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Currency Swaps, Financial Arbitrage, and Default Risk Author(s): Nilufer Usmen Source: Financial Management, Vol. 23, No. 2 (Summer, 1994), pp. 4357 Published by: Blackwell Publishing on behalf of the Financial Management Association International Stable URL: http://www.jstor.org/stable/3665738 Accessed: 15/01/2009 11:17
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Financial Currency Swaps, Default Risk Arbitrage, and
Nilufer Usmen
Nilufer Usmen is Assistant Professor in the Finance and Economics Department, RutgersUniversity, Faculty of Management, Newark,New Jersey.
Abstract: This paperconstructs modelfor measuring gains realizedby a the both counterparties a currencyswap that takes place in an international to market whichfinancialarbitrage in exist. Conditions derived are opportunities for zerosum nonzerosum and outcomesfor bothdefaultfree swapsandrisky interestrate/exchange parities.In an rate swaps in termsof statecontingent international imperfect capitalmarket, swapswithdefaultriskcangive rise to greatergains than a defaultfreeswap. Possibilityof default,state by state, becomes a screening device for favorableand unfavorable exchange rate outcomesfor each counterparty. Thus,the possibilityof default,per se, is not the sole determinant the degree of credit risk in a swap agreement. of of Covariability exchangeratesanddefaultstatesplays an offsettingrole.
* Manyrecentstudieshave addressed anal) of interest the tsis rate swaps. In these studies, there is an ongoing debate ge concerningthe importanceof financialarbitral in explain:et. ing the existence of the interestrateswap mark Some that favor financial arbitrageas a motive argue that the quality its spreaddifferentialbetweentwo marketspreser a financial of thatcan be sharedto the b>enefit both arbitrage opportunity ler Beidleman (1985, 1992), Bicks: and Chen parties. (See (1986), and Felgran (1987).) As a result of comparative advantage, their borrowing costs are unami biguously reits duced.Implied(butnot stated)in these argumer is thatboth partiesincreasetheir value throughswapping.Otherstudies ry argue against this view by noting that the vey process of should sooti eliminateit. exploiting this kind of opportunity Turbull (See Smith,Smithson,andWakeman(1986, 19J88), ond (1987), and Wall and Pringle(1989).) The sec< argument against financial arbitrageis that the swap should be a zerosumoutcomeeven if financialarbitrage the sourceof is theireconomic benefits.These studiesrightful] dismiss the ly importanceof financial arbitragein an efficient, complete, perfect,and integratedworld capitalmarket. Currencyswaps, however, have been large ignored in 'ly the swap literature.This study attemptsto fil11that gap. It focuses on currency swaps exclusively in th belief that ie substantialdifferences exist between currenc swaps and y
The author wishes to thankStavrosThomadakis, Mar Harry kowitz,Anthony Tessitore, Roger Mesznick,the formerEditor,JamesAng, the Editors,and threeanonymousrefereesfor helpfulcomments.Researchsupportfromthe RutgersUniversityResearchCouncil is gratefullyacknowledged.
interestrate swaps thatwarrant separateanalysis.l a Withcurrencyswaps,one has to framethe analysiswithin an international capitalmarketssetting.Even if the generally acceptedview is thatdomesticcapitalmarketsare integrated (efficient),thereis growingempiricalandtheoreticalsupport thatinternational capitalmarketsaresegmented(inefficient). of international Segmentation capitalmarketsmay be caused restrictions on international portfolio by government holdingsof individualinvestors.In most countries,thereare limitations on individual investor's access to foreign securities.Thus, it is plausibleto assume segmentedcapital markets as an environmentin which firms conduct their international financialand real activities. In such an environment,however, firms can design strategiesto reapthe potentialprofitscreatedby restrictions on portfolio holdings of individuals because corporate projects are not subject to the same type of restrictions.2
iFor example, principalamountsare exchanged in currencyswaps but not in interestrateswaps,whichhas a significanteffect on defaultriskexposure. in Furthermore, a pure interestrate swap (i.e., in the same currency)the source of additionaluncertainty is (besides cash flow uncertainty) interest rate fluctuations.In a credit swap (interestrate swap with two currencies involved),however,thereis bothinterestrateandexchange rateuncertainty along with cash flow uncertainty. 2This is not to say that foreign direct investment by firms is free of government regulation.To illustrate, consider the following limitations investors. imposed on foreign corporateand noncorporate In the United States. projectsinvolving naturalgas importsinto the United States must be approvedby the Economic RegulatoryAgency (ERA). the Departmentof Energy. and the Federal Energy RegulatoryCommission (FERC).Intheirreview,theagencies can limitthevalueof importsto protect
FinancialManagement,Vol. 23, No. 2, Summer 1994, pages 4357.
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/ SUMMER MANAGEMENT FINANCIAL 1994
Firmshave an advantageover individualsbecausethey have income generatedin both markets(real activities) and can design securities(claims againsttheirincome) thatwill have differential valuation in the two markets. One such
transaction is a currency swap, which firms can use as a financing alternative.
This paperanalyzeshow firms with foreignprojectscan exploit international capital market segmentation via currency swaps. I show how capital market segmentation may lead to nonzerooutcomes and why nonzerooutcomes do not necessarilyyield positive gains for both partiesas put forwardin the comparativeadvantageargumentsbased on rate differentials.3 In defaultfree currency swaps, heterogeneous expectations are sufficient to achieve this result. Anotherconcer in the swap finance literatureis a true of understanding the default implications of this contract. and are Both the counterparties the intermediary interested in knowing how to assess the creditrisks inherentin swaps. To this end, Cooper and Mello (1991) attemptto price the defaultrisk premiumsin swaps. They assume a perfectand integrated capital market in which swaps are zerosum results,such games. They obtainsomewhatcounterintuitive
U.S. public interest. In Canada, investments requiringreview must pass the "net benefit to " Canada"test andmustnot threaten cultural heritageandnationalidentity." Accordingto the Investmentin CanadaAct, investmentsrequiringreview by The Foreign InvestmentReview Agency (FIRA) include any "direct" acquisitionsof Canadianbusinesses by nonCanadianswith assets of $5 million or more and any "indirect"acquisitionsinvolving assets over $50 million. For Americans, the thresholds are $150 million for direct acquisitionsand $500 million for indirectacquisitions.These rules do not apply to investmentsthat acquirecontrolof Canadianbusinesses engaged in the productionof uranium,financialservices, transportation services, or a culturalbusiness. In Japan,The Foreign Exchange and ForeignTradeControlLaw restricts imports and exports of certain categories of goods as well as goods originating in certain countries. According to this law, inward direct investmentis also regulatedand is subjectto review. Direct investmentin several specified industries (agriculture,fisheries and forestry, 50% or in greaterownershipin mining)may not be permitted. Foreignparticipation otherindustries,such as banking,financialservices, utilities,andinsurance, is also regulatedunderspecial statutes.
as wealthtransfers fromstockholders bondholders. to Within theirframework, analysisof swap defaultalso falls short the of depicting the interactionsof default risk with capital marketimperfections,the main finding of this study. In this study,I find thatin a segmentedinternational capitalmarket. firms can enhance shareholderwealth with risky currency swapsbeyondwhattheycould achievethrougha defaultfree swap.4 This resultimpliesthatcreditriskis not an increasing functionof the probability default,as would be the case in of a perfect and integrateddomestic or world market.5 In currencyswap credit risk assessments, a second factor,the of covariability exchangeratesanddefaultstates,plays a key role.6 The second factormay offset the effect of the risk of defaultat certaintimes, and the swap partners may enhance value by defaulting. Thus, the interaction of foreign exchange risk and default risk is crucial to credit risk assessmentsfor a currencyswap. This finding is supported by an options analysis of defaultin currencyswaps. I show that the default option can best be viewed as a "hybrid" currency call option that is firmspecific and can have positive or negative values. My analysis suggests that the can counterparties design theriskycurrencyswap so thatthis optionhas positive value to both partiesto the swap. The analysis of this paper follows Thomadakis and Usmen (1991), which focused on international capita] structure decisions of firmsoperatingin segmentedmarkets Likewise, the presentpaperanalyzes the benefits that firms canreapthrough currencyswaps in a similarsetting.The key in both analyses is that firms are able to overcome barriers to arbitragebecause they have specific projects (projects with a particular of pattern cash flows acrossstates,thuswith a particular default structure) enabling them to exploil acrossthe same states.Thus specific arbitrage opportunities only those firms with these specific projects could benefil from the statedependent arbitrage profit opportunities.
I. Elements of the Modeland FinancialArbitrage
Assume a simple twocountry worldthe domestic
Similarrestrictionsapply in othercountries.Details are availablefrom the country and the foreign country. The capital market is authorupon request. ' This resultemergesbecause the presentpaper,contrary previouslycited 4This is to parallelto the wellknown result that risky debt may create valut work. bases its analyses on presentvalues ratherthanratedifferentials.As by completing the market(Senbet and Taggart (1984)). In contrast,m) Turnbull(1987) has also suggested, the latteranalysis can be misleadingif analysisassumescompletemarkets; defaultriskyswaps createvalue due t( financialinstruments differ in design andrisk.Thus,insteadof invokingrate marketsegmentation. differentialsin swapping,the conceptof value creationis invokedsince any an chargesin contracting cost savingsdue to ratedifferentials shouldnecessarilyenhanceshareholder 5Solnik (1990) finds thatthe markup intermediary of wealth. Furthermore, Wall (1987) argues that cost savings may be related a swapwitha riskyclient is a functionof the subjectiveprobability defaul to avoidanceof agency costs associatedwith longtermdebt via an interest alone. This is due to his assumptionthat interestrates and default risk are rate swap. This source of cost savings is a separateissue and may interact uncorrelated. with cost savings or dissavings due to financialarbitrage. case of savings 6Studiesthat addressthe issue of the stochastic interdependence cast In of due to financial arbitrage,savings on agency costs will furtherenhance flows and exchange rates in the firm's financing decision are rare in the value. However,if for a partytherearedissavingsdue to financialarbitrage. finance literature.Recent examples are Thomadakisand Usmen (1991 the benefit of any agency cost savings may be wiped out. 1994) in which the firm's projectfinancingdecisions are examined.
ANDDEFAULT RISK USMEN CURRENCY I ARBITRAGE, SWAPS, FINANCIAL
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costs andno complete,efficient, andperfect(no transactions assumethatinvestorsarerisk taxes) in each country.Further is neutral.Risk neutrality assumedto simplify the exposition and to derive results that are expressed in terms of familiar expectationforms. With risk aversion, similarresults could be obtained. There are constraints on internationalasset holdings, in the form of capital controls,and restrictionson shortselling by investorsof both countries.This assumption is realistic and is crucialfor the results.It allows the capital marketsof the two countriesto be segmented,which gives to rise to the potentialfor financialarbitrage exist acrossthe markets. International market segmentation due to international investment restrictions is, by now, welldocumented.(See, for example, BonserNeal,Brauer, Neal, and Wheatley (1990), Errunzaand Losq (1985), Eun and Janakiramanan (1986), Gultekin, Gultekin,and Penati and Schwartz (1986).) Another crucial (1989), and Jorion assumption is that domestic and foreign investors hold heterogeneousbeliefs aboutthe probabilitiesof futurestates of nature.Underrisk neutrality, assumptionis necessary this to have the independent gains for both partiesto be positive. With risk aversion and homogeneous beliefs, differentrisk factorswould have served the same purpose.7 adjustment Within the above framework,the following notation is defined, where S is a set of states, s is an element of S, and B is any subset of S: = stateprobabilitiesassessed by p(s), p*(s) domestic and foreign investors, respectively.The probabilityof an event B is P(B) = I p(s) and B P*(B) = I p*(s) in the domestic B and foreign market,respectively. one plus the riskfreeratein the domestic and foreign markets, respectively. cash flows of assets statecontingent denominatedin domestic and foreign currencyat t = z, respectively. spot currencyexchangerateat t = 0, expressed in units of domestic currencyper unit of foreign currency.
statecontingent spot currency exchangerate at t = x, expressedin units of domestic currencyper unit of foreign currency. The noarbitragecondition for a foreign asset with an income of X*(s) and its domesticperfectsubstituteyielding X*(s)e(s) is X*(s) (p(s) (eop)e(sp(s))=0. p(s))=O. EX*(s)
e(s)
=
(1)
In otherwords, whenevera domestic investorsells shortthe foreign asset, converts the proceeds into the domestic currency, and purchases the domestic perfect substitute, there should be zero profit. A condition sufficient for Equation(1) to hold is8 ( P*(s)  e p(s)) = 0 r r* for alls. (2)
r, r
X(s), X*(s)
Note that Equation (2) expresses a statecontingent, noarbitragerelationship between the prices of primitive securities that are denominated in different currencies. Alternatively, a positive value for the expression on the lefthand side of Equation (2) would imply potential arbitrage profitsin the shortsale of a pureclaimdenominated in the foreign currency coupled with the simultaneous purchaseof the perfect substitutein the domestic country. Likewise, a negativevaluewould indicatearbitrage potential in the simultaneous purchaseof a foreignpureclaim andsale of its perfectsubstitute the domesticmarket. the absence in In of capital controls and short selling restrictions,the above relationships,seen in Equation(2), should strictlyhold for international marketwhere every state.In such an integrated all domestic and foreign assets are tradedby both sets of will ensurethat Equation(1) always investors,no arbitrage holds. However, once one introducesrestrictionson trading of certainassets and impedimentsto shortselling, therewill be assets for which Equation(1) fails to hold. A necessary and sufficient conditionfor the expression on the lefthand side of Equation(1) to be differentfromzero for some assets is (eo p*(s) r: r? p(s)) 0 forsomes. (3)
eo
=
7For results with risk aversion in a similar setting, see Thomadakisand Usmen (1991). A relatedpaper,Tessitore (1994), considersreal decisions of oligopolistic firms in segmentedmarketsin which risk aversionfactors may differ.
SNote that with homogeneous beliefs, p(s) = p*(s) and the following condition implies that e(s) must be a constant. Thus. perfect. integrated marketsin which investorsare risk neutraland hold homogeneous beliefs about state probabilitiesis inconsistentwith flexible exchange rates.This should not be a surprisesince the marketdescribedabove will be identical to a domesticmarketwherethe unitof currencyis the same in nominalterms. eo = e(s) = 1. A fixed exchange rate regime in which e(s) = eo r/r" would also be compatiblewith this marketstructure.
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Condition (3) is my descriptionof segmentedinternational currency,is capitalmarkets.9 ) p(s)_A weakerconditionthatmight hold even in a segmented eo r e(s)r* international capital marketis an integralcondition known as Uncovered Interest Rate Parity (UIRP). Looking at which is equivalentto conditionfor a risklessforeign 1 eo Equation(1), the noarbitrage asset is given by r* rEel(s)' D rZ( ?p*(s)p(s))=0, (4)
(7)
(8)
where D* is the certainpayoff on the foreign riskless asset. If the lefthandside of Equation(4) has a nonzerooutcome, it would indicate arbitragepotential in tradingthe foreign riskless asset for the domestic investor.Equation(4) can be rewrittenin the familiarform underrisk neutralityas eo Ee(s) r r* or as r Ee(s) eo r* (5)
where E is the expectationsoperatorin the domesticmarket. the Equation(5') states thatunderrisk neutrality, price ratio of two riskless assets predictsthe rateof changein exchange for rates when opportunities arbitrage profitcease to exist. Arbitragecan take place for riskless assets in the foreign country,such as governmentbonds andgovernmentinsured bankdeposits,with the resultthatEquation(5) holds, butthis condition does not imply the absence of arbitrage opportunitiesfor all risky foreign assets. There is partial segmentation.To see this, considerEquation(1) again.It can be rewrittenas eE*X*(s)= Ee()E*(s) r + cov(Xi(s),e(s)) r (6)
Equations(4) and(7) aretriviallyequal to each otherand to zero in a complete and integrated market in which Equation (2) holds. The same statement holds true for Equations(5) and (8). One would also expect them to be simultaneously equal to zero in a segmented market whenevercapitalcontrolsandshortselling restrictions apply only to risky assets. However, underrisk neutrality,UIRP will not hold in both markets unless Ee(s) = 1/E*el(s). Clearly, this condition is possible only in a frameworkof heterogeneousexpectationsdue to Jensen's Inequality. In general,Equations(4) and (7) do not imply each other in segmented capital markets.To show this, reexpressthe terms in Equation (7) into the domestic currency by multiplyingthroughby eo to rewriteit as DEI (s p*(s)e(s) r* p(s)) = 0. (9)
where E* is the expectationsoperatorin the foreign market. It should be clear from Equation(6) thatUIRP would imply no arbitrageonly for those risky foreign assets for which X*(s) and e(s) are independentand only if expectationsare homogenous, E* = E. Inthe abovediscussions,uncoveredinterestratearbitrage was presented from the point of view of the domestic concernedthe riskfree investors.The arbitrage opportunity asset and its perfect substitute,a risky asset in the foreign domestic market. Similarly, the noarbitragecondition for the domestic riskless asset paying D and its risky perfect substitute in the foreign market, denominatedin foreign
9Note that this condition is not a result of market incompleteness.The internationalcapital market, as well as the national capital markets, are assumedto be complete in our study.
In Equation(4), therearepotentialprofitsas domesticinvestors arbitrage foreignrisklessassets andtheirrisky domestic perfect substitutes.Equation(9) demonstratesthe potential for arbitrageprofits, denominated in domestic currency, when foreign investorstradein domesticriskless assets and their risky foreign perfect substitutes. It is evident from Equation(9) thatif UIRPholds in the domestic market(and Equation (4) is valid), it will not necessarily hold in the To foreignmarket. see the significanceof thisresult,suppose one set of investors,say foreigninvestors,arerestricted from the domestic riskfree asset. Domestic investors, trading however,can tradethe foreignriskfreeasset as well as their own. Tradingby the unrestricteddomestic investors will ensure that Equation(4) holds, but this does not imply the validity of Equation (9). Since the foreign investors are restricted,arbitrageopportunitieswill still be possible in tradingthe domestic riskfree asset in the foreign market. fromtrading Obviously,if bothsets of investorsarerestricted the riskfree asset of the other country and/or there are restrictionson shortselling, neitherEquation(4) nor Equation (9) may hold. It is also interestingto note here thatany positive deviationfrom equalityin Equation(4) may not be offset by a negativedeviationfrom equalityin Equation(9). The presenceof l/e(s) in Equation(9) will make the magnitudes differentbut not necessarily the signs. The arbitrage profitsof domesticand foreign investorsdo not wash away.
USMEN CURRENCY / ANDDEFAULT RISK SWAPS, FINANCIAL ARBITRAGE,
47
This is so because the riskless assets in the two marketsare not perfect substitutes.It might also be possible that both deviationshave the same sign. This would simply imply that profitsexist for the sale or purchaseof bothdomesarbitrage tic and foreignriskfreeassets. I next consider the possibility of the forward sale and purchaseof both currenciesfor the time period [0,t]. Note that it is only possible to contracta fixed amountof future sale of a currency;there are no statecontingentforward contracts.Thus, I can carrythe arbitrageargumentthrough the riskfree assets. Note that with a forward currency market,the foreign asset and its domestic perfectsubstitute are both riskless. Covered interestrate arbitrage operations in domestic and foreign marketsyield (10) eo f
r* r
aforementionedstudies on capital market segmentation is that governmentimposed regulationson investor access to investments,such as restrictionson foreign investmentsby domestic investors and restrictions on domestic security holdings by foreigners, has resulted in an international capital market that is segmented. As a result, potential arbitrage opportunities that cannot be eliminated by restrictedinvestorspersist.Casualempiricismsuggests that in most countries where there is swap activity, these restrictions may be binding for individual portfolio transactions not for the swap transactions firms. but of
II.The Currency Swap Contract
The analysisof the currencyswapcontractwill deal with a pairof firms. To ease the presentation without sacrificing generality,I let one of these firms be a domestic firm with domestic shareholders a foreign subsidiary.The foreign and subsidiary will generate cash flows next period that are denominatedin a foreign currency,X*(s), but it needs to be financedin the foreign currencytoday. Similarly,the other firm is a foreign firm with foreign stockholders and a domestic subsidiary promising X(s) and is in need of domesticcurrency. mustemphasizethatthese two firmsare I chosen to be symmetrical in terms of their cash flow in generationopportunities orderto ease the analysis of the contract.Symmetrical,here, means that both parties swap have cash flows in the undesired(foreign) currency,which they would like to convertto the desired(domestic)currency. For example, one of the firms can be a U.K. multinational parentwho has a U.S. subsidiaryand the otherfirm can be a U.S. multinational U.K. parent parentwitha U.K. subsidiary. has U.S. dollardenominated cash inflows and outflows, but its desired currencyis British pounds. Symmetrically,the U.S. parent'sdesiredcurrencyis U.S. dollars,but due to its U.K. operations, it has cash inflows and outflows denominatedin Britishpounds. The cash flows may be tied to their respective fixedrate liabilities in their home currencies.This is the usual set up in most plain vanilla currencyswaps. Considera currencyswap contractenteredinto by these firms. Under this arrangement, there will be a transferof different currencies between two parties at t = 0, and a reversalof cash flows at t = T,10 some rate at statecontingent of exchange thatis negotiatedin advanceat t = 0. Since these contractsare nonstandard and specialized, the best means of enforcing performanceis not clear to
l?Acurrencyswapcontractmay includea multiperiod exchangeof payment streams.The exchangeof paymentson each paymentdatecan be viewed as a statecontingent forwardcontract.For this reason,the swap contractcan be viewed as a portfolioof statecontingent forward that contracts: is, Tmay
and eo r
1
1 fr*'
(11)
respectively, where f is the forward rate for exchange of foreigncurrencyinto domesticcurrencyat t = t. Assume that bothsets of investorshaveequalmarketaccess andsufficient funds. When all arbitrageopportunitiescease to exist, f equals eo r/r*,the interestrateparityforwardrate.However, with constraints tradingandshortselling, thisrelationship on not hold. This might not be a farfetchedobservation,if may one recalls the empiricallyverified deviationsfromcovered interestrateparity(CIRP).Frenkeland Levich (1975, 1977) attributedthese deviations to the existence of transactions costs. However,more recentstudies (see BahmaniOskooee and Das (1985) and Deardorff(1979)) conclude that transactionscosts cannotby themselvesexplain these deviations. it They attribute to the existence of factorsotherthantransactionscosts. One of these factorswas suggestedby Keynes (1923) and laterEinzig (1937): The institutionalconstraints thatlimit a trader'sposition taking, whetherfor arbitrage or for otherpurposes. Finally, I note that fluctuatingexchange rates since the abolition of the Bretton Woods Agreement on fixed exchange rates, and increasinglyvolatile US interestrates, since the 1979 U.S. FederalReserve Board policy change, coupled with restrictionson tradingand short selling, may have increased the likelihood that Condition (3) for the existenceandpersistenceof misalignments exchangerates of and interest rates holds. Casual observation of the past evolution of the swap marketreveals that currencyswaps emergedin responseto fluctuatingexchangerates,while the volume of interestratesswaps surgedwith increasedinterest rate volatility. Furthermore, a main theme in the
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FINANCIALMANAGEMENT/ SUMMER 199
marketparticipants. However,currencyswapagreementsare generallydesigned so thata partythatelects, at its discretion, not to pay its obligation on the due date cannot realize an economic gain. The Interest Rate and CurrencyExchange Agreement issued by the International Swap Dealer's Association (ISDA) contains a provision that makes the defaultingpartyliable for full paymentof amountsdue under contract,as well as for additionalcompensationto cover the futureloss of the other party,as long as it is solvent. Thus, for the purposeof this paper,it is reasonableto assume there is no incentive for eitherpartyto defaultat its discretion at t = T, when the truestateof natureis revealed,as long as both parties are solvent. For example, at t = T the exchange rate to may be unfavorable the domesticfirm,hence it owes more to the counterparty,the foreign firm. Thus, the domestic partyis liable to default.However,underthe currencyswap agreement,if it does default,it is legally liable for the current and future losses of the other party. In effect, both parties will be indifferentto this outcome. Thus, nonpaymenton a due date when both parties are solvent is not a problem in practice, and it is indistinguishablefrom closing out the contractor markingit to market.As far as modeling default goes, these states are nondefault states because the contractual provisions are in effect. To define the default states in the model, I consider the cases where one or both parties are insolvent. Since the ultimate recovery in the event bankruptcy occurs is I model thatis consistent uncertain, use a simple bankruptcy with the provisions of the ISDA swap documents. In my I model, I assumethatgross amounts1 areexchangedandthat if one or both partiesare insolvent and cannotperformtheir obligations,the contractis void. No paymentsare made,and each party ends up with its own cash flow. I believe this resolutionis the most sensible for swaps for two reasons:(1) it is stated in the Interest Rate and Currency Exchange Agreementthat if one or both parties are, or are about to become, insolvent,this will constitutea truedefaultstateand the swap agreementwill necessarilyterminate; (2) swaps and were introducedas legal innovationsthat were designed to be superior to parallel, or backtoback,loans, for which therewas a questionablerightof offset in the event of default by one partyto the arrangement. Swaps, however, are based
stand for any one of the scheduled payment dates. Moreover, the initial exchange may not take place. I includethat featurein my model because I latersuggest its use as an instrument sharingthe gains from swaps. Its for inclusiondoes not play a crucialrole in the resultsthatfollow. Exchangeof gross amountsinsteadof the betterknown procedureof net exchange is the rule with currencyswaps. Nevertheless,exchange of gross amountsis not a necessary restrictionfor the model to work. In my model, one of the decision variables is the swapped amount. Net exchanges can always be made biggerto matchthe gross amountsof the model if notional principalamountsare increasedwhen it pays to do so.
on contract law, which states that if one party does not perform, the contract is void and the other party has no obligationto perform.12 Thenotionthatswaps arelegal innovationsis verycrucial to modeling their treatmentunder default. An alternative modeling approachwould be to assume thatthe bankruptc courts would hold that the swap agreementremains full effective and thatboth partieswere still fully liable for the paymentobligationsafterone partybecomes insolvent. For example, if the exchange rate outcome is favorableto the defaulting bankrupt party, the other party fulfills in obligation and in returnjoins other creditors in seeking compensation.This approachhas been adoptedin Coope and Mello (1991) and Solnik (1990). In their modeling of defaults, the other party swap default, if one counterparty receives nothing even if the swap has negative value to the insolvent party and payment is due to the solvent party However, the solvent partywill have to make the payment wheneverthe swap has positive value to the defaultingparty andmoney is owed to it. Thus,the insolventpartyis released from its obligation, but the solvent party is still liable paymentis due. This type of modelingoverlooksthe fact that nonperformance one partyreleases the other partyfrom by having to performits obligation. In my model, if one party is insolvent and cannot perform,the other party, although solvent, does not performeither. Litzenberger (1992) note the validityof this approach modeling swap defaultbase to on the ISDA swap agreementprovisions. I let Do and Do denote the amountsexchanged at t = expressed in domestic and foreign currencies,respectively For simplicity,I assume thatthe initialexchangetakes place at the currentspot rate eO, i.e., Do = De0o. The amount promisedto be exchangedat t = T for certainare denotedby D and D* in domestic and foreign currencies,respectively The decision on D and D* will result in an exchange ra e = D/D*, which may be differentfrom the spot exchange ratee0 and the theoreticalforwardratef = er/r*. 13 of Note, however,thatthe currentmarkettreatment swap cash flows upon bankruptcyis far from settled. There are conflicting views concerning the enforceability of the provision in the standardized Interest and Current ExchanigeAgreementallowing the nondefaultingparty
1Fora furtherdiscussion, see Beidleman(1985, 1992) and Tessitore an Usmen (1993). 'iThe defaultfreeswap contractis indistinguishablefrom an offmarked implicit forwardforeign exchange contractexcept that it is a longerterm the instrument; average swap has a 7 to 10 year maturity.The theoretical forwardrate may be observed in the currencymarketswhere there are in obvious covered interest arbitrageopportunities.However, in longterm markets,which are the concern of this paper, the theoreticalnoarbitray ( relationship f = eo r/r*)may not hold. Thus, thereis roomfor negotiation
USMEN / CURRENCY SWAPS, FINANCIALARBITRAGE, AND DEFAULT RISK
49
Denote8V = V  V as the differencein valuedueto using a currencyswap insteadof slack to finance the investment. This function,8V, measuresthe differencein value between of engaging in a swap and the alternative using the domestic marketsand the spot currencymarkets.17 capital Recalling First, I look at the swap agreementfrom the perspective thatDo eo = Do and D*e*= D, I obtain of the domestic firm. I assume the cost of the investment opportunityin the foreign marketis known. I denote it I*. , The firm has slack in domestic currency,L. The source of 8V = D* { r (e*  e(s))p(s) + 1 jy (e(s)  e*)p(s)}. (14) r the slack is not specified, but I assume that the amount of It is interestingto note that bringing in the integrated slack will allow the firm to undertake investment.One the capitalmarketsconditionembodiedin Equation(2) will not possibility is thatproceedsfrom issuing domestic securities result in 6V = 0. Applying Equation (2), Equation (14) can be the source of slack, in which case a liability in the reducesto domestic currencyis created.Thus, the domesticfirm could issue domestic debt and convert the proceeds to foreign eo e0 (15) eP(B') 6V=D* {(er ) + P(B()PB) (15) I claimthatthe firmwill engage in a currencyswap ( currency. r* P rP ) contractto financethe investmentonly if the contractallows Similarly, the difference in value for the foreign firm the firm to createvalue above thatthe firm could realize by translated into the domesticcurrencycan be expressedas using its slack and spot foreignexchange markets. withoutloss of generality,I assumea single Furthermore, V*= D*{ eo ?(e))*(s) group of claimants in the domestic capital market, the of stockholders.Introduction other domestic claimantswill have no effect on the results of the paper since domestic (16) r* B' e(s) capitalmarketsarecomplete and integrated.15 First, I value the foreign investmentwhen slack is used. I can use Equation(2) to obtain This serves as a useful benchmark againstwhich to compare the value of the same opportunity had it been financedby a The value of the firm with slack financingis (1991), who assume thatthe nondefaultingpartymakes a paymenteven if currencyswap.
walk away when paymentis due to the defaultingparty.In some recent cases involving insolvency of one of the swap parties,the nondefaultingpartyhas enforcedthe clause and refusedto pay the due amountto the dismayof some market and participants regulators.In othercases, the nondefaulting partyhas voluntarilymade the paymentwhen the swap had positive value to the insolvent party.14While disputes relating to this clause could be settled in court, market participantsare not inclined to do so and try to avoid legal action as much as they can. Meanwhile,the enforcementof this clause andits implicationsneed to be madeclearerto the swap market.Some dealers and the ISDA would prefer to retain the clause, but others feel that the market is better served withoutthis provision.
V = (L  eo I*) +  X*(s)e(s)p(s). r
(12)
the Underthe swapagreement, valueof the sameopportunity is = (L  eo I*) + (Doeo Do) + r r B (*(s)e(s)p(s) +
r B ((X*(s)
 D *) e(s) + D) p(s),
(13)
whereB is the set of statesin which the contractis effective. Specifically, B = Is:X*(s) > D* and X(s) > D}. B'=S  B will be the set of states in which the contractis void.16
A
III.Currency Swaps in Integrated Markets Capital
in the forwardrate specified in the swap contract.Moreover,swaps with defaultriskare statecontingent forwardcontracts,andthereis no reasonfor the swap rate to equal the theoreticalforwardrate that is consistent with riskfreecovered interestarbitrage. 4Fora fuller discussion, see Shirreff(1991). '5Inthe set up of this paper,swaps wouldhave no directbearingon the cash flows received by the domestic creditors of the firm. Debt claims have and seniorityover otherclaimants,such as offmarketswap counterparties, in my model, when the firm is bankrupt, paymentis received from the no solvent counterparty. This approach standsin contrastto Cooperand Mello
the other partyis bankrupt. This paymentnaturallyadds to the liquidation value of the firmin some states,and it is the sourceof the wealthtransferto bondholdersin their paper. In my model, there are no wealth transfersto bondholders.
16This, bankruptcycondition implicitly assumes that the parent will not the It support paymentobligationof the subsidiary. may be arguedthatunder certaincircumstances parentwill backup the paymentobligationof the the to even if it is costly in the short defaultingsubsidiary maintainits reputation run.The analysisof this reputation effect is left for futureresearch. 17Another alternativeto swap financingmay be issuing foreign securities. The distinguishing aspectis thatswaps are governedby contractlaw instead of securities law. This difference in legal treatmentcan have significant defaultimplications.
50
/ SUMMER 1994 MANAGEMENT FINANCIAL
sV =;
{
(e(,s)  1)p(s)
r +
) (()
as NotethatEquation canbe rewritten (14) 8V=D' e E(1 +l r ('_ ' e )p(s)}.
e' e
)p(s)
(18)
1) p(s)}.
(18)
forward currencyswapswithdefaultriskarestatecontingent contracts. Thus, no publiclytraded forward currency contractcan substitutefor the currencyswap with default. Since default is firmspecific,currencyswaps with default risk can be tailormadefor each counterparty. Specifically, can the counterparties choose the states in which the swap should be effective. There are some practicalbenefits here. More specifically, my analysis shows how the financial managers of corporations should design risky currency swaps.
Since Equations(17) and (18) are exactly offsetting, at any negotiated e*, the benefit to one party will come at the expense of the other. Specifically, 8V = 6V* for all swaps. Result 1. A necessary18and sufficientconditionfor all currencyswaps to have a zerosumoutcome is
A. DefaultFree Swaps
Assume that investors in both marketscan freely trade the riskfree asset in the other market and that their expectations concerningfuture exchange rate variationare such that Ee(s) = 1/E'el(s). (See Equations (5) and (8).) Under these conditions, UIRP holds in both domestic and eo e(s) foreign markets simultaneously. Using these parity foralls. e?p(s) (p(s)=0 r conditions, Equations (16) and (18) can be written for a defaultfreeswap as Note that the above condition can only be true in a e eo complete and integratedinterational capitalmarket.This is V = D*( r) " (19) r the type of capital market in which the argumentsagainst financial arbitrage presented in Smith, Smithson, and and Wakeman (1986, 1988) and Turbull (1987) are valid. In e fact, Result 1 is an extension of the propositionin Tumbull 8V' = D*((20) ). (1987) appliedto currencyswaps.In such a market,financial r* r managersshould look for motivationsfor swaps other than The presentpaper,however, arguesthat Once again, 5V = 6V*, and all defaultfreeswaps (at any financial arbitrage. have a zerosumoutcome. capital marketsare segmented and that deviations from the negotiatede*) Result 2. Necessary20and sufficientconditionsfor all statecontingent paritiesare persistentlyobserved.19 defaultfiree swaps to have a zerosum outcome in an IV. Currency Swaps in Segmented international capital market that admits arbitrage in opportunities risky assets are Markets
e:
Capital
eo Ee(s) After statingthat swaps are only relevantin segmented I now analyze currency swaps first as capital markets, defaultfreeand then explore the default implications.It is 1 eo that wellacceptedin the literature swapsrepresent portfolios r$ rE*el(s) of forward contracts. Accordingly, this study models the Note that conditions (i) and (ii) together imply that defaultfreecurrencyswap as a forwardcontract.It clarifies dealt Ee(s) = 1/E' e (s). Thus,underriskneutrality, heterogeneous some of the findings of previousresearchthatprimarily with defaultfree interest rate swaps. Then I consider how expectationsarenecessaryto achieve the above proposition. defaultrisk affects currencyswaps. My analysisreveals that A common insight among practitionersis that swaps at originationhave zero economic value. My resultshows that this insightis valid for defaultfreeswaps only if UIRPholds 1SSee appendixfor proof. thatUIRP marketsarepointedout as an explanation the existence and in both domestic and foreign markets.Admitting for 9Incomplete evolution of the swaps market in Smith, Smithson.and Wakeman(1986) may not hold in longdatedmaturities,even for currencies and in Arak.Estrella,Goodman,and Silver (1988) even thoughno analysis such as U.S. dollars and deutsche marks, it is evident that of the issue in that context is provided.Note that marketincompleteness other thanmarketsegmentationmay cause the statedconditionin Result 1 swaps rarelyhave zero economic value even at origination.
not to hold. This will be true since in incompletemarketssome states will betweenthe puresecuritiesthatdo not be insuredandthe parityrelationship not exist for those states is not ensuredby arbitrage. 2()Seeappendixfor proof.
ANDDEFAULT RISK / USMEN CURRENCY ARBITRAGE, SWAPS, FINANCIAL
51
Supposethereare forwardmarketsfor the two currencies and that all arbitrage opportunities in this market are exploited through covered interest rate arbitrage This results in f = eor/r*.Using this condition operations.21 again yields Equations(19) and (20). Result 2a. With the existence of a forward currency market, a necessary and sufficient condition for all defaultfireeswaps to have a zerosum outcome is f= eo r/r*. I have shown that a defaultfreeswap has a zerosum outcome under certain conditions in the international currencyand asset markets.In segmented capital markets, however,none of the above conditionsmay hold. Therefore, I choose to analyze defaultfreeswaps using Equations(16) and (18) and assuming the existence of deviations from interestrateparities. To obtainthe totalgain froma defaultfreeswapcontract, I add Equations(16) and (18) and let B' representthe null set. The total gain function,T6V = 8V+6V*, is T6V = D* { (1 + eo(1 )p*(s)}. e* )p(s) r* r 5(I e((s)) e(s) Equation(21) can be writtenequivalentlyas T6V= D*{ p*(s) r* r p(s)) (21)
riskfreeswapshouldbe dependenton the amountsswapped, D* and D, not on e*. But since e* = D/D* by definition, the size of the gain can be stated as a function of D* and e* as well. This leads to the following implicationsof Equation (22):22 If deviationsfrom UIRP in both marketsare 1. positive, T6V will be positive and strictly increasingin e*, but limited by the riskfree borrowing potential of the parties. Thus, e* = X(s)min/X*(s)min. 2. If deviationsfrom UIRP in both marketsare negative, T6V will always be negative.Thus, thereis a disadvantageto swap contracts. If deviationsfrom both UIRPs are of opposite Iwill signs, e*= I DUIRPdomestic/DUIRPforeign yield a zerosumoutcome. If deviationfrom UIRPdomestic positive but is deviationfrom UIRPforeign negative, for T6V is to be positive e*< I DUIRPdomestic / . This implies the lower the value DUIRPforeign of e*, the higherthe gains from defaultfree swaps. If deviationfrom UIRPdomestic negative and is deviationfrom UIRPforeign positive, T6V will is be positive as long as e* > I DUIRPdomestic / DUIRPforeign This implies the higherthe I. value of e*, the higherthe gains from defaultfreeswaps.
3.
4.
5.
e(s)p) (22) e*( eO p (s)e(s)) r e(s) r* Note thatthe two termsin bracesin Equation(22) arethe domestic and foreign UIRP relations (see lefthandside of Equations(4) and (7)). Thus, a defaultfreeswap contract These implications tell us when it pays to enter into pools togetherthe deviationsfromUIRP in the domesticand markets. The first sum in Equation (22) is the defaultfreeswaps and show us how to determinethe swap foreign deviation from UIRP in the domestic market ratein certaincases. At othertimes, we can only identify the Similarly, the second sum shows the upperand lower bounds for the swap rate.In any case, it is (DUIRPdomestic). deviation from UIRP in the foreign market(DUIRPforeign). impliedthatto maximizebenefits,the swap rate,determined Also note that T6V depends on D* and e*. This result may by the amountsswappedD* andD, shouldbe differentfrom appear counterintuitivesince one expects the size of the the current spot exchange rate, contrary to customary of arbitrage gainto be independent e andexpectse* to divide currencyswap practice. It is evident from the above implicationsthat whenever the gain between the two parties. However, the swap is a mutual borrowing agreement where the domestic party a possibility for positiveT8V is discovered,D* and D, or D* borrowsin the foreigncountrypromisingD', andthe foreign and e*, should be increased (decreased) to the limit. partyborrowsin the domesticcountrypromisingD, while D However,we mustnotethatpositiveT8V does not implythat and D* are related to e*. Thus, the borrowing decision individualgains arebothpositive. Individually,the domestic variablesD and D: can be equivalentlyexpressedas D' and firm will want to set e* as high as possible, whereas the e;. Similarly,one can argue thatthe size of the gain from a foreign firm will desire the lowest possible ei. Thus, any negotiated e* will divide the total gain between the two
21I do not posit a currencyswap marketand a forwardcurrencymarket operating simultaneously. In a oneperiod model, they entail the same contractfor the defaultfreecase. Here. I make use of the CIRPrelationship to presentthe arbitrage arguments. 2"Similar implicationscan be drawn for the case where deviations from CIRPare observed.
52
/ SUMMER FINANCIAL MANAGEMENT 1994
parties. may search for an Alternatively,the marketparticipants e* such that both parties have positive gains, specifically Examination Equation of 6V > 0 and 8V* > 0 independently. (21) reveals that 6V > 0 only if e* > Ee(s). The similar conditionfor 8V* is thate* < 1/E*el(s).Thus, the following resultcan be stated: Result 3. In a defaultfreeswap contract8V and 5V*
currentspot exchangerate,eo. Thus, the commonpracticeof reversingcash flows at the originalexchange rate might be unwise in designing currencyswaps. Furthermore, financial managersshouldexploresharingrulesfor the totalgainother thanthe swap ratewhen one partyis worse off but the total gain is greaterthanit would be if both had positive gains.
B. Swaps with Default Risk
In a swap contract,besides e*, thereis a second decision variable,the swappedamount.Evidently,when the financial > e* > Ee(s). will both be positive only if E e (s) gains from swappingare positive, it is to the advantageof the swap partiesto increasethe contractamountsas much as Again, I should point to the significant role played by hetIn this section, I analyze swaps with default risk erogeneous expectations under risk neutrality.The above possible. andarguethatthe optionnot to reversethedeal in some states inequality would never hold if the expectations were the source of value. same.23Thus, implicit in the studies thatarguefor unambi at t = t is an independent I investigate default implications in a swap contractby guous gains for all parties due to comparativeadvantage (e.g., Beidleman (1985), Bicksler and Chen (1986), and examiningEquations(16) and (18). I also computethe total Felgran (1987)) is the assumptionthat the partieshave dif gains by addingthem togetherto obtain ferentexpectations.This assumptionis somewhatimpliedin = D* { E(1 & eop*(s) e(s) p(s)) T8VT6VD1X1 )( Arak, Estrella, Goodman. and Silver (1988) whose results r center aroundthe different informationsets borrowersand e* 0 lendershave. e e_X^p(s))}. (S) (23) +e (e  1)( p*(s)r r* in The choice for optimale* can be approached two ways B e(s) is One by the counterparties. alternative wherethe individual Upon examining Equations (16), (18), and (23), the are both positive, as statedin Result 3. However, it is following results become apparent. a given state, if there In gains also possible that they can choose e* and D*, thus the is a gain or loss in the defaultfreeterm,thatgain or loss will (22) be reversedif the contract becomesvoid due to defaultin that swappedamountsD* andD, so as to maximizeEquation state. Specifically, looking at Equation(16), one regardlessof relative shares in the total gain. This solution particular may dominatethe previousone in termsof totalgain, butwill can see that, for any s in the set B', what is positive in the result in one of the parties being worse off. For the latter first term is negative in the second. A furtherexplanation solution to be feasible, the counterpartieswould have to proceedsas follows. If the swap contractis set such thatit is devise sharing rules for the total gain such that each effective in everystateof the world,therewill be stateswhere is counterparty at least as well off as in the formersolution. (1  e*/e(s)) > 0, which arefavorableto the foreignfirm. But This necessitates a transferof funds from the party that is in other If states,it will be negativeandunfavorable. B' turns The transfercan take out to be the subsetwhere made better off to the counterparty. is always positive, the (1 e*/e(s)) place at the presenttime t = 0, for example, by exchanging firm loses that gain by defaulting. Thus, default must be currenciesat a ratedifferentfrom e0. avoided.On the otherhand,if B' is designed so thatin those Financial managers engaging in defaultfree currency states s in B' in which the firm would have lost in the swaps whenever a window of opportunityopens should be defaultfree swap, then default becomes desirable. The wary of at least two possibilities. First, they have to make reasonis simply the fact that,by avoiding the loss, the firm sure that the total gain is positive by examining deviations will end up with a highervalue thanit would in a defaultfree fromUIRPin domesticas well as in foreignmarkets.Second, swap. Similarargumentscan be made from the perspective they have to make sure that the swap exchange rate e' is of the and counterparty totalgains. Also note thatin any state chosen such that both partiesend up with positive gains. It s in B', whenever one party gains, the other party loses. will be a rare occasion that this rate will coincide with the However.as explainedin Section I, the gains and losses are differentmagnitudes. This impliesthatthetotalgain,T6V, factors besides of 23However,with risk aversiontherewill be risk adjustment probabilityassessments.That may lead to cases where the conditionis met of a swap with defaultrisk will never be equal to zero in an with homogeneous expectations.Thus, saying that it takes heterogeneous imperfectmarketin which (eop*(s))/r* (e(s)p(s))/rfor s in expectationsto make a horse race seems to be a necessaryconditiononly in B'. Furthermore, resultis independent whetherUIRP riskneutral valuation. this of
RISK ANDDEFAULT / ARBITRAGE, USMEN CURRENCY SWAPS, FINANCIAL
53
shouldsearch holds in bothmarkets.Thus,the counterparties for the optimal D* for any given e* where their gains are maximizedindependentlyor jointly. The essence of firms being able to reap the benefits of internationalfinancial arbitragewhen individual investors cannotlies in the factthatfirmsmay have specific realassets in foreign marketsand can issue claims againstthe incomes these real assets will generate. In other words, financial activities of firms are closely linked to their real activities. Thus, a particular project owned by a firm will generate a acrossthe statesthatcan screenthe cash flow pattern specific favorable and unfavorablepotential arbitrageprofits in a certain way. In particular,swaps with their unique default structures are a very convenient way of using the statecontingentpotentialarbitrageprofits to the benefit of as bothcounterparties, explainedin the precedingparagraph. In otherwords,risky swaps area uniquemechanismdevised by firms that can benefit from inefficiencies in capital markets caused by nonswap transactions (individual portfolioholdings). Swaps with theiruniquesecuritydesign can overcome barriers that cannot be eliminated by individualportfoliorebalancing.24 Inspectionof Equations(16) and (18) will show thatthe optimal D* will differ for each party. Hence, under this criterion,the swap contractwill not be feasible without an intermediary. The alternative criterion is where the counterparties optimizejointly. As discussed in connection with defaultfreeswaps, joint optimizationimplies a search for a common set B' whereT6V is maximized,regardlessof individual shares. I will have more to say about these solutions and criterialater in the paper in the context of a the numericalexample. Here, I choose to investigatefurther of the defaultoption on the value of a currency implications swap contract. I introducethe following function:
Surprisingly, there is a second term, the covariance of exchangeratesand defaultstates.As long as thatcovariance is positive, it will offset the value lost due to default,and an optimalB' thatmaximizes 8V can be attained. Similarly,Equation(16) can be restatedas * = D* { (e r +

eoe*Ee(s))( r
 P*(B))
(26) r* 'B v*(e((s) c }' can Clearly,similararguments be made concerningthe gain of the counterparty. of Result 4. In a swapcontract probability defaultis not a sufficient measureof the impact of default on value Covariabilityof exchange gains of each counterparty. ratesand default states may play an offsetting role. Thejoint optimizationcase whereT6V is maximizedcan as be represented T6V = D*{[(eo Ee(s) + e*( r r r* + [e*(P(B') e r ( eoE*el(s)
r*
eo e*
e(s)(B,)) r
P*(B') Ee(s)P(B')] XB')+ rcov(e(s),B)]} (27)
[
cv*(e(s),
T6V is the sum of threetermsin braces.The first termis the gain had the swap been defaultfree.The other two terms appeardue to the possibility of default.The second term is of exclusively basedon theprobability default.However,the value of this termcan be eitherpositive or negative.Thus, it is ambiguous how the total gain will be affected by the probabilityof default.25Finally, there is a third term that 1 whenevers belongs to B' depends solely on the covariances of exchange rates and 0 elsewhere XB' defaultstatesin the two countries.Also note thatthe analysis of the paperpoints to potentialgains from swap defaultand Thus, Equation(18) can be restatedas for the factorsthataffectit. The opportunities such gainsmay + V (l e( =D*{ not be pervasive due to the current practice of swap XB'P )p(s) r r e* )p(s) e(e e* l)XB,p(s)}.(24) financing. This is an empiricalquestion to be addressedin Furthersimplificationof the termsyields futureresearch.However, my analysis has implicationsfor e* Ees) cov(e(s)DX{/)}. (25) designing swap contractsthat will exploit potential gains = V= D* { ( r Ee(s)(_P(B')) + v(e(s)r ) associatedwith swap defaultrisk. r Default risk is one of the reasons why swaps cannot be The expression in Equation(25) is revealing. If there were any gains to a defaultfreeswap, the gains would be totally standardized.Default risk has intrigued the swap partiallylost due to the probabilityof default, as expected. industry since its inception. Practitioners have tried to
2"With homogeneous expectations, the probability of default would reducethe value gains due to this second term. unambiguously
24I thank an anonymous referee for pointing out this implicationof my analysis.
54
FINANCIALMANAGEMENT/ SUMMER 1994
sidestepthe creditrisk complicationsby eithermatchingthe or credit risk of counterparties by contractingwith a third party that has specialized in bearing credit risk, such as a assumesthe credit dealeror a bank.Unless this intermediary the risk of each counterparty, end users will choose to stay with counterparties that have high credit ratings. Also, currentindustrypractice is to quote the same swap rate to with differentcreditratings.This paperbrings counterparties a new outlook to swap default risk considerations.Swap need not be so conservativeconcerning marketparticipants credit ratings. It may be possible that a AAArated swap partygains morewhen it entersintoa swap with a BBBrated The gain depends than with an intermediary. counterparty not only on the probabilityof default,in a negative way, but also on a second factor, covarianceof e(s) and the default states. The desired covariability might be achieved by otherthana risklessone. Also, swappingwith a counterparty thereis a differentswap for each pairof swap counterparties, thatmaximizes their gains and thatdepends on the rate, e*, amounts swapped, and thus on their specific default It structures. will be suboptimalfor all partiesto use the same rate. My results do not diminish the function of an swap intermediary. My model allows for intermediation for reasons other than credit specialization.The intermediation functionis indispensableto matchquantitiesswappedsince optimal swap amountsmay be differentfor different swap counterparties.
collection of stateswheree(s)
>
e. This implies thatthe call
valuemaybe positive or negativedependingon the e* chosen and on the cash flows of the counterparties. Thus, one can interpretthis default term as a "hybrid" call option, where the payoffs are identicalto those of a call on the domestic currencybut are effective in those states in which the counterpartiesdefault.26A perfectly analogous argumentcan be made for the foreign firm. Result 5. The value gain of a counterpartydue to financingthrougha currencyswap is equal to the value of a defaultfree forward contract on the domestic currency plus the value of a "hybrid" currency call option. The value of this call option can be positive or negative. The taskof financialmanagersis to design the swap contract so thatthis call option has positive value to both parties.
V. NumericalExample
By assigning plausible values to the marketparameters concerningthe 8V and8V* functions,I next show how swap can wealthin segmented counterparties increaseshareholder international capitalmarkets. The following numericalexampleuses the datapresented in Table 1. In the computationof 8V, 8V*, and T8V, there are two decision variablescontrolledby the counterparties, C. Default on a Currency Swap as a Call Option namely, the swapped amountin foreign currency,D*, and The default features of currency swaps are highly the rate at which the exchange occurs at t = T, e*. In my suggestive of an option contract.To analyzethe optionlike discreteexample, I let D* representthe discrete cash flows propertiesof swap default,look againat Equation(14). Note of the foreign investmentopportunity, is D* = X"(s) for that that the value of a defaultfreeswap contractis identicalto a s. particular thatof a forwardcontract.This is no surprisesince I modeled Implicit in the given data is that deviation from the swap agreement after a forward contract. What is of is UIRPdomestic 0.08 and deviation from UIRPforeign interestis the second termthatemergesdue to the possibility thatone of the counterparties might default. Table 1. Data Recall that the payoffs to a call option written on a States X*(s) e(s) p(s) p*(s) X(s) domestic currencycan be expressed as max[0,(e(s)  e')], 1 75 150 0.19 0.30 0.60 wheree* is the exercise price.Specifically,the payoffs to this 2 call option are positive in those statesin which e(s) > e* and 100 200 0.09 0.02 0.30 are equal to (e(s)  e*). These payoffs appearin the second 3 125 250 0.13 0.08 0.45 term of Equation(14). Had B' been equal to {s: e(s) > e* }, 4 0.21 0.25 0.65 100 50 those states that are unfavorableto the domestic firm, the 5 150 300 0.26 0.70 0.30 value of the defaultoption would be identicalto a call option 6 25 50 0.12 0.40 0.05 on the domestic currency.However,this is not the case, and r= 1.05 E e'(s) = 1.683 eo = 0.5 B' = Is:X*(s) < D* and X(s) < D'e;). Evidently, B' is = 0.566 of basedon r = 1.09 Ee(s) dependenton nonperformance thecounterparties theircash flows and the amountswapped,ratherthanon the 26Whittaker (1987) also views risky swaps as options; however, this last relationship between e* and et(s). In particular,B' is a point is not madeclear in his work.
USMEN CURRENCY / ANDDEFAULT RISK ARBITRAGE, SWAPS, FINANCIAL
55
is +0.1805. From Equation (22), we know that any e* > 10.08/+0.1805  or e* > 0.4432 will yield T6V > 0 for Result 3 implies thatin the defaultfreeswaps. Furthermore, > e* > 0.566, both 6V and 6V* will be positive. range0.594 Thus, in the numericalexample, I let e* equal 0.4, 0.58, and 0.8, respectively.Foreach valueof e* chosen, thereis a series to of D values corresponding the D* values describedabove since D = D*e*. The cash flows presentedin Table 1, with these D* and D values, determinethe breakdownof S into subsets B and B'. The results of the computationsfor each e* chosen are presentedin Table 2. The values of 8V, 8V*, and T6V for differentcases of defaultaredetailedin the same table.I first examine the defaultfreecases where e* is the only decision variable.When e* is low, the foreign counterparty gains at the expense of the domesticcounterparty. However,the total gain is negative, which makes it impossible for the contract to be implemented.At high e*, the situationis reversed,and the resulting total gain is positive. A swap contract is possible, but sharingrules have to be developed since one of the partiesreceives negative gains. Only when e*= 0.58 do both parties to the swap agreement augment value, simultaneously depictedby positive values of 8V and8V* in B of Table 2. panel The more interestingissue concems the possibility that can the counterparties do betterby increasingthe amounts In thatcase, the swap is no longer defaultfree.A swapped. numberof cases emerge. In general,each partycan obtaina better outcome at some higher level of swapping. This is intuitivesince at some level of D* defaultoccursin the states that are unfavorableto a particular party.However, optimal amountsof swappingassociatedwith the best outcomes for each partydo not necessarilymatch. Looking at panel B of Table 2, the domesticfirm would like to set D* = 150, while the foreign firm would independently like it to be 50. However, total gain will be maximized at D*=150. Noting that 6V* at D* = 150 is almost as large as T6V at D* = 50, the solution to this examplecan reasonablybe D* = 150. Finally, it seems that both parties will be better off by exchangingat a higherratethane* = 0.58. This is suggested by the higher value achieved for the best outcome of T6V when e* = 0.8. It should also be noted thatthe best outcome correspondsto a lower level of swapping. This can be a can superioralternativeonly if the counterparties develop rules such that both can benefit from the swap. sharing Obviously, these considerations lead to inclusion of an functionandtransactions intermediation costs, which areleft for futureresearch.
Table 2. Value Gains from a Currency Swapa
A. that Panlel Assuming e* = 0.4 D 25
50
D 10 o
20
se B'
6V 3.95
V* +3.75
+7.50
T6V 0.20
0.41
D
7.91
100 150 200 250 300
40 60 80 100 120
6 4,6 1,4,6 1,2,4,6 1,2,3,4,6
15.81 16.22 14.38 20.12 22.29
+14.99 +15.88 +12.00 +15.76 +17.64
0.82 0.34 2.38 4.36 4.65
Panel B. Assuming that e* = 0.58
D 25 50 100 150 200 250 300
D 15 29 58 87 116 145 174
se B' qD 6 4,6 1,4,6 1,2,4,6 1,2,3,4,6 S
6V +0.33 0.36 +0.68 +1.56 2.73 7.43 00
6bV +0.27 +1.05 +0.86 +0.67 +2.60 +5.90
T6V +0.60 +0.69 +1.54 +2.22 0.13 1.53 0
Panel C. Assuming that e = 0.8
D 25
50 100 150
D
20 40 80
s; B'
5V 6v +5.57 +8.86 3.97 6.79
T6V +1.60 +2.07
0F 6 1,4,6
+11.10
+10.21
6.34
7.22
+4.76
+2.99
120 160 200
240
1,2,4,6 S S S
200 250
300
0 0 0
0 0 0
0 0 0
aRulingout the cases whereT6V < 0, the best outcome,if positive, in each columnis boldfaced.
VI. Conclusion
In this paper,I developed a model to measurethe value in gains of the counterparties a currencyswap. The model links the value gains to statecontingent interest rate conditions rate/exchange disparities.Given these market decide on and expected cash flows, the swap counterparties rateandthe amountto be swapped.In an integrated the swap market all swaps are zerosum games. In a segmented market, all defaultfree swaps are zerosum games
56
MANAGEMENT / SUMMER FINANCIAL 1994
conditional on a twoway uncovered interest rate parity. Swaps with default in a segmentedmarketcan createvalue gains beyondthatof a defaultfreeswap. Withthe possibility of default, two sources of uncertaintycash flows and exchange ratesinteract. The default option, state by state, becomes a screening device for the favorable and unfavorableexchange rateoutcomes. Evidently,a chance to eliminatethe unfavorableoutcomes emerges. My findings suggest thatfinancialmanagersshouldlook whenthey for bothriskfreeandrisky arbitrage opportunities Riskfree arbitrage does not design currency swaps. necessarily imply positive gains to both partiesat any swap such thatit rate.The optimalswap ratecan be approximated lies betweenthe expectedexchangeratesin the two markets. is Even if riskfreearbitrage not possible, financialmanagers should look to benefit fromrisky swap contracts.If they can tailor currency swapsstatecontingent forward currency contractssuch that default states and exchange rates are positively correlated, they will be able to enhance wealth. shareholder Finally, my results have empirical implications for successful, wealthenhancing, as well as unsuccessful, wealthreducing, swap outcomes. Any empiricaltest should examine the wealth gains to both parties under a swap
agreement and distinguish between cases where both are positive, botharenegative,or they aremixed. Therearethree empirical implications. First, for defaultfree swaps, a positive marketreaction to a swap announcementis more likely if the differential effective yields on riskfree borrowingsin the two countriesare significantand have the desirable signs. Note that these deviations are pairwise countryspecific and thus can be more easily tested with observationsfromthe same countrypair.Second,againwith defaultfreeswaps, a positive marketreactionis more likely for both parties whenever the swap rate is bounded by expected exchange rates that are different in the two countries.Otherwise,the market reactionis morelikely to be negative for both or mixed. Third, with risky swaps, empirical tests may be misleading if they ignore a second factor besides differential effective yields as a source of positive market reaction. My study shows that a positive market reaction is more likely with risky swaps if the covariance of exchange rates and default contingencies is positive. This implicationis projectspecific.Those projects thattend to generatelow income when the respectivehome currenciesare undervaluedwill be more likely to cause a positive marketreactionfor both parties. I
References
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Appendix
Proof of Necessity in Result 1
state SupposeEquation(2) is not satisfiedfor a particular and there is an asset with a payoff only in that state. s, T8V ? 0 for thatstate.This contradicts statementthatall the swaps will have a zerosumoutcome.
Proof of Necessity in Result 2
ConsiderEquation(22). Since e* > 0, both sums have to be zero (conditions (i) and (ii) are both valid) to have T6V = 0 in all defaultfreeswaps.
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