一级模拟考试二教育专业领先增值

7.072%（即半年支付3.5365）即说明7.072%Answer:当利率期限结构是向上倾斜时，c>a>b；当利率期限结构是向下倾斜时，b>a>cAnswer:48％的债券的空头。由于利息抵消，那么当期的现金流是90－2×80=－70,10年后的现金流是200－100=100。所10年期的即期利率为：1ln1000.0357;3.57 6个月的即期利率是21n(1+6/94)=12.38%;12个月的即期利率是ln(l+11/89）=11.65%;l.5年的即期利率为R4e0.12380.54e0.11651.0104e1.5RRR=11.52年期债券的即期利率为R5e0.12380.55e0.11651.05e0.1151.5105e2Re2RRR=11.3Answer:1

债券收益率0.286.804.2560.002债券的价格应当从86.80增加到87.54另外法，目前债券收益率为11%，下降0.2%至10.8%，具有收益率为10.8％的债Answer:合约的有效期限为5个月，其中有3个月的红利率为2%,2个月的红利率为5%,均月红利率为13225%3.2%,所 价格5300e0.090.0320.4167307.34Answer:0.65e0.16670.080.030.6554，而实际的价格比这个价格高。那么者就可借买法郎现货，并且卖空法郎。Answer:九个月成本的现值是：0.060.06e6e7610.011266.252

大约23如果季计复利，且以实际/360计算天数，则利率为4.8%；如果以实际/实际计算天数，那么利率变成:4.8%*365/360=4.867%;如果以连续复利计算，那么利率变成：4ln(1+0.4867/4)=4.84%.因此，以连续复利计算的远期利率为4.84-0.23=4.61%。ThetreasurershouldshortTreasurybondfuturescontract.Ifbondpricesgodown,thisfuturespositionwillprovideoffsettinggains.Thenumberofcontractsthatshouldbeshortedis10,000,000×7.1/(91,375×8.8)=Roundingtothenearestwholenumber88contractsshouldbeTheEurodollarfuturescontractpriceof89.5meansthattheEurodollarfuturesrateis10.5%perannumwithquarterlycompoundingandanactual/360daycount.This es10.5×365/360=10.646%withanactual/actualdayThisis：41n(1+0.25×0.10646)=0.1051or10.51%withcontinuousTheforwardrategivenbythe91-dayrateandthe182-dayrateis10.4%withcompounding.ThissuggeststhefollowingarbitrageBuyEurodollarBorrow182-day3.Investtheborrowedmoneyfor914个月后收到6百万并支付4.80百万。10个月后将收到6百万并支付4个月对于支付浮动利率的一方而言，互换的价值为103.328-101.364=1.964百万。对于支付1.11/

22.739(百万 32.6 1.01/1.05对于支付英镑的一方而言，互换的价值为32.916-（22.739*1.65）=-4.604百万；对于支付的浮动支付价值为0.5*0.08*1000=40万，净收益为50-40=10万，即每次支付的现金流为10万。第3年末到第5年末的现金流为：3年：5万3.5年：10万4年：10万4.5年：10万5年：10万约成本41.3万。 ：KertS4 1执行价格的现值为60e ，股利的现值为0.80e 56457. ：CS0D但是从空头方可以至少获得现值64-57.65-0.79=5.56的利润。如果价格在到期时的价格超过了60，者获得的现值为5.56-5.00=0.56。

SKCPSKe美式看跌看涨存在如下关系： Theimplieddividendyieldisthevalueofqthatsatisfiestheput--callparityequation.Itisthevalueofqthatsolves154+1400exp(-0.05×05)=34.25+1500exp(-ThisisThedeltaindicatesthatwhenthevalueoftheeuroexchangerateincreasesby$0.01,thevalueofthebank'spositionincreasesby0.01x30,000=$300.The indicatesthattheeuroexchangerateincreasesby$0.01thedeltaoftheportfoliodecreasesby0.01x80,000=800.Fordeltaneutrality30,000eurosshouldbeshorted.Whentheexchangeratemovesupto0.93,weexpectthedeltaoftheportfoliotodecreaseby(0.93--0.90)x80,000=2,400sothatit 27,600.Tomaintaindeltaneutrality,anet27,600havebeenshorted.Whenaportfolioisdeltaneutralandhasanegativeg,alossisexperiencedwhenthereisalargemovementintheunderlyingassetprice.WecanconcludethatthebankislikelytohavelostThedeltaoftheportfoliois：-1,000×0.50-500×0.80-2,000×(-0.40)-500X0.70=-450Theg oftheportfoliois：-1,000×2.2-500×0.6-2,000×1.3-500×1.8=-6000Thevegaoftheportfoliois:-1,000×1.8-500×0.2-2,000×0.7-500×1.4=-Alongpositionin4,000tradedoptionswillgiveag-neutralportfoliosincethelongpositionhasag of4,000×1.5=+6,000.Thedeltaofthewholeportfolio(includingtradedoptions)isthen:4,000×0.6-450=1,950Hence,inadditiontothe4,000tradedoptions,ashortpositionin1,950isnecessarysothattheportfolioisbothg anddeltaneutral.。所以投资组合的日方差为 。所以，5天的标准差为 汇率日变动百分比等于SP561.5x,即P到组合10天的99%VAR是0.588 0.018230020.01225002 .60.0180.012 1019.99黄金投资的10天97.5%的VAR为 101.9633470；白银投资的1097.5%VAR为6000101.96 =7438Thetraderwouldneedtoadjustthehedgeasfollows:$89.8million×1.0274=$92.26millionThus,thetraderneedstopurchaseadditionalTIPSworth$2.46million.Firstconvertthecutoffpointsof32and116intostandardnormaldeviates.Thefirstz32802,andthesecond

z116801.5 Fromnormaltables,P2Z1.5PZ1.5Z20.93320.0228Applyingthediscountfactorsimpliedbythethreebasebonds,thepresentvalueofthe2.0%bondis$96.594.Asthebond'smarketpriceis$99.00,the2.0%11/30/2014mis-pricedbondis"tradingrich":marketpriceof$99.00>model(PV)priceof$96.594.ThearbitragetradewillbetoselltherichbondandbuythereplicatingWedon'trequireallthreetrades,onlythetradewithrespecttothe6.0%1.5-yearbasebondbecauseonlyonecashflowisinvolvedat1.5years.Replicationrequiresthefinalcashflowstomatchsuchthat:F(1.5)*(1+6%/2)=(1+2%/2),andF(1.5)=(1+2%/2)/(1+6%/2)=98.058%=0.98058.So,thereplicatingportfoliotradeincludesapurchase(long)of98.058%ofthefaceamountofthe6%couponbondwhichhasacostof98.058%*$102.40=$100.4117.combinedwithashortof1-.857%ofthe4%couponbondandshort-1.894%ofthe5.0%bond,thenetcosttobuy(long)thereplicatingportfoliois$96.594,whichcoincideswiththemodel(PV)priceofthe2.0%bond.Thiswillcreateperfectlyoffsettingcashflowsyetproduceaninitialprofitof$99.00(i.e.,sellthetradingrichbond)-$96.594(i.e.,buythereplicatingportfolo)=$2.406arbitrageprofit.Calculatorapproach:CF0=-10;CF1=4;CF2n=3;CF3=4;I=10→NPV=-$0.879038Heteroskedasticityexistsifthevarianceoftheresidualsisnotconstant.Inaheteroskedasticregression,thet-statisticswillbeincorrectlycalculatedusingordinaryleastsquaresmethods.Thecapitalassetpricingmodel(CAPM)assumestheInvestorsdesiretoizetheirexpectedutilityofwealthattheendofnextInvestorsareriskInvestorsareonlyconcernedwiththemeanandstandarddeviationofAssetsarefullyAresultisstatisticallysignificantifitisunlikelytohavehappenedbychance.Thedecisionruleistorejectthenullhypothesisifthep-valueislessthanthesignificancelevel.Ifthep-valueislessthanthesignificancelevel,thenweconcludethatthesampleestimateisstatisticallydifferentthanthehypothesizedvalue.AnysecuritywitharatingbelowBBBbyS&PorBaabyMoody’sisaspeculativeornon-investmentgradeinstrument.BondCisthecheapest-to-deliverbond,at Costof TheVaRofthisinvestmentcanbeinterpretedaseither(1)thereisa95%probabilitythattheportfoliowilllosenomorethan$18milliononagivendayor(2)thereisa5%probabilitythattheportfoliowilllosemorethan$18milliononagivenday.Hedgedposition:$2,500,000SGDx$0.80CAD/SGD=$2,000,000CADUnhedgedposition:$2,500,000x$0.73CAD/SGD=$1,825,000CADThesimplelinearregressionF-testteststhesamehypothesisasthet-testbecausethereisonlyoneindependentvariable.TheF-statisticisusedtolyouifatleastoneindependentvariableinasetofindependentvariablesexinsasignificantportionofthevariationofthedependentvariable.Itteststheindependentvariablesasagroup,andthuswon’tlyouwhichvariablehassignificantexnatorypower.TheF-testdecisionruleistorejectthenullhypothesisiftheF>Fc.Usingtheinterestrateparityformula,thefuturesexchangerateiscomputedasN(Tnote)=$40,000,000*0.025/0.062=Themodelcorrespondsto=0.05,=0.92,and=0.000005.Because=1--,itfollowsthat=0.03.Becausethelong-runaveragevariance,VL,canbefoundbyVL=/,itfollowsthatVL=0.000167.Inotherwords,thelong-runaveragevolatilityperdayimpliedbythemodelissqrt(0.000167)=1.29%. =(0.3*0.2)/(0.2*0.3+0.5*0.3+0.3*0.2)=Atlowyields,acallablebondexhibitsnegativeconvexitybutthisdoesnotimplynegativeduration;rather,itimpliesonlythatdurationisincreasingratherthandecreasing(morespecifically,aslowyieldsincrease,negativeconvexityimpliesthedollarduration[theslopeofthetangentline]isdecreasingfromnegativetomorenegative.Asthenegativeconvexitygivesoverto"regular"convexity,thedollarduration[theslope]continuestobenegativebutincreasingtolessnegative.Regardless,evenwiththenegativeconvexity,thedurationisalwayspositive(i.e.,theslopeofthetangentisalwaysnegative)IisamodelfailureandIIisaninternalfailure.ThesearetypesofoperationalIfthedaily,90%confidencelevelValueatRisk(VaR)ofaportfolioiscorrectlyestimatedtobeUSD5,000,onewouldexpectthat90%ofthetime(9outof10),theportfoliowillloselessthanUSD5,000;equivalently,10%ofthetime(1outof10)theportfoliowillloseUSD5,000ormore. Fixedratecoupon=USD300millionx7.5%=USD22.5Valueofthefixedpayment=Bfix=22.5e0.07+322.5e0.08*2=USD295.80Valueofthefloatingpayment=Bfloating=USD300million.Sincethepaymenthasjustbeenmadethevalueofthefloatingrateisequaltothenotionalamount.Valueoftheswap=Bfloating-Bfix=USD300-USD295.80=USD4.2Thecalculationisasfollows:Two-thirdsoftheequityfundisworthUSD40million.TheOptimalhedgeratioisgivenbyh=0.89*0.51/0.48=0.945ThenumberoffuturescontractsisgivenN=0.945*40,000,000/(910*250)=166.26≈167,rounduptonearestAnswer:JuneJuneJuneJuneJuneAnswer:RiskpremiumattributabletoF(1)=B(A,1)*(9.0%-2.0%)=0.40*7.0%=RiskpremiumattributabletoF(2)=B(A,2)*(11.0%-2.0%)=0.80*9.0%=7.20%;andExpectedreturntoportfolio(A)=2.0%+2.80%+7.20%=12.00%.Aisincorrect.Whencallsaredeepin-the-moneyandputsaredeepout-of-the-money,deltasareNOTmostsensitivetochangesintheunderlyingasset.Bisincorrect.Whenbothcallsandputsaredeepin-the-money,deltasareNOTmostsensitivetochangesintheunderlyingasset.Cisincorrect.Whenbothcallsandputsaredeepout-of-the-money,deltasareNOTmostsensitivetochangesintheunderlyingasset.Discorrect.Whenbothcallsandputsareat-the-money,deltasaremostsensitivetochangesinunderlyingasset, sarelargestwhenoptionsareat-the-Answer：Aisincorrect.ThechanceofBBBloansbeingupgradedover1yearis4.08%(0.02+0.21+Bisincorrect.ThechanceofBBloansstayingatthesamerateover1yearisCiscorrect.88.21%representsthechanceofBBBloansstayingatBBBorbeingupgradedover1Disincorrect.ThechanceofBBloansbeingdowngradedover1yearis5.72%(0.04+0.08+0.33+5.27). ThedailyVaRat95%confidencelevelisgivenbythefifthworstlossovertheperiodwhich P(NEUTRAL|Constant)=P(Constant|Neutral)*P(Neutral)/=0.2*03/(0.1*0.2+0.2*0.3+0.15*0.5)=ThisistheThisistheThisistheProb(Neutral|ThebasicproblematBaringswasoperationriskcontrol.NickLeesonswasinchargeoftradingandsettlement.Thisdualresponsibilityallowedhimtohidelossesbycrossingtradesatfabricatedprices.Hethenbookedtheprofitablesideofthetradeinaccountsthatwerereportedandtheunprofitablesideinanunreportedaccount.Thelackofsupervisionalsopermittedhimtoshiftfromhedgedtradingstrategiestospeculativestrategiesinanefforttohidepreviouslyincurredlosses.Clearlyhisreportingtomultiplemanagersinaconvolutedorganizationalstructureledtoambiguityconcerningwhowasresponsibleforperformingspecificoversightfunctions.LeesonusedashortstraddlestrategyontheNikkei225andheldspeculativedoublelongpositionsinthemarketforNikkei225futurescontracts.LiquiditywasanissueintheMetallgesellschaftandLTCMcases,notStandards3.1and3.2relatetothepreservationofity.Thesimplest,mostconservative,andmosteffectivewaytocomplywiththeseStandardsistoavoiddisclosinganyinformationreceivedfroma,excepttoauthorizedfellowemployeeswhoarealsoworkingforthe.IftheinformationconcernsillegalactivitiesbyMTEX,Blackmaybeobligatedtoreportactivities Buyingacall(put)optionwithalowstrikeprice,buyinganothercall(put)optionwithahigherstrikeprice,andsellingtwocall(put)optionswithastrikepricehalfwaybetweenthelowandhighstrikeoptionswillgeneratethebutterflypaymentpattern.Twootherwronganswerchoicesdealwithbullandbearspreads,whichcanalsobereplicatedwitheithercallsorputs.Abullspreadinvolvespurchasingacall(put)optionwithalowstrikepriceandsellingacall(put)optionwithahigherexerciseprice.Abearspreadistheexactoppositeofthebullspread.Astackisabundleoffuturescontractswiththesameexpiration.Overtime,afirmmayacquirestackswithvariousexpirydates.Tohedgealong-termriskexposure,afirmwouldcloseouteachstackasitapproachesexpiryandenterintoacontractwithamoredistantdelivery,knownasaroll.Thisstrategyiscalledastack-and-rollhedgeandisdesignedtohedgelong-termriskexposureswithshort-termcontracts.Usingshort-termfuturescontractswithalargernotionalvaluethanthelong-termrisktheyaremeanttohedgecouldresultinoverhedging”dependingonthehedgeratio.Allelseequal,convexityincreaseforlongermaturities,lowercoupons,andlowerBondswithembeddedoptions(e.g.,callablebonds)exhibitnegativeconvexityovercertainrangesofyieldswhilestraightbondswithnoembeddedoptionsexhibitpositiveconvexityovertheentirerangeofyields.Thedifferenceofthedifferencesis(12%-10%)-[LIBOR+1%—(LIBOR+0.5%)]Whenforwardpricesareasadiscounttospotprices,abackwardationmarketissaidtoexist.Therelativelyhighspotpricerepresentsaconvenienceyieldtotheconsumerthatholdsthecommodityforimmediateconsumption.Fabozzi:“Oneimportantriskiseliminatedinazero-couponinvestment—thereinvestmentrisk.Becausethereisnocoupontoreinvest,thereisn’tanyreinvestmentrisk.Ofcourse,althoughthisisbeneficialindeclining-interest-ratemarkets,thereverseistruewheninterestratesarerising.Theinvestorwillnotbeabletoreinvestan estreamatrisingreinvestmentrates.Thelowertheratesare,themorelikelyitisthattheywillriseagain,makingazero-couponinvestmentworthlessintheeyesofpotentialholders.”TherelationshipstillProbabilityofzerodefaults=97%^3=91.26%andprobabilityofexactlyonedefault(binomial)=nCk*p^k*(1-p)^(n-k)=3*3%^1*97%^2=8.468%,s.t.cumulativeProb[zerooronedefault]is99.74%.Boththe95%VaRand99%VaRareonedefault.The10%losstailincludes5%ofnoloss(i.e.,the90%to95%CDF)and5%ofthelossevent.Theaverageofthis10%tailisthereforegivenby:50%*0+50%*[E(loss|lossevent)]=50%*[20%*10+50%*18+30%*25]=$