2015年11月FRM一級測試卷（附答案）

1.Consideraconvertiblebondthatistradingataconversionpremiumof20percent.Ifthevalueoftheunderlyingstockrisesby25percent,thevalueofthebondwill:

A.Risebylessthan25%.

B.Riseby25%.

C.Risebymorethan25%.

D.Remainunchanged.

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2.Ifacashflowof$10,000intwoyears'timehasaPVof$8,455,theannualpercentagerate,assumingcontinuouscompoundingisCLOSESTto:

A.8.13%.

B.8.39%.

C.8.75%.

D.8.95%.

3.Thecurrentvaluesofafirm'sassetsandliabilitiesare200millionand160millionrespectively.Iftheassetvaluesareexpectedtogrowby40millionandliabilityvaluesby30millionwithinayearandiftheannualstandarddeviationofthesevaluesis50million,thedistancefromdefaultintheKMVmodelwouldbeclosestto:

A.0.8standarddeviations.

B.1.0standarddeviations.

C.1.2standarddeviations.

D.Cannotnotbedetermined.

4.Whatisthesemiannual-paybondequivalentyieldonanannual-paybondwithayieldtomaturityof12.51percent?

A.12.00%.

B.11.49%.

C.12.51%.

D.12.14%.

5.Youwanttotestatthe0.05levelofsignificancethatthemeanpriceofluxurycarsisgreaterthan$80,000.Arandomsampleof50carshasameanpriceof$88,000.Thepopulationstandarddeviationis$15,000.Whatisthealternativehypothesis?

A.Thepopulationmeanisgreaterthanorequalto$80,000.

B.Thepopulationmeanislessthan$80,000.

C.Thepopulationmeanisnotequalto$80,000.

D.Thepopulationmeanisgreaterthanis$80,000.

Answers:

1.Correctanswer:A

Theconvertiblebondimplicitlygivesbondholdersacalloptionontheunderlyingstock.Thedeltaofthisoptionwillvarybetween0(whentheoptionisextremelyoutofthemoney)and1(whentheoptionisextremelyinthemoney).Inthiscase,thebondistradingataconversionpremiumof20%sothedeltamustbesomewherebetweenzeroandone,andhencethepriceoftheconvertiblebondwillrisebylessthanthepriceoftheunderlyingstock.金程題庫--全球財經(jīng)第一題庫（精題真題、全真?？枷到y(tǒng)、名師答疑）點擊進入【FRM題庫】

2.Correctanswer:B

Continuouslycompoundedrate=ln(FV/PV)/N=ln(10000/8455)/2=8.39%.

3.Correctanswer:B

Distancefromdefault=(Expectedvalueofassets-Expectedvalueofliabilities)/Standarddeviation=(240-190)/50=1.0.

4.Correctanswer:D:

Thesemiannual-paybondequivalentyieldofanannual-paybond=2*[(1+yieldtomaturityontheannual-paybond)*0.5-1]=12.14%.

5.Correctanswer:D

Thealternatehypothesisisthestatementwhichwillbeacceptedifthenullhypothesisisprovenwrong.Therefore,wemakewhateverwearetryingtotestasthealternatehypothesis-inthiscasethatthemeanpriceofluxurycarsisgreaterthan$80,000,andthenullhypothesisastheopposite(themeanpriceofluxurycarsislessthanorequalto$80,000).Thisproblemisacommonexampleofhowstatisticiansestablishhypothesesbyprovingthattheopposite(i.e.thenullhypothesis)isfalse.

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