate is unlikelyto have a considerabledirect influence upon the average expected rate of all the speculators,so that the aggregatespeculative demand can be expectedto be a decreasingfunc- tion of the currentforward rate. It has been pointedout above that a speculatorin foreignexchange may speculate on the spot marketas well as on the forwardmarket. Speculative purchasesof spot exchange,however, unlike those of for- ward exchange,cost the speculator interestcharges and the sacrifice of liquidityon the local currencyfunds that he must raise in orderto buy the foreignexchange. On the otherhand, the spot foreignexchange he purchasedcan earn him interestand convenienceabroad until the time he decides to part with it. The converseis true for speculative sales of spot exchange. The equilibriumcondition for a spot speculatorwould be ERit-SRt= rit+ SRt [(It+ t)-(I+P )] (23) whereSRt is the currentspot rate, rjt the marginalrisk of extending his currentlong position in foreignexchange, It and Ib the current short-termrates of interestat home and in the foreigncenter, and pat and pit the marginalsubjective yield of convenience(or liquidity) to the speculatorconcerned of fundsat home and in the foreigncenter, respectively.Since the possibilitiesof speculatingon the spot market and on the forwardmarket are both open to the speculatorconcerned, this equilibriumcondition must exist side by side with equation (16), i.e., ERjt - FRt=rjt, if he indulgeshimself in both formsof speculation. The marginalrisk of extendinghis currentlong (or short) positionby

This content downloaded by the authorized user from 192.168.52.68 on Wed, 14 Nov 2012 22:10:02 PM All use subject to JSTOR Terms and Conditions 92 INTERNATIONAL MONETARY FUND STAFF PAPERS spot or forwarddealings must be the same, since the risk of loss in- volved in a wrongexpectation is the same. That is, rjtin (23) and (16) must be the same. When the left-handand right-handsides of (16) are subtractedfrom the correspondingsides of (23), the resultis FRt-SRt =SRt[ (It+p9 )-(I b+p t)] which is identical in formto the equilibriumcondition of a typical interestarbitrager stated in equation (5) above. Thus a speculatorwho speculates on the spot exchangemarket may, in fact, be regardedas actingimplicitly in the combinedcapacity of an interestarbitrager and a forwardexchange speculator. If he speculatesby buyingspot foreign exchange (instead of buyingforward exchange), what he is doing is in fact equivalentto acting firstas an interestarbitrager in buyingspot exchangeagainst a sale of an equal amount of forwardexchange and thenas a forwardspeculator in buyingthe forwardexchange from him- self (in the formercapacity) in the expectationthat the futurespot rate will rise higherthan the currentforward rate and yield him a pure speculativegain. If he speculates by sellingspot exchange (instead of forwardexchange), he is in fact actingfirst as an interestarbitrager in selling spot exchange against an equal amount of forwardpurchase, and then as a forwardspeculator in selling the forwardexchange to himselfin the formercapacity in the expectationthat the futurespot rate will turnout to be lowerthan the currentforward rate. Thus the tentativeassumption stated above, that all speculationin foreignexchange is carriedon in the forwardmarket, does not impair the generalityof our analysis as long as speculatorswho in effect speculatein the spot marketare treatedaccording to theirimplicit dual capacity, namely,first as interestarbitragers and then as speculators in forwardexchange. In fact, speculatorsin foreignexchange will speculate in spot ex- change only if they find it cheaper to performthe implicitinterest arbitragethemselves rather than to leave it to the professionalarbi- tr4gers,i.e., banks. In other words, unless they find that they can carrythe speculativestock of spot exchangeat a lowernet interestand liquiditycost than the banks,they will preferto concentrateon specu- lative operationsin the forwardmarket only.

Hedging in Connection with Foreign Trade Under the wide definitionfor speculationthat has been adopted in this paper, a merchantwho takes a chance in not coveringhis commit- mentsin foreignexchange with a forwardpurchase or sale is treatedas

This content downloaded by the authorized user from 192.168.52.68 on Wed, 14 Nov 2012 22:10:02 PM All use subject to JSTOR Terms and Conditions THE THEORY OF FORWARD EXCHANGE 93 a speculator;therefore, it will be assumed that all foreigntrade trans- actions contractedfor futurepayments automaticallylead to corre- spondingamounts of purchasesor sales of forwardexchange. A current importcontract would automaticallygive rise to a demandfor forward exchange (on the part of the domesticimporter if the contractedpay- mentis stipulatedin foreigncurrency, or on the part of the foreignex- porterif the paymentis stipulatedin domesticcurrency). A current exportcontract would automaticallygive rise to a supply of forward exchange (on the part of the domesticexporter if the paymentis stipu- lated in foreigncurrency, or on the part of the foreignimporter if the paymentis stipulatedin domesticcurrency). It is true that, by immediatepurchases or sales of spot exchange importersand exporterscan equally get rid of the risksconnected with the exchangerate uncertaintyat the time of payment.Thus, for in- stance, an importercould pay for his order either in advance or so many days afterreceiving the documentsof shipment.As Spraos has pointedout,13 however, hedging by purchaseor sale of spot exchangeis really equivalentto a combinationof hedgingby means of forwardex- change and an interestarbitrage operation by the hedger himself. This can be demonstratedmore precisely in the followingway. The cost of eliminatingthe exchangerisk of an importerby means of a forward purchase may be representedas ERs - FR, whereER8 is the expected futurespot rate of the importerconcerned. On the otherhand, the cost of eliminatingthe exchange risk by an immediatepurchase of spot exchange may be representedas ERs-SRl1+ (Ia+p) - (Ib+pb)] whereIa is the domesticrate of interestthat the importerhas to pay to raise the fundsfor the immediatepurchase of spot exchange;pa is the sacrificeof liquidity at the margin for thus divertingthe use of his fundsor borrowingpower; and (Ib+pb) may be regardedeither as the discounthe can obtain fromhis tradingpartner for advance payment- in whichIb and pb representthe interestrate in the foreigncenter and the marginal conveniencehis partnercan receive fromthe funds-or as the interestand conveniencehe can obtain himselfby puttingthe exchangefunds aside in the foreigncenter pending the futuredate of payment. It may then be observedthat hedgingby advance purchase of spot exchangereally implies an interestarbitrage operation by the hedger himself;for ERs-SR[1 + (Ia+pa) - (Ib+pb)]= ERs-FR+FR-SR[1 + (Ia+pa) -(Ib + pb)] That is, hedgingby advance purchaseof spot exchangeis equivalentto acting firstas an interestarbitrager in buying spot exchange against

13 Spraos, op. cit., pp. 92-95.

This content downloaded by the authorized user from 192.168.52.68 on Wed, 14 Nov 2012 22:10:02 PM All use subject to JSTOR Terms and Conditions 94 INTERNATIONAL MONETARY FUND STAFF PAPERS a sale of an equal amountof forwardexchange and then as a hedgerin buyingthe forwardexchange supplied by himselfin the formercapacity. If the hedgerconcerned attains his equilibriumas an implicitinterest arbitrager,so that, in conformityto (5) above, FR-SR P= SR = (Ia+p)-- (Ib+pbI) SR or FR=SR[1 +(Ia+p) - (Ib+pb)] then ERa-SR[1+ (Ia+pa)- (Ib+p )]= ERa-FR i.e., the two ways of hedgingwould be indifferentto him. Mutatis mutandis,the analysis is the same forexporters who hedge by advance sale of spot exchange (includingthe discountof draftson theirtrading partners or theirpartners' banks). Thus it may be assumed that all currentlycontracted imports and exportsthat need hedging (which means practically all importand export contractsthat are not directlyfinanced by foreignlong-term investment)automatically constitute demands forand supplies of for- ward exchangeon the forwardmarket, as long as those importersand exporterswho hedge theircommitments by advance purchasesor sales of spot exchangeare treated as both hedgersin the forwardexchange marketand implicitinterest arbitragers. It is sometimespointed out that, apart frominternational trade in goods and services,foreign investments and the holdingsof internation- ally traded commoditiesmay give rise to demands for hedging by forwardexchange. However, as describedabove, hedgingof short-term foreigninvestments by means of forwardexchange is simplya compon- ent part of coveredinterest arbitrage. The demandsfor (or suppliesof) forwardexchange arising from such operationshave already been clas- sifiedas arbitrager'sdemands (or supplies) (see section,Covered Inter- est Arbitrage,above). As for long-termforeign investments, the ex- change risks involvedtherein cannot be adequately hedged by means of forwardexchange. An exchangecontract due in threemonths is an inappropriatehedge for a ten-yearbond. Insofar as holdingsof inter- nationallytraded commoditiesare concerned,the facilitiesof hedging are much more adequately providedby the futuresmarkets in those commodities. Therefore,the assumptionwill be made here that the demand and supply of forwardexchange for hedging purposes arise almost entirely fromcontracts of importsand exportsof goods and services,and that other sources of demand or supply for hedgingpurposes either are already accountedfor as arbitragers'demands or are negligible.

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Equilibrium of the Forward and Spot Exchange Markets

The forwardrate of exchange,like all otherprices on a freemarket, will be determinedat the level wheredemand equals supply.If supply is treatedas negative demand,as it was above, then the forwardrate will be determinedat the level whereaggregate net demand (or excess demand) for forwardexchange on the part of all dealers in the for- ward marketis zero. That is to say, if it is assumed that there is no governmentintervention, the equilibriumcondition of the forwardex- change marketis 2Dit + ZDjt+ (Mt-M ) - (Xt-X*) =0 (24) whereZDit is the aggregatenet demand forforward exchange on the i part of interestarbitragers (including the implicit arbitragerswho operateas speculatorsor hedgersat the same time); ZDjt is the aggre- i gate net demand on the part of speculators(including those merchants who deliberatelyleave parts of their foreignexchange commitments unhedged); Mt measures import contracts currentlyentered into; M* is the part of currentimport contracts directly financed by long- term foreigninvestments; Xt representsexport contracts currently enteredinto; and X* is the part of currentexport contracts directly financedby long-terminvestment abroad by domesticresidents. Since the amount that importerswould actually have to pay for theirforeign exchange obligations, including the premiumfor exchange risks, and the amount that exporterswould actually receive in do- mesticcurrency for their sales proceedsabroad, net of the premiumfor exchangerisks, are governedby the forwardrate, currentimports and export contractsare primarilyfunctions of the currentforward rate ratherthan of the currentspot rate; viz., (Mt-M*) = M{ FRt (25) (Xt-X) =X{ FRt} (26) Provided that the spot exchangerate is given, e.g., pegged by the monetaryauthorities, equations (15), (22'), (24), (25), and (26) would be sufficientto determinethe currentforward rate togetherwith the aggregatedemand for forwardexchange on the part of all arbitragers (implicit as well as explicit); the aggregatedemand of forwardex- change on the part of speculators; currentimport contracts; and cur- rentexport contracts. The determinationof the forwardrate is illustratedby Diagram 1.

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DIAGRAM 1 Exchonge Rote Mt- Mt Xt-xt

\Rt· j

In this diagram, (M -M*) is representedby a ratherinelastic down- ward sloping line, and (Xt- X*) by a ratherinelastic upward sloping line. The aggregatespeculators' demand for forwardD|t, exchange, s. Ditt~~~i

equals ER*, speculators' demand wwould ould beI negative\ (i.e., -ER- \Yi r Yi4

the forwardrate and the spot rate (ratherthan a functionof the ab- solute level ofthe former),the positionof this curve would obviously shiftwith any change in t spothe rate. If the spot rate is pegged,as is assumed forthe time being,the forwardrate is determinedas fol-

14See equation (22') above. When FRt=ER*, equation (22') becomes

i i,Yi I'Yi Thus speculators' aggregate demand will be negative at the forwardrate equal to ER'j,solut if the right-hand side of this equation is negative; and conversely.

This content downloaded by the authorized user from 192.168.52.68 on Wed, 14 Nov 2012 22:10:02 PM All use subject to JSTOR Terms and Conditions THE THEORY OF FORWARD EXCHANGE 97 lows: Add the horizontaldistances between the speculators'demand curve(ED,t) and the verticalaxis to the correspondinghorizontal i distancesbetween (M -M*) andthe axis to formthe (Mt-M*+ ED j) curve.The equilibriumforward rate (giventhe spot rate, SRt) willthen be therate at whichthe excess of the demand of importers and specula- torsover the supplyof exporters,CD in Diagram1, is exactlyequal to thearbitragers' supply (negative demand), AB; thatis, (Mr-M*) + ED t-(Xt-Xt*) = -EDt, as indicatedby (24). j i If thespot exchange rate is notpegged by themonetary authorities butmust be regardedas an endogenousvariable dependent upon, inter alia, arbitragers'purchases or sales of spotexchange, then the system ofequations outlined above is notdeterminate until one more equation is added,viz., that for equilibrium of the spot exchange market. In other words,the forwardrate is indeterminateunless the spot rate is de- terminedat thesame time. For the sake of simplification,assume that all importand export contractsuniformly stipulate for payments in 90 days,to coincidewith thelength of forwardexchange contracts; then the equilibrium of the spotexchange market (i.e., equality between the supply of and demand forspot exchange) may be writtenas (Mt_90-M-9o) - (Xt-90-X_t-9) +[Lt- (X*-M*) ]= (Dit- 2Dit_9o)+Gt (27) i i where(Mt_9o-M*_ 9) denotes importorders, not directlyfinanced by foreignlong-term investment at home,that are currentlydue forpay- ments; (Xt_9o-X*_90)denotes exportorders (excludingthose directly financedby domesticlong-term investment abroad) currentlydue for receiptof payments; Lt representsnet currentlong-term capital out- flow (or inflowwhen negative) and, therefore,Lt-(X*-M*) denotes the changein net currentlong-term capital movementnot used directly to financeexports or imports;(ZDit-, Di-t_o), as already explained above,represents the net sales (or purchaseswhen negative) of spot exchangeby arbitragersto coverthe netincreases (or decreaseswhen negative)in theirforward positions; and Gt is thenet sale (purchase whennegative) of spotexchange by themonetary authorities of either ofthe two countries concerned15 for stabilization purposes. In thisequation, all thelagged variables are ofcourse predetermined andhence totally independent of the current spot rate. Only ED t,Gt, i Lt,X*, and M* are functionsof the currentspot rate,and the last 15 The sale of sterlingfor local currencyby the U.S. monetaryauthorities is equivalentto the purchaseof dollarswith local currencyby the Britishmonetary authorities.To avoid confusion,however, we mustcontinue to call one currency (say, sterling)the foreignexchange and the other (say, dollars) the domestic currency.

This content downloaded by the authorized user from 192.168.52.68 on Wed, 14 Nov 2012 22:10:02 PM All use subject to JSTOR Terms and Conditions 98 INTERNATIONAL MONETARY FUND STAFF PAPERS threemay not be veryelastic with respect to thecurrent spot rate. The role ofEDit is particularlyimportant inasmuch as it is not onlya functionof the spot rate, but is also a functionof theforward rate. It thusprovides the vital linkbetween the spot and forwardmarkets. In fact,by singlingout ZDit and shiftingit to one side, (24) and (27) can be combinedinto a singleequation, as follows: 2Dit= (Xt-X*) - (Mt-M*) -2Djt = [L- (X -M*) ]-Gt i j

+- { Dit_so+- (Mt-9o-M*)-(Xt90-X -90) 1 (28) i

This meansthat the forward and spotrates will be jointlydetermined in sucha waythat, at thejoint equilibrium of both markets, the excess supply(or demandif negative)of forwardexchange (excluding arbi- tragers'demand for foreign exchange) on theforward market and the excessdemand (or supplyif negative)for spot exchange(again ex- cludingarbitragers' supply of spot exchangein orderto covertheir currentpurchases of forward exchange) on thespot market would both be equalto thedemand for forward exchange on thepart of arbitragers underthe equilibriumforward and spotrates (i.e.,under the equilib- riumforward premium or discount). This jointequilibrium condition of the two markets is illustratedby Diagram2. At theequilibrium spot rate, OH, theexcess supply of spot

DIAGRAM 2 Spot Rote ForwardRote Mt- Mt Xt- Xt

0Dit E F

A + H ...... Mt-M.1 JDjt

0 Amount of spot exchange

This content downloaded by the authorized user from 192.168.52.68 on Wed, 14 Nov 2012 22:10:02 PM All use subject to JSTOR Terms and Conditions THE THEORY OF FORWARD EXCHANGE 99 exchange (exclusive of arbitragers'demand for spot exchange) is AB; and at the equilibriumforward rate, O'F, the excess demand for for- ward exchange (exclusiveof arbitragers'supply, in the presentcase, of forwardexchange) is CD. The joint equilibriumcondition expressed in equation (28) implies that AB=CD=EF, where EF is arbitragers' O'F-OH supplyof forwardexchange, given the forwardpremium, OH In Diagram 2, the functionGt, i.e., the supply of spot exchangeby the monetaryauthorities, has been drawnas a fairlyelastic increasing functionof the spot rate. The shape and elasticity of this function depend,of course,upon the stabilizationpolicy adopted by the mone- tary authorities;no attemptis made here,however, to discuss this in detail.

Implications for Forward Exchange Rate Policy The theoryoutlined above should shed some lighton the moot ques- tion of whetherthe monetaryauthorities should intervenein the for- ward exchangemarket-a questionwhich has been debated ratherex- tensivelyin the United Kingdom.16 It has been assumed in equation (24) above that thereis no official interventionin the forwardexchange market. If the monetaryauthor- ities of the countrywhose currencyis underspeculative pressure in the forwardexchange market attempt to offsetthe speculativepressure, the equilibriumcondition on the forwardexchange market would be Dit = (Xt-X*) - (M,-M*) - 2Di+ Vt (24') i i where Vt is the amount of officialintervention (sales) in the forward exchangemarket, which may be presumedto have a sign oppositeto that forthe net aggregatespeculative demand (purchases), EDjt. i The equilibriumcondition of the spot exchangemarket remains as stated in equation (27), whichmay be rearrangedas follows: D,= [Lt- (X*-M*) ]-Gt+ { (Mt_so-M_ 0) - (Xt_-o-X*_9) + ZDit_o (27') i i It is assumed that officialintervention in the spot exchangemarket is

16 See John Spraos, "Exchange Policy in the Forward Market: Case for an OfficialPeg," A.E. Jasay, "Case for OfficialSupport," and anonymous, "Case for the Status Quo," all in The Banker, Vol. CVIII (April 1958). See also A.E. Jasay, "Making Currency Reserves 'Go Round,'" The Journal of Political Economy, Vol. LXVI (August 1958), and "Forward Exchange: The Case for Intervention," Lloyds Bank Review (October 1958).

This content downloaded by the authorized user from 192.168.52.68 on Wed, 14 Nov 2012 22:10:02 PM All use subject to JSTOR Terms and Conditions 100 INTERNATIONAL MONETARY FUND STAFF PAPERS carried out by the monetaryauthorities of the countrythat is inter- veningin the forwardmarket through Vt. The crucial questionis what effectan increasein officialsales of forwardexchange in supportof the forwardrate (i.e., an increasein Vt) would have upon officialsales of spot exchange out of reservesin support of the spot rate (i.e., Gt), both (i) immediatelyand (ii) afterthe currentforward sales contracts mature.

(i) The immediate effectof officialintervention on the forwardex- change market The firstpart of this questioncan be answeredeither by differentiat- ing (24') and (27') withrespect to Vt,or by makinguse of Diagram 2, showingthe joint equilibriumof the forwardand spot exchangemar- kets. Let it be assumed that thereis a strongspeculative demand for forwarddollars in the United Kingdom,which pushes forwarddollars to a highpremium in termsof sterling,and that the Britishauthorities attemptto intervenein the forwardmarket to reducethe forwardpre- miumon the dollar (or the forwarddiscount on sterling).If the act of interventiondoes not directlycause any shiftin the demand and sup- ply curvesfor forward and spot exchange,shown in Diagram 2, the im- mediate effectsupon the forwardand spot rates,speculators' and arbi- tragers' demand and supply for forwardand spot exchange,and the drawingupon officialreserves, can all be read offthe diagramby adding the assumed amountof governmentintervention (sales of forwardex- change) to the supply curve of forwardexchange by exporters.This is shownin Diagram 3. A shiftof the (Xt-X*) curveto the rightby the distance Vt would reducethe excess demand forforward exchange that has to be supplied by the arbitragers.The forwardrate of the dollar would tend to fall. At the same time,the spot dollar rate would also tend to fall, because the arbitragers,having sold fewerforward dollars, would buy fewerspot dollars. If the spot dollar rate were always rigidlypegged, this would mean less drain on reserves,but no changein the spot rate. If the spot rate were officiallysupported but not rigidlypegged, this would mean botha reductionin the drawingon reservesand some declinein the spot rate of the dollar in termsof sterling.A fall in the spot dollar rate, however,would cause a downwardshift in the supply-demandcurve of arbitragers,and hence a furtherdecline in the forwardrate but a slight increasein the sales of forwardexchange by arbitragers.Joint equilib- rium in the forwardand spot marketswill be restoredfinally when C'D'=E'F'-A'B', i.e., when the equilibriumconditions (24') for the forwardmarket and (27') forthe spot marketare simultaneouslyre-

This content downloaded by the authorized user from 192.168.52.68 on Wed, 14 Nov 2012 22:10:02 PM All use subject to JSTOR Terms and Conditions THE THEORY OF FORWARD EXCHANGE 101 stored.At thenew equilibrium, both the forward and spotrates of the foreigncurrency would be reduced,the arbitragers'supply of forward exchangeand demandfor spot exchangewould be reduced,and so wouldthe drawing upon official reserves, if the spot rate were officially supported.

DIAGRAM 3 Spot Rate ForwardRate

Mt-Mt

X-X+sumof

Dtit (

GtF

.(C -~' 8',,,, -...... ,...... : : : ::::::::::::

Lt-XI+Mt sum of logged voriablesin equation(28) tX-XtVt 0 Amountof spotexchonge 0 Amountof forwaordexchonge

This is exactlywhat the advocatesof interventionargue in favorof intervention.This argumentis, however,conditioned upon the proviso madeabove, that the act of interventionwould not directly cause any shiftin the demandcurves for forward exchange-in particular, the rathervolatile demand of speculators.If theact ofintervention by the authoritiesshould strengthen the confidence of speculators in thefuture of sterling(i.e., lower their expected dollar rate), their demand curve for forwardexchange would be shifteddownward. The conclusions obtainedabove withregard to the effectsof interventionwould cer- tainlyapply a fortiori.If, on theother hand, as contendedby someof the opponentsof intervention,l7the act of interventionshould further shakethe confidence of speculatorsin the futureof sterling(i.e., raise theirexpected dollar rate), theirdemand curve for forward exchange mightbe shiftedupward. If theupshift of speculators'demand for for- wardexchange as a directresult of officialintervention is substantial, theeffects on forwardand spotrates and drawingson officialreserves couldobviously be reversed. 17See "Case forthe Status Quo" (cited in footnote16), pp. 234-35.

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Occasional interventionby the authoritiesis certainlyunlikely to have any appreciableadverse effectupon the confidenceof speculators in the futureof domesticcurrency. Indeed, the determinationof the authoritiesto supportthe forwardrate and the checkto the outflowof reservesbrought about as the immediateeffect of officialintervention may very well increase confidence.On the otherhand, if intervention is prolonged,and in particularwhen it has to be carriedout on an ever increasingscale to maintainthe forwardrate, the cumulativeforward commitmentsof the governmentmight possibly cause more damage to confidencein the futureof the currencythan the additionaldecline in reservesthat would have occurredin the absence of intervention.For, as may be observedfrom Diagram 3, underthe preliminaryassumption of no effectupon expectation,the amountof governmentsales of for- ward exchangein supportof the forwardrate of the domesticcurrency must always exceedthe resultingsaving in reservesby the inducedde- teriorationin the trade balance plus the increase in speculators'pur- chases. Unless the reductionin the decline of reserveshas a weightier effectupon confidencethan the pilingup of governmentcommitments in forwardexchange, there might be a net adverse effecton confidence when interventionhas been carriedout on an ever increasingscale for some lengthof time. This questionwill be taken up later, followingour discussionof the effectsof an increasein officialsales of forwardexchange after the cur- rentforward sales contractshave matured.

(ii) The deferredeffects of officialintervention on the forwardex- change market The deferredeffects of officialintervention are far morecomplicated than the immediateeffects. Both equations (24') and (27') are differ- ence equations of high orders,since arbitragers'and speculators'de- mands forforward exchange are dependentupon theirown demandsin past periods.Under our specificassumption that forwardcontracts are uniformlyof 90 days' maturity,dependence upon the past in bothcases reaches back 89 days. Interventionby the authoritiesduring the cur- rentday, even if it is discontinuedlater, would have some repercussions on supply and demand in later days. Such repercussionsmay be ex- amined by differentiatingthe pair of equations correspondingto (24') and (27') for periods t+1, t+2, . . . etc., with respect to Vt and s r d(FRt+±) d(FRt+2) d(SRt+1) d(SRt+2) solvingfor . . etc., and, d d,Vt abt dVt dVt .. etc. This is a verylaborious process and we are not,in fact,much

This content downloaded by the authorized user from 192.168.52.68 on Wed, 14 Nov 2012 22:10:02 PM All use subject to JSTOR Terms and Conditions THE THEORY OF FORWARD EXCHANGE 103 interestedin thepossible minor repercussions of a currentintervention. Of greaterinterest is thedeferred effect upon official reserves when the currentofficial forward sales contractsmature. This effectmay be ob- servedreadily from the equilibriumcondition for the spot exchange market. Thereis, however,one falsenotion which should first be set aside, i.e.,the notion that current purchases of forward exchange by specula- torswould automatically lead to a claimfor actual deliveryof spot exchangeupon maturityof the forwardcontracts. This is quite in- correct.For, upon the maturity of a forwardcontract entered into by a speculator,he may decidenot to speculatefurther on the basis of the newcircumstances. He wouldthen simply settle the maturing contract by takingthe profit or loss involvedin thedifference between the new currentspot rate and theforward rate stipulated in thematuring con- tractwithout demanding actual deliveryof spot exchangefrom his oppositeparty or payingthe local currencysum on his own part. Whetheror nothe woulddecide to speculatefurther depends entirely uponhis expectation,his riskposition, and thenew forward rate then prevailing.Even ifhe shoulddecide to renewor extendhis speculative longposition in foreignexchange, it doesnot necessarily follow that he woulddemand spot exchange to hold,a courseof actionwhich, as has beenpointed out above,is equivalentto a combinationof an interest arbitrageand a speculativepurchase of forwardexchange. He will choosethis particular form of speculationonly when the new market conditionsare favorablefor such an implicitinterest arbitrage opera- tion.Thus, the question of the extent to whichspeculators who bought forwardexchange in the past woulddemand actual deliveryof spot exchangeupon maturity depends upon the aggregatearbitragers' de- mandfunction formulated above in equation(11), whichincludes im- plicitas wellas explicitarbitraging operations, applicable at thetime of maturity.The factthat some speculators have contractsof forward purchases(or sales) maturingat the momenthas no directinfluence uponthe aggregate arbitragers' demand for spot exchange.18 18 It may,however, have some remoteindirect effect upon arbitragers'demand forspot exchange.For the maturingof forwardcommitments previously entered into would alter,to some extent,the risk positionof the speculatorconcerned and thusmight affect his willingnessto makenew speculativepurchases and sales, as indicatedin equations(18) and (21). Indirectly,this might affect the spot ex- changemarket through the forwardrate, with interest arbitragers acting as the link betweenthe two markets.However, as equation (18) shows,the effectsof past commitmentsupon the marginalrisk of a speculatordiminishes in weight withthe proximityto maturity,so that the eventualmaturing of a forwardcon- tractshould not have any abrupteffect upon the marginalrisk of the speculator concerned.

This content downloaded by the authorized user from 192.168.52.68 on Wed, 14 Nov 2012 22:10:02 PM All use subject to JSTOR Terms and Conditions 104 INTERNATIONAL MONETARY FUND STAFF PAPERS The moredirect effects of officialintervention in the currentfor- wardexchange market on the futurespot exchange rate and thedrain uponofficial reserves, when the current forward contracts mature, may be observedfrom the lagged variables in ourequation for the equilib- riumof the spotexchange market, i.e., equation(27'). Whencurrent forwardcontracts mature (say, at t+90), theequilibrium condition of thespot market would be

Dit+90o= Lt+90o-X*+90+M*+90-G-+9+ { (Mt-M*) - (Xt-X*) +DDit) (27") t t The termsinside the parentheses are thevariables in theequation for the currentequilibrium of the forwardexchange market, i.e., equation (24'), thatwould be immediatelyaffected by currentofficial interven- tionin the forwardexchange market. They would, in turn,affect the futureequilibrium of the spot exchange market when they reappear as laggedvariables in equation(27"). The termEDit reappearsas a laggedvariable in the equilibrium conditionfor the spot exchangemarket because the net demandfor spotexchange on the part of arbitragersto covertheir net changein forwardpositions at thetime of maturity of current forward contracts, i.e., at t+90, is equal to - (ZDit+9o-EZDit). The maturityof arbi- i i tragers'current net forwardpurchase contracts (a positiveZDit) i at t+90 would,other things being equal, oblige them to add thatmuch spotexchange to theirholdings in orderto maintaina zeronet position. On theother hand, the maturity of their current net forward sales con- tracts (a negativeEDit) wouldenable them to releasethat much i spot exchangefrom their holdings and still maintaina zero net position. Thus,if currentintervention by the authoritiessucceeds in reducing arbitragers'net sales offorward exchange (and hencetheir current net purchasesof spotexchange), then, at thematurity of currentforward contracts,the spot exchange that might be releasedby the arbitragers wouldbe correspondinglyreduced. In otherwords, the currentreduc- tionin arbitragers'demand for spot exchange brought about by official interventionis merely shifted to a laterperiod when current forward contractsmature. Considerationshould also be givento thedeferred effects of the ad- verse influencesof officialintervention upon currentimports and exports,(Xt-X*) and (Mt-M*). As pointedout above,the profit- abilityof an importor exportcontract net of exchangerisks depends uponthe current forward rate rather than the current spot rate. Official interventionin the forwardexchange market at present,by loweringthe

This content downloaded by the authorized user from 192.168.52.68 on Wed, 14 Nov 2012 22:10:02 PM All use subject to JSTOR Terms and Conditions THE THEORY OF FORWARD EXCHANGE 105 currentforward rate (i.e., bolsteringthe forwardvalue of the domestic currency),would thereforehave an adverse effectupon the current balance of trade at the contract stage. Obviously, this would later have an adverse effecton the actual balance of paymentsin spot ex- change,in additionto the postponeddemand forspot exchangeon the part of arbitragers.l9 Therefore,unless the veryact of interventiondirectly exerts a favor- able influenceon speculators'confidence and expectationas to the sta- bilityof the domesticcurrency, official intervention can be expectedto relievethe currentpressure on the spot exchangemarket (and henceto cut the currentdrain on officialreserves if the spot rate is officiallysup- ported) merelyby shiftingthe currentpressure to a later periodand at the cost of worsening,to some extent,the currentbalance of trade. Unless the currentpressure on the balance of paymentsis expectedto be reversedshortly, or is expectedto be curtailed by the confidence inspiredby the very act of intervention,there does not seem to be a strongcase forintervention. This pointmay be illustratedby consideringan imaginarycase where the currentpressure on the exchangeis expectedto continuefor more than threemonths (say, a year), and is expectedto disappear aftera year but not to be reversed.During the firstthree months, the author- ities can generallysucceed in offsettingthe currentpressure on the for- ward and spot exchangerates and stoppingthe drain on officialreserves by an appropriateamount of officialsales of forwardexchange. If the same pressurecontinues into the next threemonths, however, the au- thoritieswould have to double their interventioneffort in order to achieve the same result; forthey must, at the same time,offset the ad- verse pressureshifted from the firstthree months to the currentperiod. By the same token,the authoritieswould have to trebletheir interven- tion in the thirdquarter and quadrupletheir intervention in the fourth quarter.By then it is quite possible that the cumulativelyexpanding scale of interventionand forwardcommitments in foreignexchange on the part of the governmentmight cause more damage to confidence than the extradecline of reservesthat would have occurredbut foroffi- cial intervention;for, as was shown above, unless officialintervention has a directfavorable effect upon speculators'expectation, the pilingup ofthe government'sforward commitments would always proceedfaster than the lesseningin the decline of reservesbrought about by inter- vention.Even if this net damage to confidencecan be avoided by such

19 The deferred effectson the spot exchange market of an officialintervention in the forwardexchange market appear to be totally neglected by the participants on both sides of the debate on forward exchange (see articles in The Banker, cited above in footnote 16).

This content downloaded by the authorized user from 192.168.52.68 on Wed, 14 Nov 2012 22:10:02 PM All use subject to JSTOR Terms and Conditions 106 INTERNATIONAL MONETARY FUND STAFF PAPERS devices as keepingthe government'sforward commitments undisclosed, it is clear that, afterthe period of stressis over,the accumulatedpres- sure of the past fourquarters would still be shiftedto, and concentrated in, the next period.To offsetthe postponedand cumulatedpressure of past periods,the authoritieswould still have to draw upon officialre- serves unless they should resortto furtherpostponement by continued intervention.The dangerof such a policy of postponement,apart from its real cost of worseningthe currentbalance of trade,is that it might be habitually adopted as the line of least resistance,to the neglectof the monetaryand fiscal correctivemeasures that are really necessary to correctthe basic balance of paymentsdifficulties. The conclusion,therefore, is that,while officialintervention (or offi- cial counterspeculation)in the forwardexchange market is a useful instrumentto offsetshort-run speculative pressure on the exchangerate, it is of doubtfulvalue in copingwith prolonged weakness in the balance of payments.

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