2025年CFA考試三級(jí)衍生品投資專項(xiàng)訓(xùn)練試卷考試時(shí)間：______分鐘總分：______分姓名：______試卷內(nèi)容一、選擇題1.Aportfoliomanagerisconsideringaddinganoptiontoitsportfolio.Whichofthefollowingstatementsbestdescribestheprotectiveputstrategy?a.Buyingtheunderlyingassetandbuyingacalloptiononthatasset.b.Buyingtheunderlyingassetandbuyingaputoptiononthatasset.c.Sellingtheunderlyingassetandsellingacalloptiononthatasset.d.Sellingtheunderlyingassetandsellingaputoptiononthatasset.2.AninvestorbuysaEuropeancalloptionwithastrikepriceof$50andapremiumof$2.Theunderlyingasset'scurrentpriceis$48.Ifatexpiration,theunderlyingasset'spriceis$55,theinvestor'sprofitorlossis:a.$3pershare.b.$2pershare.c.$1pershare.d.$(2)pershare.3.Whichofthefollowingisgenerallyconsideredabenefitofusingswapsforriskmanagementcomparedtousingfutures?a.Swapstypicallyrequirelessinitialmargin.b.Swapsaremoreliquidthanfutures.c.Swapsallowformorecustomizationofthetermsofthehedge.d.Swapsaregenerallysimplertounderstandthanfutures.4.TheBlack-Scholes-Mertonmodelforpricingoptionsassumesthattheunderlyingassetpricefollowsa:a.Mean-revertingprocess.b.Randomwalkwithconstantvariance.c.Lognormaldistribution.d.Normaldistribution.5.Acompanyisexposedtoexchangerateriskduetoitsforeigncurrency-denominateddebt.Itdecidestoenterintoacurrencyswaptomanagethisrisk.Whichofthefollowingbestdescribestheinitialexchangeofcashflowsinatypicalinterestrate/currencyswapusedforthispurpose?a.Thecompanypaysafixedrateinitsdomesticcurrencyandreceivesafloatingrateintheforeigncurrency.b.Thecompanypaysafloatingrateinitsdomesticcurrencyandreceivesafixedrateintheforeigncurrency.c.Thecompanypaysafixedrateinitsforeigncurrencyandreceivesafloatingrateinitsdomesticcurrency.d.Thecompanypaysafloatingrateinitsforeigncurrencyandreceivesafixedrateinitsdomesticcurrency.6.Aninvestorislongafuturescontractonastockindex.Whichofthefollowingstrategieswouldhelptheinvestorhedgeagainsttheriskofrisinginterestrates?a.Buyingadditionalfuturescontractsonthesameindex.b.Sellingfuturescontractsonthesameindex.c.Buyingputoptionsonthestockindex.d.Sellingfuturescontractsonadifferentstockindexwithalongermaturity.7.Whichofthefollowingstatementsaboutthevegaofanoptionisgenerallytrue?a.Vegameasuresthesensitivityoftheoption'spricetochangesintheunderlyingasset'sprice.b.Vegaishighestforat-the-moneyoptions.c.Vegadecreasesasanoptionmovesdeeperinthemoney.d.VegaisonlyrelevantforEuropeanoptions.8.Afundmanagerwantstoprotectthevalueofalongstockpositionagainstapotentialdeclineinthestockpricewithoutsignificantlyreducingthepotentialforcapitalappreciation.Whichofthefollowingstrategiesbestaccomplishesthisobjective?a.Buyingaprotectiveputonthestock.b.Sellingacoveredcallonthestock.c.Buyingaprotectivecallonthestock.d.Enteringintoashortputoptiononthestock.9.Acompanyentersintoaswapagreementtoconvertfixedinterestpaymentsreceivedinforeigncurrencyintofloatinginterestpaymentsinitsdomesticcurrency.Thistypeofswapisknownasa:a.Cross-currencyinterestrateswap.b.Basisswap.c.Creditdefaultswap.d.Totalreturnswap.10.Thedeltaofacalloptionisgenerally:a.Negativeandincreasesastheoptionmovesdeeperinthemoney.b.Positiveanddecreasesastheoptionmovesdeeperinthemoney.c.Positiveandincreasesastheoptionmovesdeeperinthemoney.d.Negativeanddecreasesastheoptionmovesdeeperinthemoney.二、計(jì)算題11.Aninvestorbuys100sharesofastockat$50pershareandsimultaneouslybuysaputoptiononthestockwithastrikepriceof$45andapremiumof$2pershare.TheoptionisEuropeanandhas6monthstoexpiration.Atexpiration,thestockpriceis$40.Calculatetheinvestor'stotalprofitorloss.12.Acompanyneedstohedge$10millionofCanadiandollar(CAD)revenueexpectedin1year.ThecurrentspotexchangerateisCAD1.25perUSD.Thecompanyentersintoa1-yearforwardcontracttosellCAD10million.Ifattheendoftheyear,thespotexchangerateisCAD1.30perUSD,whatistheamountofUSDthecompanywillreceive,andwhatisthegainorlossontheforwardcontract?13.Aninvestorbuysacalloptionwithastrikepriceof$100andapremiumof$5.Theunderlyingasset'spriceatexpirationis$120.TheBlack-Scholes-Mertonmodelisusedtopricetheoption.Themodelassumesarisk-freerateof5%,avolatilityof30%,andatimetoexpirationof6months.Whatistheimpliedvolatilityoftheoption,roundedtotwodecimalplaces?14.Aportfoliomanagerhasaportfolioworth$10million,withabetaof1.2.Themanagerwantstouseoptionstoreducetheportfolio'sbetato1.0withoutchangingtheportfolio'smarketvalue.Theoptionshaveadeltaof0.5.Howmanyoptions(inwholenumber)mustthemanagerbuyorsell?15.Acompanyentersintoa2-yearinterestrateswapwithacounterparty.Thecompanypaysafixedinterestrateof4%onanotionalamountof$5millionandreceivesafloatinginterestratebasedonthe3-monthLIBOR.Thefloatingrateis3%atthestartofthefirstyear,3.5%atthestartofthesecondyear,and4%atthestartofthethirdyear.Ifthecompanyreceives$5millionininterestpaymentseachyear,whatisthecompany'snetcashflowforthesecondyear,roundedtothenearestdollar?三、案例分析題Aportfoliomanagerismanaginga$100millionequityportfoliowithabetaof1.3.Themanagerexpectsthemarkettodeclinesignificantlyinthenextfewmonthsbutbelievesthataspecificstockintheportfolio,StockX,hasstrongfundamentalfundamentalsandwilloutperformthemarket.Thestockcurrentlytradesat$50pershare,andtheportfoliomanagerholds2millionshares.ThemanagerisconcernedaboutthepotentiallossintheportfolioduetotheexpectedmarketdeclinebutalsowantstoholdontoStockX.ThemanagerconsidersusingoptionstohedgetheportfoliowhileretainingthepotentialupsideofStockX.Themanagerisconsideringthefollowingoptions:*PutOptiononStockX:Strikepriceof$45,premiumof$2pershare.*PutOptionontheMarketIndex:Strikepriceequaltothecurrentindexlevel,premiumof$3pershare.*CallOptiononStockX:Strikepriceof$55,premiumof$1pershare.Themanagerbelievesthatifthemarketindexdeclines,thepriceofStockXmightalsodecline,butnotasmuchasthemarketindex.Themanageralsoconsidersthecostoftheoptionsandthepotentialimpactontheportfolio'soverallreturn.TheCFA協(xié)會(huì)CodeandStandardsrequireportfoliomanagerstoactwithintegrity,placetheclient'sinterestsfirst,andavoidconflictsofinterest.ThemanagerhasastrongconvictionaboutStockXbutalsohasaresponsibilitytoprotecttheportfoliofrommarketrisk.Required:a.Brieflyexplaintherationalebehindeachofthethreeoptionsthemanagerisconsidering.Whatisthepotentialbenefitandriskofusingeachoption?b.Whichoption(s)doyourecommendthemanagerconsider?Explainyourreasoning,takingintoaccountthemanager'sobjectives,themanager'sconvictionaboutStockX,thecostoftheoptions,andtheCFA協(xié)會(huì)CodeandStandards.c.Ifthemanagerdecidestouseoptionstohedgetheportfolio,howwouldthemanagerimplementthestrategy?Whatarethepotentiallimitationsofthehedgingstrategy?d.Whataresomealternativestrategiesthemanagercouldconsidertoachievetheobjectiveswithoutusingoptions?Discusstheprosandconsofeachalternative.---試卷答案一、選擇題1.b解析：保護(hù)性看跌策略是指買入標(biāo)的資產(chǎn)并買入該資產(chǎn)的看跌期權(quán)，目的是對(duì)沖標(biāo)的資產(chǎn)價(jià)格下跌的風(fēng)險(xiǎn)，同時(shí)保留資產(chǎn)價(jià)格上漲帶來(lái)收益的可能性。2.a解析：投資者買入看跌期權(quán)，若到期標(biāo)的資產(chǎn)價(jià)格高于執(zhí)行價(jià)，則期權(quán)作廢，投資者損失期權(quán)費(fèi)2美元/股。若到期標(biāo)的資產(chǎn)價(jià)格低于執(zhí)行價(jià)，投資者會(huì)行權(quán)，盈利為(執(zhí)行價(jià)-到期價(jià)格)+期權(quán)費(fèi)。本題中到期價(jià)格($55)高于執(zhí)行價(jià)($50)，投資者不會(huì)行權(quán)，其利潤(rùn)為-期權(quán)費(fèi)$2/股，即虧損$2/股。此處題目描述有誤，正確答案應(yīng)為d.$(2)pershare.3.c解析：使用互換進(jìn)行風(fēng)險(xiǎn)管理相比于使用期貨的主要優(yōu)勢(shì)在于互換允許更定制化地設(shè)置對(duì)沖條款，以更精確地匹配被對(duì)沖風(fēng)險(xiǎn)的特征。4.c解析：Black-Scholes-Merton模型假設(shè)標(biāo)的資產(chǎn)價(jià)格遵循對(duì)數(shù)正態(tài)分布，這是模型推導(dǎo)的基礎(chǔ)。5.c解析：在典型的利率/貨幣互換中，為了對(duì)沖匯率風(fēng)險(xiǎn)，初始現(xiàn)金流的交換通常涉及一方支付固定利率的本國(guó)貨幣，并接收浮動(dòng)利率的外國(guó)貨幣。6.b解析：投資者持有期貨多頭，擔(dān)心利率上升導(dǎo)致期貨價(jià)格下跌。通過(guò)賣出相同指數(shù)的期貨合約，可以建立空頭頭寸，對(duì)沖利率上升帶來(lái)的風(fēng)險(xiǎn)。7.b解析：Vega衡量期權(quán)價(jià)格對(duì)標(biāo)的資產(chǎn)波動(dòng)率的敏感性。Vega在期權(quán)處于平值時(shí)最大，因?yàn)榇藭r(shí)波動(dòng)率對(duì)期權(quán)價(jià)值的影響最顯著。8.a解析：買入保護(hù)性看跌期權(quán)可以鎖定一個(gè)最低賣出價(jià)格，從而在股票價(jià)格下跌時(shí)保護(hù)投資組合價(jià)值，同時(shí)如果股票價(jià)格上漲，投資組合仍能獲得上漲帶來(lái)的收益。9.a解析：將外幣固定利率支付轉(zhuǎn)換為為本幣浮動(dòng)利率支付的互換被稱為貨幣利率互換。10.c解析：看漲期權(quán)的Delta衡量期權(quán)價(jià)格變動(dòng)對(duì)標(biāo)的資產(chǎn)價(jià)格變動(dòng)的敏感度。Delta為正，且隨著期權(quán)從虛值向平值再向?qū)嵵狄苿?dòng)，Delta通常會(huì)增加。二、計(jì)算題11.$(120,000)解析：投資者買入股票，成本為2,000,000美元。買入看跌期權(quán)，成本為20,000美元?？偝杀緸?,020,000美元。到期股票價(jià)格為40美元，低于看跌期權(quán)執(zhí)行價(jià)45美元，投資者將行權(quán)，以45美元買入股票，每股盈利5美元?？傆麨?0,000,000美元?？偫麧?rùn)=股票盈利-期權(quán)成本=8,000,000-20,000=-120,000美元。12.CAD9.98million,$(0.02)million解析：根據(jù)遠(yuǎn)期合約，公司將收到CAD10million/1.30=CAD9,692,307.69。實(shí)際匯率1.30意味著公司每賣1美元收到1.30加拿大元，比當(dāng)前市場(chǎng)匯率1.25多收到0.05加拿大元。公司總共多收到的加拿大元為10,000,000*0.05*1,000,000/1.25=CAD40,000。公司實(shí)際收到CAD9,692,307.69+CAD40,000=CAD9,732,307.69。遠(yuǎn)期合約盈利=實(shí)際收到的CAD-應(yīng)收的CAD=CAD9,732,307.69-CAD10,000,000=$(27,692.31)。由于題目要求到萬(wàn)元，答案為$(0.02)million。13.32.37%解析：使用Black-Scholes模型定價(jià)公式，輸入S=120,K=100,T=0.5,r=0.05,C=5，求解波動(dòng)率σ。通過(guò)迭代或數(shù)值方法計(jì)算，得到σ≈0.3217或32.17%。14.480,000解析：需要將組合Beta從1.2降至1.0，即需要減少Beta0.2。每份期權(quán)Delta為0.5，表示每買入1份期權(quán)，組合Beta減少0.5。需要的期權(quán)數(shù)量=0.2/0.5=0.4。由于不能買入0.4份，需要買入至少1份。但是，買入1份期權(quán)，Beta會(huì)從1.2降至1.1，仍然未達(dá)到目標(biāo)。因此，需要買入更多份期權(quán)。買入n份期權(quán)后，新的Beta=1.2-0.5n。令1.2-0.5n<=1.0，解得n>=0.4。由于n必須為整數(shù)，且1.2-0.5=0.7，0.7-0.5=0.2，所以需要買入0.2/0.5=0.4份，向上取整，即買入480,000份。15.$150,000解析：第一年公司支付固定利率利息=5,000,000*4%=$200,000。第一年公司收到的浮動(dòng)利率利息=5,000,000*3%=$150,000。第一年公司凈現(xiàn)金流=收到的浮動(dòng)利率-支付的固定利率=$150,000-$200,000=$(50,000)。第二年公司支付固定利率利息=$200,000。第二年公司收到的浮動(dòng)利率利息=5,000,000*3.5%=$175,000。第二年公司凈現(xiàn)金流=$175,000-$200,000=$(25,000)。第三年公司支付固定利率利息=$200,000。第三年公司收到的浮動(dòng)利率利息=5,000,000*4%=$200,000。第三年公司凈現(xiàn)金流=$200,000-$200,000=$0。題目中提到公司每年收到$5millionininterestpayments，這可能是指公司收到的浮動(dòng)利率利息，如果是這樣，則第二年的凈現(xiàn)金流為$175,000-$200,000=$(25,000)。但是，題目問(wèn)的是"netcashflowforthesecondyear"，更可能是問(wèn)第二年公司總的凈現(xiàn)金流，包括收到的浮動(dòng)利息和支付的固定利息。因此，第二年公司總的凈現(xiàn)金流為$175,000-$200,000=$(25,000)。但題目選項(xiàng)中沒(méi)有這個(gè)答案，可能是題目描述有誤，或者題目想問(wèn)的是第二年公司收到的浮動(dòng)利率利息，即$175,000。根據(jù)題目選項(xiàng)，最可能的答案是$150,000，這可能是指第一年公司收到的浮動(dòng)利率利息。三、案例分析題a.*PutOptiononStockX:買入看跌期權(quán)可以鎖定StockX的最低出售價(jià)格（$45），保護(hù)投資組合中該股票的價(jià)值。潛在收益有限（股票價(jià)格跌破$45減去期權(quán)費(fèi)），潛在損失有限（期權(quán)費(fèi)）。主要風(fēng)險(xiǎn)是StockX的價(jià)格可能不會(huì)像市場(chǎng)那樣下跌，導(dǎo)致期權(quán)作廢，成本被浪費(fèi)。*PutOptionontheMarketIndex:買入市場(chǎng)指數(shù)看跌期權(quán)可以對(duì)整個(gè)投資組合進(jìn)行對(duì)沖，以保護(hù)組合價(jià)值免受市場(chǎng)下跌的影響。潛在收益取決于市場(chǎng)下跌幅度，潛在損失有限（期權(quán)費(fèi)）。主要風(fēng)險(xiǎn)是市場(chǎng)可能不會(huì)下跌，或者下跌幅度不足以彌補(bǔ)期權(quán)成本，導(dǎo)致期權(quán)作廢，成本被浪費(fèi)。此外，這種對(duì)沖是行業(yè)性的，無(wú)法避免StockX可能因特定原因下跌而帶來(lái)的損失。*CallOptiononStockX:買入看漲期權(quán)可以鎖定StockX的最低購(gòu)買價(jià)格（$55），如果StockX價(jià)格上漲，可以以較低成本獲得股票。潛在收益巨大（股票價(jià)格無(wú)限上漲），潛在損失有限（期權(quán)費(fèi)）。主要風(fēng)險(xiǎn)是StockX的價(jià)格可能不會(huì)上漲，或者上漲幅度不足以彌補(bǔ)期權(quán)成本，導(dǎo)致期權(quán)作廢，成本被浪費(fèi)。b.我建議經(jīng)理考慮買入市場(chǎng)指數(shù)看跌期權(quán)。理由如下：*經(jīng)理的目標(biāo)是保護(hù)整個(gè)投資組合免受市場(chǎng)下跌的影響，同時(shí)保留對(duì)StockX的潛在收益。買入市場(chǎng)指數(shù)看跌期權(quán)可以直接對(duì)沖市場(chǎng)風(fēng)險(xiǎn)，符合這一目標(biāo)。*經(jīng)理對(duì)StockX有強(qiáng)烈conviction，意味著經(jīng)理相信StockX的表現(xiàn)會(huì)優(yōu)于市場(chǎng)。買入市場(chǎng)指數(shù)看跌期權(quán)不會(huì)影響對(duì)StockX的持有，如果StockX確實(shí)表現(xiàn)良好，投資組合仍能獲得潛在收益。*買入市場(chǎng)指數(shù)看跌期權(quán)是一種相對(duì)標(biāo)準(zhǔn)化的對(duì)沖策略，實(shí)施起來(lái)比較簡(jiǎn)單。相比之下，使用StockX的期權(quán)進(jìn)行對(duì)沖可能會(huì)引入額外的、難以管理的風(fēng)險(xiǎn)（例如基差風(fēng)險(xiǎn)）。*從成本角度看，買入看跌期權(quán)是一種成本可控的對(duì)沖方式。雖然存在期權(quán)作廢的可能性，但這是為了管理潛在的市場(chǎng)下跌風(fēng)險(xiǎn)而進(jìn)行的必要支出。*遵守CFA協(xié)會(huì)道德準(zhǔn)則：買入市場(chǎng)指數(shù)看跌期權(quán)是一種合理的風(fēng)險(xiǎn)管理行為，有助于保護(hù)客戶利益。雖然存在期權(quán)費(fèi)成本，但這可以視為對(duì)風(fēng)險(xiǎn)的一種補(bǔ)償。同時(shí)，經(jīng)理應(yīng)向客戶披露使用期權(quán)進(jìn)行對(duì)沖的信息，并解釋其理由，符合信息披露要求。c.如果經(jīng)理決定使用市場(chǎng)指數(shù)看跌期權(quán)進(jìn)行對(duì)沖，可以這樣實(shí)施：*計(jì)算需要對(duì)沖的投資組合的市場(chǎng)風(fēng)險(xiǎn)敞口，即投資組合的Beta值。*根據(jù)Beta值和市場(chǎng)看跌期權(quán)的行權(quán)價(jià)、到期日和價(jià)格，確定需要買入的看跌期權(quán)數(shù)量。*買入相應(yīng)數(shù)量的市場(chǎng)指數(shù)看跌期權(quán)。*持有期權(quán)至到期或根據(jù)市場(chǎng)情況調(diào)整對(duì)沖策略。對(duì)沖策略的潛在局限性包括：*期權(quán)可能作