金融市場學(xué)計算題

Chapter3

3.

If

,whatisthemarketconsensusforecastabouttheone-yearforwardrateoneyearfromnow?Isthisrateaboveorbelowtoday'sone-yearinterestrate?Explain.

ANSWER:

Theone-yearforwardrateoneyearfromnowis:

If

,thentheone-yearforwardrateoneyearfromnowmustbebelowtoday'sone-yearinterestrate.

6

a.

Acorporationisplanningtosellits90-daycommercialpapertoinvestorsofferingan8.4percentyield.Ifthethree-monthT-bill’sannualizedrateis7percent,thedefaultriskpremiumisestimatedtobe0.6percentandthereisa0.4percenttaxadjustment,whatistheappropriateliquiditypremium?

ANSWER:

Ycp,n=Rf,n+DP+LP+TA

LP=Ycp,n–Rf,n–DP–TA

LP=8.4%–7%–0.6%–0.4%

LP=0.4%

Chapter6

1.

Assumeaninvestorpurchasedasix-monthT-billwitha$10,000parvaluefor$9,000andsolditninetydayslaterfor$9,100.Whatistheyield?

ANSWER:

2.

Newlyissuedthree-monthT-billswithaparvalueof$10,000soldfor$9,700.ComputetheT-billdiscount.

ANSWER:

1.Assumeaninvestorpurchasedsix-monthcommercialpaperwithafacevalueof$1,000,000for$940,000.Whatistheyield?

ANSWER:

4.

StanfordCorporationarrangedarepurchaseagreementinwhichitpurchasedsecuritiesfor$4,900,000andwillsellthesecuritiesbackfor$5,000,000in40days.Whatistheyield(orreporate)toStanfordCorporation?

ANSWER:

8.AU.S.investorobtainsBritishpoundswhenthepoundisworth$1.50andinvestsinaone-yearmoneymarketsecuritythatprovidesayieldof25percent(inpounds).Attheendofoneyear,theinvestorconvertstheproceedsfromtheinvestmentbacktodollarsattheprevailingspotrateof$1.52perpound.Calculatetheeffectiveyield.

ANSWER:

%changeinS=1.52–1.50/1.50=0.0133=1.33%

Ye=(1+Yf)(1+%changeinS)–1

Ye=(1.25)(1.0133)–1=0.2666=26.66%

Chapter8

1.

Assumethefollowinginformationforanexistingbondthatprovidesannualcouponpayments:

Parvalue=$1,000

Couponrate=11%

Maturity=4years

Requiredrateofreturnbyinvestors=11%

a.

Whatisthepresentvalueofthebond?

ANSWER:

PVofBond=PVofCouponPayments+PVofPrincipal

=$110(PVIFAi=11%,n=4)+$1,000(PVIFi=11%,n=4)

=$110(3.1024)+$1,000(.6587)

=$341+$659

=$1,000

b.

Iftherequiredrateofreturnbyinvestorswere14percentinsteadof11percent,whatwouldbethe

presentvalueofthebond?

ANSWER:

PVofBond=PVofCouponPayments+PVofPrincipal

=$110(PVIFAi=14%,n=4)+$1,000(PVIFi=14%,n=4)

=$110(2.9137)+$1,000(.5921)

=$321+$592

=$913

c.

Iftherequiredrateofreturnbyinvestorswere9percent,whatwouldbethepresentvalueofthebond?

ANSWER:

PVofBond=PVofCouponPayments+PVofPrincipal

=$110(PVIFAi=9%,n=4)+$1,000(PVIFi=9%,n=4)

=$110(3.2397)+$1,000(.7084)

=$356+$708

=$1,064

2.

Assumethefollowinginformationforexistingzero-couponbonds:

Parvalue=$100,000

Maturity=3years

Requiredrateofreturnbyinvestors=12%

Howmuchshouldinvestorsbewillingtopayforthesebonds?

ANSWER:

PVofBond=PVofCouponPayments+PVofPrincipal

=$0+100,000(PVIFi=12%,n=3)

=$100,000(.7118)

=$71,180

3.

Assumethatyourequirea14percentreturnonazero-couponbondwithaparvalueof$1,000andsixyearstomaturity.Whatisthepriceyoushouldbewillingtopayforthisbond?

ANSWER:

PVofBond=PVofCouponPayments+PVofPrincipal

=$0+1,000(PVIFi=14%,n=6)

=$1,000(.4556)

=$455.60

11

a.

Azero-couponbondwithaparvalueof$1,000maturesin10years.Atwhatpricewouldthisbondprovideayieldtomaturitythatmatchesthecurrentmarketrateof8percent?

ANSWER:

PV=C/(1+k)n

PV=1,000/(1+0.08)10=$463.19

b.

Whathappenstothepriceofthisbondifinterestratesfallto6percent?

ANSWER:

PV=C/(1+k)n

PV=1,000/(1+0.06)10=$558.39

c.

Giventheabovechangesinthepriceofthebondandtheinterestrate,calculatethebondpriceelasticity.

ANSWER:

Pe=percentchangeinP/percentchangeink

Pe=(558.39–463.19/463.19)/(6%–8%/8%)

Pe=0.20553/–0.25=-0.822

Chapter11

1.

Assumethefollowinginformationoverafive-yearperiod.

Averagerisk-freerate=6%

AveragereturnforCranestock=11%

AveragereturnforLoadstock=14%

StandarddeviationofCranestockreturns=2%

StandarddeviationofLoadstockreturns=4%

BetaofCranestock=.8

BetaofLoadstock=1.1

Determinewhichstockhashigherrisk-adjustedreturnswhenusingtheSharpeIndex.Whichstockhashigherrisk-adjustedreturnswhenusingtheTreynorIndex?Showyourwork.

ANSWER:

SharpeIndex

ofCranestock=(11%–6%)/2%=2.5

SharpeIndex

ofLoadstock=(14%–6%)/4%=2.0

TreynorIndex

ofCranestock=(11%–6%)/.8=.0625

TreynorIndex

ofLoadstock=(14%–6%)/1.1=.0727

CranestockhasahigherSharpeIndexwhileLoadstockhasahigherTreynorIndex.

2.

AssumeMessstockhasabetaof1.2.Iftherisk-freerateis7percent,andthemarketreturnis10percent,whatistheexpectedreturnonMessstock?

ANSWER:

Expectedreturn

=7%+1.2(10%–7%)

=10.6%

3.

Using,youfoundthatIBMisexpectedtogenerateearningsof$4.38persharethisyear,andthatthemeanP/Eratioforitsindustryis$27.195.UsingtheP/Evaluationmethod,whatshouldbethevalueofIBMshares?

ANSWER:

Value=(ExpectedearningsofIBMpershare)x(MeanindustryP/Eratio)

Value=$4.3827.195

Value=$119.114

Chapter12

3.

Supposethatyoubuyastockfor$48bypaying$25andborrowingtheremaining$23fromabrokeragefirmat8percentannualizedinterest.Thestockpaysanannualdividendof$0.80pershare,andafteroneyear,youareabletosellitfor$65.Calculateyourreturnonthestock.

ANSWER:

R=(SP–INV–LOAN+D)/INV

R=($65–$25–$24.84+$.80)/$25

R=63.84%

4.

UsingtheinformationfromProblem3,calculatethereturnonthestockifyouhadusedonlypersonalfundstomakethepurchase.

ANSWER:

R=(SP–INV–LOAN+D)/INV

R=($65–$48–0+$.80)/$48

R=37.08%

5.

UsetheinformationinProblem3,butassumethatattheendofoneyearyousellthestockfor$40.Whatisthereturnifyouusedonlypersonalfunds?

ANSWER:

R=($40–$48+0+$.80)/$48=–15%

Chapter13

3.

TolandCompanysoldTreasurybillfuturescontractswhenthequotedpricewas94.00.Whenthispositionwasclosedout,thequotedpricewas93.20.Determinetheprofitorlosspercontract,ignoringtransactioncosts.

ANSWER:

Sellingprice

=$940,000

Purchaseprice

=$932,000

Profit

=$940,000–$932,000

=$8,000