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NBERWORKINGPAPERSERIESANALYZINGTHEACCURACYOFFOREIGNEXCHANGEADVISORYSERVICES:THEORYANDEVIDENCERichardM.
LevichWorkingPaperNo.
336NATIONALBUREAUOFECONOMICRESEARCH1050MassachusettsAvenueCambridgeMA02138April1979Iwishtothankthemanykindpeoplewhosupplied,orarestillplanningtosupply,theirforecastdata.
HelpfuldiscussionswithA.
Brillembourg,C.
Ramond,andB.
Smitharegratefullyacknowledged.
Anyremainingerrorsaremyown.
TheresearchreportedhereispartoftheNBER'sresearchprograminInternationalStudies.
AnyopinionsexpressedarethoseoftheauthorandnotthoseoftheNationalBureauofEconomicResearch.
NBERWorkingPaper336April1979AnalyzingtheAccuracyofForeignExchangeAdvisoryServices:TheoryandEvidenceSUMMARYWiththeintroductionoffloatingexchangerates,thevari:biiityofunanticipatedexchangeratechangeshasincreaseddramatically.
Asmallforecastingindustryhasdevelopedtoprovideinformationaboutfutureexchangerates.
Fromanacademicviewpoint,itisofinteresttoexaminesomeofthestatisticalpropertiesoftheseforecastsandtorelatetheforecasterrorstootherfundamentaleconomicvariablesinamodelwithrationalbehavior.
Second,fromamorepracticalviewpoint,wewoululiketoknowifforeignexchangeforecastsareusefultodecisionmakers.
Thepurposeofthispaperistoprovideanobjectiveanalysiswhichaddressessomeoftheabovequestionsforalargesampleofforecasts.
Onthebasisofthecurrentresearch,wecandrawseveralconclusions.
First,mostadvisoryserviceforecastsarenotasaccurateastheforwardrateintermsofmeansquarederror.
Second,judgmentalforecastersaresuperiortoeconometricforecastersforshort—termforecasts;therelationshipisreversedforlonger—termforecasts(oneyear).
Third,twostatisticaltestsindicatethatthefractionof"correct"forecastsissignificantlylargerthanwhatwouldbeexpectediftheadvisoryserviceswereonlyguessingatthedirectionofthefuturespotrate.
Inthissense,theforecastservicesappeartodemonstrateexpertiseandusefulness.
However,afullanalysisoftherisk—returnoppor-tunitiesavailabletoadvisoryserviceusersisstillincomplete.
Itshouldbecautionedthatiftheforwardratecontainsariskpremium,thenweexpectadvisoryservicemodelstobeattheforwardrateaccordingtothetestswehaveoutlined.
Inthiscasewemustmeasurespeculativereturnsrelativetoariskmeasure.
Whileadvisoryserviceforecastsmayleadtoprofits,theymaynotbeunusualafteradjustingforrisk.
RichardM.
LevichNewYorkUniversityGraduateSchoolofBusiness100TrinityPlaceNewYork,N.
Y.
10006(212)285—61761.
I.
Int.
o4nctionWiththeintroductionoffloatingexchangeratesintheearly1970's,thestatisticalvariabilityofexchangeratesincreaseddramatically.
TheseexchangeratecL13werenotperfectlyanticipated.
Hence,thevariabilityofunanticipatedexchangeratechangesalsoincreased.
Themorethanfiveyearhistoryoffloatingexchangerateshassetnperiodsofbothrelativecalmandturbulence.
Inparticular,duringthelastyearunanticipatedexchangeratechangesincreasedtounpreci-dentedhighlevelsformanycurrencies(Levich1978).
Inthissettingitisobviousthatfirmsandinvestorscouldhaveenjoyedhigherearningsiftheyhadmoretimelyandaccurateinformationaboutfutureexchangerates.
1Inthepresentfloatingrateperiod,accurateinformationaboutfutureexchangeratesappearstobeascarceresourceand,correspondingly,ithasahighvalue.
Asmallexchangerateforecastingindustryhasdeveloped.
2Ingeneral,thesefirmssellinformationaboutfutureexchangerates.
Theirspecificmethodologyandproductscoverawiderangeofpossibilities.
Somefirmsrelyonastrictlyqualitativeapproach;othersarehighlytechnical,utilizingsimultaneousequationmodels,spectralanalysis,orcatastrophetheory.
Theoutputfromthesemodelsmaybeapointestimateofthefuturespotrate,thequarterlyaverageforsomefutureperiod,orpossiblyjustthefuturetrendmovement.
Forecastsplaytwoimportantrolesineconomicanalysis.
First,theabilitytopredicttheconsequencesofchangesinunderlyingcircumstancesisanimportantpartofeconomicsas2.
apositivescience.
Analysisofeconomicforecastsisanessentialdiagnosticcheckoftheadequacyofatheoryormodel.
Second,economicdecisionsonconsumptionandinvestmentdependoninformation,whichincludespredictionsoffutureevents.
Sincethefuturevalueofeconomicvariablesmaybe(currently)unobservable,economicagentsmustrelyonforecasts.
Themotivationforthispaperisoexaminehypothesesbasedonthesetworoles.
First,fromanacademicview-point,itisofinteresttoexaminetheadequacyofforeignexchangeforecastingmodels.
Specifically,wewouldliketodetermine(1)Howaccurateareprofessionalforecasters,(2)Doforecastersproducerational,unbiasedforecasts,(3)Doforecastersrevisetheirpredictionssothattheirforecasterrorsareseriallyuncorrelated,(4)Whatfundamentalfactorsareassociatedwithforecasterrors,andCS)Whatdeterminestheheterogeneityofforecastsacrossadvisoryservices.
Second,fromamorepracticalviewpoint,wewouldliketoknowifforeignexchangeforecastsareusefultodecisionmakers.
Specifically,wewouldliketoexamine(1)Ifthepredictionsofadvisoryservicesaremoreaccuratethantheforwardrate,(2)Howtheaccuracyofpredictionvariesacrosscinrency,forecastinghori-zon,andtimeperiodaswellasforecastingserviceand(3)Whetherthepredictionsofanyforecastingservicewouldhaveresultedinunusualspeculativeprofits.
Thesetwomotivationsare,ofcourse,highlycomplementary.
2a.
Thepurposeofthispaperistoprovideanobjectiveanalysiswhichaddressessomeoftheabovequestionsforalargesampleofforecasts.
Onthebasisofthecurrentre-search,wecandrawseveralconclusions.
First,mostadvisoryserviceforecastsarenotasaccurateastheforwardrateintermsofmeansquarederror.
Second,judgmentalforecastersaresuperiortoeconometricforecastersforshort-termfore-casts;therelationshipisreversedforlonger-termforecasts(oneyear).
Third,twostatisticaltestsindicatethatthefractionof"correct"forecastsissignificantlylargerthanwhatwouldbeexpectediftheadvisoryserviceswereonlyguessingatthedirectionofthefuturespotrate.
Inthissense,theforecastservicesappeartodemonstrateexpertiseandusefulness.
However,afullanalysisoftherisk-returnopportunitiesavailabletoadvisoryserviceusersisstillincomplete.
ThepapercontinuesinsectionII,wherewepresentatheoreticaldiscussionoftheconditionsunderwhichforeignexchangeforecastsarelikelytoconveyvaluableinformation.
InsectionIIIwediscussalternativetechniquesforevalua-tingforecasts.
TheempiricalanalysisofrecentexchangerateforecastsispresentedinsectionIV.
3.
II.
TheValueofInformation--rnrhouldYuEverPayforaForecastA.
EfficientMarketTheoryandExpertiseAcriticalbuildingblockinmicroeconomictheoryistheroleofpricesinaggregatinginformation.
Asubstantialliteratureineconomicsandfinancedealswiththeprocessbywhichinformationisreflectedinpricesanditsconsequencesforinvestors.
Inthemostsimple,frictionless,textbookeconomywhereinformationisfreelyavailabletoall,itisclearthatnoonewillpayforinformation.
Furthermore,therewillbenooptimalstrategyforfirmsorinvestorstofollow;eachinvestmentisfairlypricedrelativetoitsriskandtheavailableinformation.
Intherealworld,informationiscostlytocollect.
Thisfactimpliesthatproductionofinformationwillbelimitedtothepointwherethemarginalcostandmarginalbenefitfromanadditionalunitofinformationareequalized.
Whileinformationmaybecostlytogenerate,thereareenormouseconomiesofscaleinthedistributionofexistinginformation(e.
g.
,vianews-papers,television,ornewswires).
Animplicationoftheaboveisthatinvestorsmayearnthecompetitiverateofre-turnontheirinvestmentininformationonlyiftheyhavemono-polis±icaccesstoth'eiiformation.
Oncetheinformationispubliclyavailable(i.
e.
,apublicgood),itisreflectedinpricesandofnofurthervalue.
6Theconventionalwisdom.
.
onthevalueofinformationandtheexistenceof(forecasting)expertiseseemstohavecom-pletedacycle.
Attheriskofgeneralization,priortothe1960'sthepredominantimageofthefinancialcommunitywasoneofprofessionalismandexpertiseinpickingwinxiers.
Themid-1960'sthroughthe1970'switnessedanexplosionofaca-demicandprofessionalresearchtestingtheefficientmarkethypothesis.
Thegeneralimpressionleftbythisliteraturewasthattheperformancerecordofmanyprofessionalstrategiesandmany"insiders"didnotsurpasstheperformanceofnaiveandlow-costalternativestrategiesforinvestment.
Astheevidencefavoringmarketefficiencyaccumulated,thevalueofprofessionalexpertiseseemedtodecline.
Passivestrategieswhichemphasizedlowmanagementfeesandlargediversificationgainsseemedtodominatemoreactivestrategieswhichemphasizedforecastingindividualstockreturns.
Howevertheextremeefficientmarketsview--thatpricescontinuouslyreflectallavailableinformationandsosuperiorperformanceisnotpossible--dependsonaverystrictsetofassumptions.
8Inthepastfewyears,academicresearchhasattemptedtoexploremodelswhichrelaxsomeoftheseassump-tions.
Theresultsareshiftingtheacademicviewbacktoward5.
aviewmorepalatabletothefinancialcommunity-i.
e.
theredoexistrationalmodelsofbehaviorinwhichinvestorswillseekoutandpayforprofessionaladvice.
Theearlyliteratureonmarketefficiencyexplicitlyrecognizedthispointbygroupingempiricalresearchintoweak,semi-strong,andstrongformteststodescribetestsbasedonvariousinformationsets--historicalprices,publicinformation,andallavailableinformation.
Severalstudies(LoneandNiederhoffer1968,Scholes1972,McDonald1973,andJaffe1974)reportevidencewhichsuggeststhatinsiderscananddoearnunusualreturnsrelativetothemarket.
MorerecentresearchbyGrossmanandStiglit:(1976)hasintroducedanexplicitcostforinformation.
Costlyinformationimpliesthatinvestorswillnotcollectallinfor-mation,somarketswillneverbefullyefficient(i.
e.
strong-form).
IntheGrossinan/Stiglitzmodel,thosewhochosetobeinformedearnhigherprofitsthanthosewhochosetoremainuninformed.
Butthegreaterprofitisonlytocompensateforthecostofinformation.
Aslongastheinformationcollectionindustryiscompetitivewithfreeentryandexit,therewillbenoexcessreturnsearnedbycollectinginformation.
However,iftheinformationindustryisnotfullycompetitive,theninforma-tiontakesonan"inside"characterandexcessreturnsarepossible.
7.
Whilethisisoneexplanationforinvestorpurchasesofinformation,thereareatleasttwounansweredquestions.
First,totheextentthattheWSJtendstosurveyspecificanalysts,theseanalystsshouldbeabletochargeahigherpricesincetheirrecommendations(potentiallyandinitially)willreceiveawiderdistribution.
Asecondproblemis"selectionbias!
.
'ThereisevidencethatthoserecommendationswhichreachtheWSJhavevalue,buthowmanyotherswerenotselectedAndhowdoestheWSJmakeitsselectionsWemaybebackinthe)eynesianbeautycontest.
AnotherrecentapproachtomarketefficiencywhjchallowsforsomeindividualstooutperformthemarketisdevelopedinFiglewski(1978a,1978b).
TradersinFiglewski'smodelhaveheterogeneousinformation,buttheyalsoarealloweddiversepriceexpectations,riskaversion,predictiveabilityandwealth.
Basedonthesefactors,tradersmaketheirinvestmentsinperio41.
Traderswithsuperior(inferior)abilitygenerallyincuranincrease(decrease)inwealthinperiod2.
Thetransferofwealth("dollarvotes")towardtraderswithsuperiortrackrecordsgivesthemarketadynamicpropertyandlong-runtendencytofullefficiency.
AnimplicationofthisanalysisisthattraderswithsuperiorabilityearnunusualreturnsrelativetOthemar-ket.
Onceagain,ifthereisamarketfortradingskills--e.
g.
expertisecanbeincreasedthroughschoolingoron—thejobtraining--thenthetradermayearnonlythefairrateofreturnbasedonhisinvestment.
6.
ArecentstudyonthevalueofinformationisreportedbyLloyd-DaviesandCanes(1978).
TheauthorsselecttheWallStreetJournalandits"HeardontheStreet"columnfortheirdatabase.
Thiscolumnsummarizesinformation(e.
g.
,earningsestimates,stockpriceprojections)aboutspecificfirmsrecentlypreparedbyleadingfinancialanalysts.
Lloyd-DaviesandCanesfindthatinthetwentydayspriortotheWallStreetJournalpublication,thereissomesmall(butsig-nificant)pricemovementinthedirectionprojectedbytheanalyst,butthemajor(andsignificant)movecomesonthepublicationdate.
Lloyd-DaviesandCanesrationalizetheseresultswiththefollowingscenario.
Intheinitialround,thefinancialanalysts'informationandrecommendationsreachonlyasmallgroupofinvestorswithlimitedcapital.
Becauseofportfolioconsiderations,theywillnotcommitalargefractionoftheircapitaltoanysingleasset.
Insomesense,then,theseinsidersstopshortinplacingafairvalueontheassetbecausethiswouldaddexcessivediversifiablerisktotheirportfolios.
WhentheinformationispublishedintheWallStreetJournal,morecapitalisattractedtotheassetandtheportfoliocon-straintisnolongerbinding.
Theassetpricenow"fullyreflects"thenowpublicinformation.
Thosewhopaidforearlyaccesstotheinformationearnareturn.
8.
Butifthereisnomarketforexpertise--e.
g.
tradersareendowedwithnon-transferableskills"thenthetradermaycaptureeconomicrentsbasedonhisspecialendowment.
10B.
InformationintheForeignExchangeMarketItisimportanttoconsiderwhattypesofinformationmightbeworthcollectinginordertoforecastexchangerates.
Inthisregard,itisinterestingtocontrasthowtheproduc-tioitanddistributionofinformationdiffersintheforeignexchangemarketandtheU.
S.
securitiesmarket.
Sincethegreatmajorityofstockpricevariationisexplainedbyfirmspecificandindustryspecificfactors,informationonthesevariablesisextremelyimportanttoinvestors.
TheSecuritiesExchangeCommissionrequiresfirmstoreportextensivedataontheiroperations.
Accountingproceduresarelargelystandardized.
Brokerscannotactoninsideinformation;theymustmakeitpublic.
Ifinformationappearscontradictoryorifrumorsappeartobethecauseofspeculativepricemovements,theSECcansuspendtradingandrequirethefirmtomakeaclarifyingstatement.
Incontrast,foreignexchangemarketbehaviordependsmainlyoncountryspecificorworldspecificfactors.
Thesefactorsmaybedeterminedbypoliticalforcesratherthanmarketforces.
Thereisnointernationalwatchdogagencytopromotethedistributionofinformation.
Institutions,accountingstandards,andaccuracyofdatavarygreatly.
Tradersrelyoninsideinformationandarenotrequiredtopublicizethisinformation.
9Giventhecontrastingcharacterofthesemarketinstitutions,itcouldbearguedthatalargerfractionofinformationispubliclyavailableinthestockmarketthanintheforeignexchangemarket.
Asaresult,thediversityofbeliefsaboutindividualcurrenciesislikelytobegreaterthanthediversityofbeliefsaboutindividualstocks.
Anotherimportantfactorwhichpertainstocurrencyforecastingi5thelinkbetweenbasicinformationandtheforecast.
Itisveryoftenassumedthatifallinformationisefficientlyreflectedintoday'sforwardratethentheforwardrateistheoptimal,publiclyavailableforecastofthefuturespotrate(St+).
Thisargumentignoresthepossibilitythatariskpremiumortransactioncostsmayexist,sothatthetrueforward-spotrelationshipis(1)St+t,n++T+wherePCX)isariskpremiumwhichdependsonothervariables,X.
T.
jsatransactioncostsmeasure.
isarandomerrorterm.
If(1)isthecorrectrelationship,thenadvisoryservicesshouldbeexpectedtoproducefoiecastswhicharemoreaccuratethantheforwardrate.
Asaresult,usersoftheseforecastswillearnspeculativereturns,butitremainstobeshownthatthesereturnsarelargerelativetotheriskincurred.
Thisisanimportantissuewhichwillbebroughtupagaininthenextsection.
10.
Weconcludethatcrediblemodelsofmarketbehaviorexistwhichallowforinvestmentsininformationandyetremainconsistentwithmarketefficiency.
Theoryalsopermitsinvestorstobeendowedwitharangeofanalyticalskillsortooccupypreferredlocationsinthemarket,bothofwhichcharacteristicsmay.
notbetradeable.
Thereareclearlynumerousexamplesofinsideinformationleadingtounusualprofits.
However,itisbynomeansclearthattheforeigflmarketexchange/producestheoptimalamountofinformation--orequivalently,whetheradditionalinvestmentsininformationwillleadtoaprofit.
III.
AnalyzingForeignExchangeForecastsTheanalysisofforeignexchangeforecastsisatrickyprocedure.
Withoutdirectinformationonthecostsofforecastingerrorsorontheinvestor'sutilityofwealth,thereisnotauniformprocedureforanalyzingdifferentforecastingmethods.
Thereisagreementthat,insomesense,theforecastshould"beatthemarket.
"Therearetwogeneralapproachestodetermineifanadvisoryservicepossesses"expertiseFirst,wecanexaminevariousstatisticalpro-pertiesoftheforecasterrors.
Second,wecancalculatethespeculativereturnsearnedbyusingtheforecast.
11.
StatisticalAnalysisofForecastErrorsUnderabroadrangeofconditions,accarisonofsimplestrystatisticscanbeusedtodistinguishforecasts.
Forexample,tomaximizeutility,investorswithasyimnetriclinearlossftuctionshouldse-lecttheforecastwiththemininu.
meanabsoluteerrorwhileinvestorswithasymeetricquadraticlossfmctionshouldselecttheforecastwiththemininnmeansquaredforecasterror.
However,theinvestor'$lossftctionmaybeasymetricordiscontinuousatapointintime(e.
g.
theinvestorwelcomesprofitsbutcamotlosemorethansomeamo*mtwith-outlosinghisjobordeclaringban1tcy)oritcanbevariableovertine(e.
g.
smalllossesovernineconsecutiveperiodsareacceptableaslongastheinvestorispositionedtocatchthebigexchangeratemoveinperiodten).
Intheselattercases,othercriteriaaplyforselectingaforecastingmodel.
Figire1illustratesapotentialpitfallifforecastsarejudgedonthebasisofmeanormeansquarederrors.
Assi.
mtetoday'sforwardrateis$2.
00andtalternativeforecastsofthefuturespotrateareandS2—$2.
08.
Iftheactualspotrateturnsouttobe$2.
02,thesecothforecast(S2)issuperioreventhoughitresultedinalargerforecasterrorbecauseitadvisedinvestorstotakelongandprofitableforwardsterlingpositions.
Consequently,wheninvestorsareinterestedonlyinthesignoftheirprofitsthefractionofperiodswheretheforecastcorrectlypredictsonlythedirectionofmovementintheexchangerate,becomesavalidcriterionforjudgingforecasts.
Directioncanbedefinedrelativetothecurrentspotrate(Sr),thecurrentforwardrateorsomeother.
,''/.
fl'.
°°*S.
'Figure1:IllustratingaPitfallinForecastErrorAnalysisFigure2:IllustratingaTestforAdvisoryServiceExpertise1/I'50/4012.
decisionvariable.
(e.
g.
theforwardrateplusariskpremiumasin(1)).
Ananalysisofdirectionrelativetothecurrentforwardratewouldbeaconservativetestifthemarketpriceincludesariskpremium.
Wecanconstructthefollowingtest.
Wewishtoestimatetheprobability(p)ofcorrectadviceinanyperiodandthentoinferwhetherthisprobabilityisgreaterthanone-half.
Moreformally,wearetesting12H0:p0.
5(advisoryservicehasnoexpertise)H1:pO.
5(thereisforecastingexpertise)Forexample,inasampleofn—100observations,assumethattheadvisoryserviceproducesr60correctforecasts.
Thepro-bability(p1)thatthis60%trackrecordcouldhaveoccurredunderthenullhypothesisis2.
3w.
ThereforepA_r/nisonemeasureofforecastingexpertiseandp1isameasureofourconfidencethatpisgreaterthan0.
5.
(thetypeIerrorprobability).
Inaddition,wecancalculatetheprobability(p2)thatwejudgeaservicetohavenoexpertise(pCURRENCYSERVICE>123.
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FOOTNOTES11nthecasewhereriskneutralfirmscantradeforwardexchangecontractsatapriceequaltotheexpectedfuturespotrate,Baron(1976)demonstrateSthatthereisnowelfarelossfromexchangerateuncertainty.
Consequently,inourexample,theownersofinformationwillreceiveanincometransferfromtherestoftheworld.
(Theforwardmarketisazerosumgame).
However,ifinvestorsareriskaverse,theproductionofaccurateinforma-tionshouldreduceuncertaintyaboutfuturerelativeprices.
In-creasedtradeingoodsandcapitalresultsinanincreaseinworldincome.
2AhighlyinformativeandreadablesurveyofforeignexchangeadvisoryservicesisinEuromoney,August1978.
3TheimportanceofpredictionisstressedbyFriedman(1953)whostates"theonlyrelevanttestofthevalidityofahypothesisiscomparisonofitspredictionswithexperience.
"Withrespecttoeconometricprediction,christ(1951)makesthestrongerstate-mentthat"Theultimatetestofaneconometricmodel.
.
,comeswithcheckingitspredictions.
"4Twoearlierpapershavereportedontheaccuracyofadvisoryserviceforecasts.
ling(1978)aggregatedforecastsacrossadvisoryservicestoformasimpleaverage"professional"forecast.
Duringthesevenquarterperiod1976-Ito1977-Ill,theprofessionalfore-castwassuperiortotheforwardrateforecastonlyforthe1DM.
Xingsuggestedthatthisisasurprisingresultsincethe1DMmarketisveryactiveandspeculatorsshouldactsothattheinformationintheforecastisquicklyreflectedintheforwardrate.
Analternativeexplanation,whichweconsi4erfurtherinsectionII,isthatspeculatorsareriskaverseandasaresulttheforwardrateisnotnecessarilythebestpubliclyavailableforecast.
Goodman(1979)analyzedbothmedium-term,economicorientedadvisoryservicesandshort-termtechnicaladvisoryservices.
Whiletheformergroupappearednomoreaccuratethantheforwardrate,Good-manconcludedthatthetechnicalservicescouldleadtolargeprofitsfollowingadailytradingstrategy.
"(Thetechnically-orientedservices')consistentlyverystrongpredictiveperformancesupportstheviewthatspeculativerunsdooccurintheexchangemarketandthattheforeignexchangemarketisnotefficient.
"5See,forexample,Fama(1970)andBlack(1971).
6Thisisessentiallyarestatementofthesemistrongformtestsofassetmarketefficiencywhichpositsthatpricesreflectpubliclyavailableinformation.
OnestraightforwardtestofthishypothesisisreportedinScholes(1972).
70n.
importantstudyinthisregardwasbyJensen(1968)whoconcludedthatprofessionall)'managedmutualfundsdidnotingeneralachieveunusualreturnsrelativetotheriskandmanagementcostsincurred.
Thegeneraldeclineinstockmarketprices(inrealterms)overthisperiodalsohelpedtotarnishtheimageofprofessionalismandexpertise.
8Theseassumptionsincludecontinuoustrading,notransactioncostsandnoinformationcosts.
Theefficientmarkethypothesis4oesallowforheterogeneousexpectations,butthealgebraicfoi-mulationandempiricaltestingofamodelwithheterogeneousex-pectationsisconsiderablymorecomplex.
p-39Weshouldnotethatweareconsideringinformationpurchasesonlyforthepurposeof"pickingwinnersorbeatingthemarket.
"Investorswhodonotwishtodothiswillstillrequiresomeinfor-mationtomatchaportfoliototheirriskpreferences.
10Asatheoreticalmatter,eventhislattercaserequiresfur-therqualification.
Otherinvestorsmayimitatethetraderwithexpertiseandindoingsolowerhisprofits.
Alternatively,traderswithoutexpertisemayloseovertimeandleavethemarketsothatthetraderwithexpertisecomestodominateandbecomethemarket.
Foradetaileddiscussionoftheseissues,seeaaiffaandSchaifer(1968),especiallyChapter6.
l2p(O.
5,theadvisoryservicehasnoexpertise.
Butinthiscase,investorscansimplyreversetheadvisoryservicerecommendations.
23AttheChicagoMercantileExchange,interestearningU.
S.
Treasurybillsareacceptabletomeetmarginrequirements.
141ftheinvestorownsaU.
S.
dollarasset,hemustsellitandgiveupreturni.
15DooleyandShafer(1976)recognizethispointintheiranalysis.
6The"ModernTheory"approachpopularizedbyGrubel(1966)presentsapartialequilibriummodel.
Speculatorsareassumedtoberiskaversealthoughthereisnooperationalmodelforestimatingtheforeignexchangeriskpremium.
MorerecentpapersbyRollandSolnik(1977)andGrauer,F-4Litzenberger,andStehie(1976)presentageneralequilibriumframework,butthereisdisagreementabouthow,orif,thesemodelscanbemadeoperational.
SeethediscussionintheJournalofFinance,May1977.
17Asinourearliertestforforecastingexpertise,wemustaassumetheprobabilityofcorrectpredictionisconstantovertime.
Inaddition,however,wemustassumethatthedistributionofspeculativereturnsisconstantovertime.
Whenthisassumptionisnotmet,theH-statisticcangivemisleadingresults.
Forexample,supposeaforecastingserviceprovidesincorrectforecastsinnineconsecutivepreiods,howeverineachperiodthelossissma-1($.
01percontract)0Assumefurtherthatinperiodtentheservicecorrectlypredictsalargeexchangeratechange($.
41).
JudgingbytheH-statistic(H$.
32actualprofit/$.
S0potentialprofit-64%),theadvisoryserviceisdoinganadmirablejob.
Howevertheprobabilityofcorrectadviseinanysingleperiodislow(pr/n—0,10)andsignificantlyworsethanguessing.
18Theproblemofselectinganhistoricalsetofspotratestorepresentthemarketpricebringsintofocustheissueofselectingaróasonablestandardforassessingforecastingaccuracy.
Wehaveobservedthatexchangeratessometimestradewithin.
a1%or2%dailyrange;recentlyfortheSwissfrancandtheJapaneseyen,therangehasa-preached4%-5%.
Forexample,onJanuary1at9:00a.
m.
,thethree-monthforwardratemaybe$2.
00.
OnApril1at9:00a.
m.
thespotratemayby$2.
00andthenproceedtocloseat$2.
06.
Isthisa3%forecasterrorevenifthetradercouldhavesoldhisF-SpositionduringthedayatafavorablerateForthisobservation,theselectionofanopeningrate,anoonrateoraclosingratehasagreatimpactontheforecasterror.
Wecanaddthatatanymomentoftime,foreignexchangeratesalsomayvarysomewhatacrosstheworld'smanytradingrooms.
9Sincetheforecastfrequencyisgenerallyoneobservationpermonth,theone-monthpanelalsorepresentsanindependentsample.
20Weusetheexactbinomialcalculationforsamplessmallerthan18,andthenormalapproximationotherwise.
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