HOMEWORK3SOLUTION

Chapter8

1. AssumethatyourcompanyexportstoJapanandearnsyenrevenues,thusforecastsoftheYen/$rateare important.Suppose two forecasters issue theirpredictions for theYen/$exchangerate.ThecurrentspotrateisYen90/$.ForecasterApredictsarateof98nextmonthandforecasterBpredictsarateof88.Theforwardrateisat89,reflectingtheinterestratedifferentialbetweenthetwocurrencies.Onemonthlater,thespotratereaches92Yen/$.

a. WhichoftheforecastersA,Bortheforwardratemadethemostaccurateforecast?

b. Whichoneisthemostuseful?

SOLUTIONS:

a. Threeforecasters(SA,SB,andSForward)forecast98,88and89Yen/$respectively.ThefuturespotrateSt+1=92Yen/$.Theforwardratewasthemostaccuratewithanerrorof3/92or3.26%.

b. ForecasterAhadthemostusefulforecastsincehecorrectlypredictedthattheyenwouldfallagainstthedollar.ForecasterBwouldhaveadvisednottohedgeandthefirmwouldhaveincurredaforeignexchangelossonitsJapanesesales.Eventhoughtheforecastisfaroff,ForecasterAgavethecorrectadviceleadingtoacorrectahedgingdecisionbythefirm.ForwardsaleofYenat89wouldhavesavedthefirmsomeforeignexchangelosses

2. Youare the treasurerofa largemultinational company. Suppose thatyou receiveeverymonthexchangerateforecastsfortheYen/$exchangeratefromfivedifferentforecastinginstitutions:A,B,C,D,andE.Fromyourpastexperience,thebestforecasterhasbeenfirmC,followedbyA,D,B,andE.

ThehistoricRMSE(standarddeviationofforecastingerrors)forthefiveforecastersandthecurrentpredictionsareshowninthefollowingtable:

Forecaster RMSE YenForecast

A 7 80

B 15 82

C 5 85

D 10 81

E 20 88

a. Calculatethecompositeforecastthatresultsfromevenlyweightingthesefiveforecasts.

b. Calculateacompositeforecastasdescribed inthechapterthatassignsgreaterweighttoforecastswithgreateraccuracy.

c. Discusstheadvantagesanddisadvantagesofusingtheforecastin(b)versus(a).

SOLUTIONS:

a. Theevenlyweightedforecastis0.2x80+0.2x82+0.2x85+0.2x81+0.2x88=83.2

b. Thissystemassignsweightsinverselyproportionaltoeachforecaster'sstandarddeviation.TheseweightsarewA=25.53%,wB=11.91%,wC=35.74%,wD=17.87%,andwE=8.94%.Thecompositeforecast:25.53%x80+11.91%x82+35.74%x85+17.87%x81+8.94%x88=Yen82.92/$

c. Composite forecast (b) shouldbea superior forecastwitha smallerRMSEand lessbiassince it places greater weights on forecasters that have been more accurate. Thesuperiorityof composite forecast (b),however,dependsupon the individual forecastersretaining their relativeaccuracy ratings. If the rankingsofRMSEwere tochange, thenasimpleevenlyweightedcompositeforecast,asin(a),couldbesuperior.

3. Supposeyouareevaluatingtwoforecastersbasedonthefollowinginformation.

ForecasterAmade30"correct"forecastsofatotalof50forecastsduringthelastyear.ForecasterBmade114"correct"forecastsofatotalof200forecastsduringthelastyear,.

a. WhatistheprobabilitythatforecasterA'strackrecordofcorrectforecastswassimplyduetochance?(Note:youmayusethenormalapproximationtothebinomialdistribution.)

b. WhatistheprobabilitythatB'strackrecordofcorrectforecastswassimplyduetochance?(Note:youmayusethenormalapproximationtothebinomialdistribution.)

c. DiscusswhetheryouwouldprefertousetheforecastspreparedbyAorB.

SOLUTIONS:

a. A's track record isp= r/n=30/50=60%.This isgreater than50%.Butwithonly50observations, the standard error of the estimate is fairly large, 0.0707 = (0.5*(10.5)/50)0.5=(p*(1p)/n)0.5.Sothetvalueagainstthenullhypothesisthatp=0.5[t=(0.600.50)/0.0707] is1.414,whichdoesnot fall intotherejectregionat=0.025 level (t2.009)andwefailtorejectthenullhypothesis(Astrackrecordofcorrectforecastswassimplyduetochance).

b. B's track record isp= r/n=114/200=57%.This isalsogreater than50%.With200

observations,thestandarderroroftheestimateissmaller,0.0354=(0.5*(10.5)/200)0.5

= (p*(1p)/n)0.5. So the tvalue against the null hypothesis that p=0.5 [t=(0.57 0.50)/0.0354] is1.977,whichdoes fall into the rejection regionat =0.025 level (t 1.960)andwerejectthenullhypothesis(Bstrackrecordofcorrectforecastswassimplyduetochance)andacceptthealternative.

c. ThereisatradeoffbetweenAandB.Aappearstohaveabetterrecord,butitisbased

on a shorter history sowe have less confidence in it.B's track record is slightly lessimpressive,butstillshowssignificantexpertisewithatrackrecordbetterthan50%.

4. AsamultinationalfirmwithsalesinJapan,yourequireforecastsoftheYen/$exchangerate.Youhavebeenusingaprofessionalforecastingfirm,CrystalBallAssociates,andnowwanttomeasuretheperformanceof theirpredictions.Following isa table showing theCrystalBall forecasts, theactualendofperiodratesandtheoneperiodaheadforwardrates.

a. CalculatetheperformanceoftheCrystalBallforecastsandtheforwardrateusingtheMSEandRMSEmethodtomeasuretheiraccuracy.

b. Calculate the performance of the Crystal Ball forecasts and the forward rate using thepercentagecorrectmethodtomeasuretheirusefulness.

c. HasCrystalBallAssociatesdemonstratedunusual forecastingexpertiseaccording to thepercentagecorrectmethod?

d. Compareyourresultsusingthetwomethods.Whatdoyouconclude?

SOLUTIONS:

a. For the forward rate,MSE = 0.0022; RMSE = 0.0468 or 4.68% error in the onemonthforecast.FortheCrystalBallforecast,MSE=0.0015;RMSE=0.0392or3.92%errorintheonemonthforecast.

b. CrystalBallAssociatesforecastswere"correct"orontherightsideoftheforwardrate10timesoutof12months,or83.3%.Thepercentagecorrectmethodcannotbeusedfortheforwardrate.

Period

1

2

3

4

5

6

7

8

9

10

11

12

CrystalBall

Forecast

(endofperiod)

100

106

102

108

115

109

103

95

93

90

91

85

Actualspotrate

(endofperiod)

101

110

108

105

110

110

98

90

91

85

88

84

1periodforwardrate

98

105

100

102

108

112

105

98

90

89

90

86

c. Crystal Ball Associates track record, 83.3%, is highly unusual, signifying expertise andmakingtheforecastveryuseful.Theprobabilityofgetting10,11or12correctforecastsoutof12(assumingthattheforecasterhasnoexpertise)is(66+11+1)/4096=1.9%,sothisisavery rare and statistically significant event. The forecaster appears to have significantexpertise.[NOTE:66=12!/(10!2!);11=12!/(11!1!);1=12!/(12!0!);and4096=212whichrepresentsthenumberofpatternsfortossingafaircointwelvetimes.]

d. CrystalBallAssociatesarenotmuchmoreaccuratethantheforwardrate,buttheycouldbeveryusefulifthefirmhashedgingdecisionstomakeonaonemonthhorizon.

Chapter9

3. GeneralMotorsfinancesitself,amongotherchannels,byusingoneyear,floatingratenoteswhoseratesarerecalculatedeverythreemonthsatLIBOR+1/8.Anew$250,000,000issueisplannedformidSeptember2001withaoneyearmaturity.

a. Describe how GM could hedge its interest payments for the year. [For convenience,assumethatCMEmaturitydatescoincidewiththefirm'srolloverdates.]

b. UsingTable9.3,whatistheyearlyratethatGMcansecureifithedges?

c. CalculateGM'stotalcostsforthe$250,000,000issueassumingthatithedges.

SOLUTIONS:

a. GM could sell250 Eurodollar interest rate futures foreverymaturitywhere its interestpaymentsaresetinitiallyorreset;thatis,SeptemberandDecember2001andMarchandJune2002.

b. Forthenextyear,GMcan lock inLIBORratesof7.13%(Sept2001at92.87);7.17%(Dec2001at92.83);7.11%(Mar02at92.89);and7.11%(June02at92.89).TheannualLIBORrateis:7.13%/4+7.17%/4+7.11%/4+7.11%/4=7.13%/4=1.7825%;or(1+7.13%/4)x(1+7.17%/4)x(1+7.11%/4)x(1+7.11%/4)1=2.33%.

c. GMwillpay$250,000,000*(0.017825+0.00125)=$4,768,750.

4. TheABCfirmisconsideringborrowing$50,000,000foroneyeareitheratafixedrateof6.50% inthe US domestic market or at a floating rate indexed to threemonth LIBOR+1/4 in theEurocurrencymarket.Currently,3monthLIBORis5.25%andexpectedtoremainconstantfortheyear.

a. HowmuchwouldABCsaveifitusestheEuromarketsandtheseexpectationsaremet?[Forconvenience,assumethatCMEmaturitydatescoincidewiththefirm'srolloverdates.]

b. WhataretherisksinusingaEuromarketloan?

c. Calculate theeventual saving forABC in the casewhere LIBOR increasesby .50%everythreemonths.

SOLUTIONS:

a. Savingsare1%oftheoutstandingamountforoneyear,or$500,000.

b. TherisksareinterestrateriskbecausetheEuromarketloanisonfloatingrateterms,androlloverriskifthebankhastheoptiontorefusetoreneworrollovertheloan.IfABChasacommitment for the year, then it has no rollover risk as long as the bank remains inoperation.

c. Fixedratecosts:6.5%of$50,000,000=$3,250,000

Floatingratecosts:(1+5.5%/4)*(1+6.0%/4)*(1+6.5%/4)*(1+7.0%/4)=1.0625,oracostof6.25%.On$50,000,000principaltheinterestbillwillbe$3,125,000;stillbetterthana6.5%fixedrate.

5. Suppose that threemonthEurodollarsarequoted in the interbankmarketsat6.0% 6.125%byLondonbanks,and6.25%6.375%bySingaporebanks.

a. Explainhowyoucouldattempttomakearbitrageprofitsintheabovecase.

b. Howlargeistheprofitfromarbitraging$1,000,000inthiscase?

c. Whatrisksand/orcostsdoyoufaceinattemptingthearbitrage?

SOLUTIONS:

a. A traderwould attempt to borrow dollars from a bank in London at 6.125% and thendepositthematabankinSingaporefor6.25%.

b. The potential profit is 0.00125 * $1,000,000 / 4 = $312.50. Remember, these are perannuminterestratesforathreemonthperiod.

c. The trader carries the political risk of deposits in Singapore. If fundswere blocked inSingapore,hemightnotbeable topaybackhisLondon loan.TimedifferencesbetweenLondonandSingaporemayalsoincreasethedifficultyofthistransaction.

Chapter10

1. Suppose IBM is issuing$100million in7yearEurobondspricedatU.S.Treasuryminus25basispoints.Thereisgreatdemandfortheissueandyouarewillingtobid102for10%oftheissue.

a. Ifyouactuallygetyourbidexecuted,howmuchwillyoupayforthebond?

b. Ayearlater,theIBMEurobondsaretradedontheLuxembourgExchangeat105.Whatisthevalueofyourinvestment?Whatisyourcapitalgain(loss)?

c. Youdecidetosellthebondattheabovepricetopursueotheropportunities.Whatamountofwithholdingtaxesareyourequiredtopay?

SOLUTIONS:

a. Priceis102%ofparor1,020perbond;102%*10%*100million=$10.20millionforyourshareoftheissue.

b. Priceis105%*10%*100=$10.50million.Gainis$300,000.

c. NowithholdingtaxesapplyintheEurobondmarket.

2. SupposeCreditSuisseFirstBoston(CSFB)isthesoleleadmanagerina$100millionboughtdealfortheWorldBank.CSFBdecidestopricethesevenyearissueatpartoyield8%.

a. WhatwillbeCSFBspositioniftheFeddecidestoincreaseshortterminterestratesby50basispointsduringtheofferingperiod?

b. InsteadoftheFedmovedescribedinaabove,supposethatinternationaltradetalksbreakdown leading to adepreciationof thedollaron currencymarkets.WhatwillbeCSFBspositioninthiscase?

c. Calculatethegainor lossforCSFB ifthesevenyearEurobondraterisesto8.25%ontheofferingday.(Note:Eurobondspayinterestonlyonceeachyear.)

d. SupposeCSFBcollects2% infeesforleadmanagingtheissue.Again,calculatetheoverallgainorlossforCSFBifthesevenyearEurobondraterisesto8.25%ontheofferingday.

e. (Optional)HowcouldCSFBhedgetherisksdescribedin(a)and(b)?

SOLUTIONS:

a. Theyieldrequiredbythemarketon longtermbondsmaychange inresponse to the50basispointincreaseinshorttermrates.Iflongterminterestratesrise,thenbypledgingtosell theEurobondsatpar,CSFBwill lose thedifferencebetweenparand thenew lowerpriceofthebond.Longterminterestratesmayfall,however,ifthemarketsensesthattheincreaseinshorttermrateswillreducelongerruninflationarypressures.Inthiscase,CSFBenjoysacapitalgain.

b. Sameasin(a).Toattractinvestorsthatshyawayfromdollarassets,CSFBwillhavetolowertheEurobondpricetoalevelattractivetolenders.

c. TheEurobondpricefallsto$987.09per$1,000.00facevalue.

Theunderwriterloses1.291%onthe$100,000,000issueor$1,291,000.

d. IfCSFBcollects2.0%infees,ittransfersonly$980perbond,or$98,000,000ontheentireissuetotheWorldBank.CSFB'snetprofitisthen$2,000,000$1,291,000=$709,000.

e. CSFBcanhedgetheincreaseininterestratesbysellinginterestratefutures.

1.0825

1000+1.0825

80 = $987.09 7T7

=1T