投资学精要(博迪)(第五版)习题答案英文版chapter9&10

EssentialsofInvestments(BKM5thEd.)AnswerstoSuggestedProblems–Lecture7BondPricingExamplesforExam3:Problem9(a)inChapter9providesanexampleofabondpricecalculation(answershownbelow).Asadditionalexamples,page69inyourcoursepacketprovidesseveralbondpricingproblemsforbondswithvariousmaturity,yield,andcouponcharacteristics.Thebondpricesfortheseexamplesareasfollows(noteallbondspaycouponssemi-annually):8%coupon,8%marketyield,10yearstomaturity:B=$1,000.008%coupon,10%marketyield,10yearstomaturity:B=$875.388%coupon,6%marketyield,10yearstomaturity:B=$1,148.778%coupon,8%marketyield,20yearstomaturity:B=$1,000.008%coupon,10%marketyield,20yearstomaturity:B=$828.418%coupon,6%marketyield,20yearstomaturity:B=$1,231.156%coupon,8%marketyield,10yearstomaturity:B=$864.106%coupon,10%marketyield,10yearstomaturity:B=$750.766%coupon,6%marketyield,10yearstomaturity:B=$1000.00Chapter9:4.Lower.Interestrateshavefallensincethebondwasissued.Thus,thebondissellingatapremiumandthepricewilldecrease(towardparvalue)asthebondapproachesmaturity.5.True.UndertheExpectationsHypothesis,therearenoriskpremiabuiltintobondprices.Theonlyreasonforanupwardslopingyieldcurveistheexpectationofincreasedshort-termratesinthefuture.7.Uncertain.Liquiditypremiumwillincreaselong-termyields,butlowerinflationexpectationswillreducelong-termyieldscomparedtoshort-termrates.Theneteffectisuncertain.8.Iftheyieldcurveisupwardsloping,youcannotconcludethatinvestorsexpectshort-terminterestratestorisebecausetherisingslopecouldeitherbeduetoexpectationsoffutureincreasesinratesorduetoaliquiditypremium.9.a)Thebondpays$50every6monthsCurrentprice=$1052.42Assumingthatmarketinterestratesremainat4%perhalfyear:theprice6monthsfromnow=$1044.52b)Rateofreturn=[1044.52-1052.42+50]/1052.42=.04or4%per6months14.Zero8%coupon10%coupona)Currentprices$463.19$1,000$1,134.20b)Pricein1year$500.25$1,000$1,124.94Pricechange$37.06$0.00$-9.26Couponincome$0.00$80.00$100.00Totalincome$37.06$80.00$90.74Rateofreturn8.00%8.00%8.00%33.a)Theforwardrate,f,istheratethatmakesrollingoverone-yearbondsequallyattractiveasinvestinginthetwo-yearmaturitybondandholdinguntilmaturity:(1.08)(1+f)=(1.09)2whichimpliesthatf=0.1001or10.01%b)Accordingtotheexpectationshypothesis,theforwardrateequalstheexpectedshortratenextyear,sothebestguesswouldbe10.01%.c)Accordingtotheliquiditypreference(liquiditypremium)hypothesis,theforwardrateexceedstheexpectedshort-termratefornextyear(bytheamountoftheliquiditypremium),sothebestguesswouldbelessthan10.01%.35.a.Weobtainforwardratesfromthefollowingtable:Maturity(years)YTMForwardratePrice(forpartc)110.0%$909.09($1000/1.10)211.0%12.01%[(1.112/1.10)–1]$811.62($1000/1.112)312.0%14.03%[(1.123/1.112)–1]$711.78($1000/1.123)b.Weobtainnextyear’spricesandyieldsbydiscountingeachzero’sfacevalueattheforwardratesderivedinpart(a):Maturity(years)PriceYTM1$892.78[=1000/1.1201]12.01%2$782.93[=1000/(1.1201x1.1403)]13.02%Notethatthisyear’supwardslopingyieldcurveimplies,accordingtotheexpectationshypothesis,ashiftupwardinnextyear’scurve.c.Nextyear,thetwo-yearzerowillbeaone-yearzero,anditwillthereforesellat:($1000/1.1201)=$892.78Similarly,thecurrentthree-yearzerowillbeatwo-yearzero,anditwillsellfor$782.93.Expectedtotalrateofreturn:two-yearbond:%00.101000.0162.811$78.892$==−three-yearbond:%00.101000.0178.711$93.782$==−37.d)2e)3f)2g)4Chapter10:1.∆∆BBDyy=−⋅+1-7.194*(.005/1.10)=-.03272.IfYTM=6%,Duration=2.833yearsIfYTM=10%,Duration=2.824years6.a)BondBhasahigheryieldsinceitissellingatadiscount.Thus,thedurationofbondBislower(itislesssensitivetointerestratechanges).b)BondBhasaloweryieldandiscallablebeforematurity.Thus,thedurationofbondBislower(itislesssensitivetointerestratechanges).9.a)PV=10,000/(1.08)+10,000/((1.08)2)=$17,832.65Duration=(9259.26/17832.65)*1+(8573.39/17832.65)*2=1.4808yearsb)Azero-couponbondwith1.4808yearstomaturity(duration=1.4808)wouldimmunizetheobligationagainstinterestraterisk.c)Weneedabondpositionwithapresentvalueof$17,832.65.Thus,thefacevalueofthebondpositionmustbe:$17,832.65*(1.08)1.4808=$19,985.26Ifinterestratesincreaseto9%,thevalueofthebondwouldbe:$19,985.26/((1.09)1.4808)=$17,590.92Thetuitionobligationwouldbe:10,000/1.09+10,000/((1.09)2)=$17,591.11oranetpositionchangeofonly$0.19.Ifinterestratesdecreaseto7%,thevalueofthebondwouldbe:$19,985.26/((1.07)1.4808)=$18,079.99Thetuitionobligationwouldbe:10,000/(1.07)+10,000((1.07)2)=$18,080.18oranetpositionchangeof$0.19.**Theslightdifferencesresultfromthefactthatdurationisonlyalinearapproximationofthetrueconvexrelationshipbetweenfixed-incomevaluesandinterestrates.11.a)Thedurationoftheperpetuityis1.05/.05=21years.Letwbetheweightofthezero-couponbond.Thenwefindwbysolving:w×5+(1–w)×21=1021–16w=10w=11/16or.6875Therefore,yourportfoliowouldbe11/16investedinthezeroand5/16intheperpetuity.b)Thezero-couponbondnowwillhaveadurationof4yearswhiletheperpetuitywillstillhavea21-yearduration.Togetaportfoliodurationof9years,whichisnowthedurationoftheobligation,weagainsolveforw:w×4+(1–w)×21=921–17w=9w=12/17or.7059Sotheproportioninvestedinthezerohastoincreaseto12/17andtheproportioninthep