养老金计划的风险管理-养老金证券化ppt课件

养老金计划的风险管理,1,.,概念,多头：是指投资者对股市看好，预计股价将会看涨，于是趁低价时买进股票，待股票上涨至某一价位时再卖出，以获取差额收益。空头：指虽然当前股价相对较高，但是投资者对股市前景不看好，预计股价将会下跌，于是趁相对高价时卖出股票，待股票下降至某一价位时再买入，以获取差额收益期货（Futures）与现货完全不同，现货是实实在在可以交易的货（商品），期货主要不是货，而是以某种大宗产品如棉花、大豆、石油等及金融资产如股票、债券等为标的标准化可交易合约。因此，这个标的物可以是某种商品（例如黄金、原油、农产品），也可以是金融工具。,2,.,互换swap。亦作：掉期；互换交易；掉汇。名。指交易双方约定在未来某一时间相互交换资产的协议。更确切地说，互换是当事人之间约定在未来某一期间相互交换现金流量的协议。还可以被当作一系列远期合约的组合。由于两个最终用户之间进行互换很困难，通常需要互换交易商作中介。最常见的互换交易为利率互换.期权又称为选择权，是在期货的基础上产生的一种衍生性金融工具。指在未来一定时期可以买卖的权利，是买方向卖方支付一定数量的金额（指权利金）后拥有的在未来一段时间内（指美式期权）或未来某一特定日期（指欧式期权）以事先规定好的价格（指履约价格）向卖方购买或出售一定数量的特定标的物的权利，但不负有必须买进或卖出的义务。,3,.,看涨期权（calloption），看涨期权又称买进期权,买方期权,买权,延买期权，或“敲进”，是指期权的购买者拥有在期权合约有效期内按执行价格买进一定数量标的物的权利。看涨期权是这样一种合约：它给合约持有者(即买方)按照约定的价格从对手手中购买特定数量之特定交易标的物的权利。看跌期权又称卖权选择权、卖方期权、卖权、延卖期权或敲出。看跌期权是指期权的购买者拥有在期权合约有效期内按执行价格卖出一定数量标的物的权利，但不负担必须卖出的义务。,4,.,9.1THEOBJECTIVEOFHEDGING,Theobjectiveofhedging(orriskmanagementorriskmitigation)istotransferriskfromoneindividualorcorporationtoanotherindividualorcorporation.Thecounterpartyoffloadingtheriskisthehedger;thecounterpartytakingon(orassuming)theriskistheinsurerorspeculator.Forexample,ifapensionfundhasalongposition(assetposition)incash-marketsecurities,thefundmanagerwillbeconcernedaboutthepricesofthosesecuritiesfallingandwillwanttoprotectagainstthispossibility.Alternatively,ifthepensionfundhasashortposition(liabilityposition)incash-marketsecurities,thefundmanagerwillbeconcernedaboutrisingpricesandwillwanttoprotectagainstthispossibility.,5,.,Inordertohedgesuccessfullyandsotransferall(oratleastmost)risk,thehedgerwillhavetoselectasuitablehedginginstrument.Threeofthemostsuitablehedginginstrumentswillthereforebeinstrumentsthatarederivativeuponcash-marketsecuritiesnamely,financialfutures,optionsandswaps.,6,.,9.2HEDGINGWITHFUTURES,Futurescontractscanbeusedtohedgeinterest-raterisk(bothshort-termandlong-term),stock-marketriskandexchange-raterisk.Therearesomesimplerulesforhedgingwithfutures:ifshortcash(i.e.expectingacashinflowandworriedthatpriceswillriseorinterestrateswillfall),thenbuyfutures(i.e.putonalonghedge);iflongcash(i.e.holdingcashorsecuritiesandworriedthatpriceswillfallorinterestrateswillrise),thensellfutures(i.e.putonashorthedge).,7,.,Thenumberoffuturescontractsrequiredtohedgeacashpositionisdeterminedasfollows.Weconstructahedgeportfoliofromalongpositioninthecashsecurityandashortpositioninhunitsofthecorrespondingfuturescontract(wherehisthehedgeratio).thevalueofthehedgeportfolio(VH)isgivenby:wherePSisthevalueofthecashsecurityandPFisthevalueofthefuturescontract.,8,.,sothatthehedgeratioisdeterminedas:Ifthepriceofthecash-marketsecurityhappenstobemorevolatilethanthatofthefuturescontract,thenthehedgeratiowillexceedunity,sothatmorefuturescontractswillbeneededtohedgetheunderlyingcashpositionthanthefacevalueofthatposition.Theoppositeholdsiffuturesaremorevolatilethancash.Thenumberoffuturescontractsnecessarytohedgeacashsecurityisgivenby:,9,.,Withthenumberofcontractsdeterminedinthisway,thehedgewillbeperfect(pletelyrisklessforsmallchangesinsecurityprices).,10,.,9.2.1Hedgingwithstock-indexfutures,Supposethaton1Aprilapensionfundmanagerisuncertainaboutwherethemarketisgoingoverthenextthreemonthsandwishestohedge1mofhisequityportfolio,whichhasabetaof1.15.On1ApriltheFTSE100indexisstandingat2204.0andthevalueoftheJunecontractonLIFFEis2300.0.Becausethefundmanagerislonginthecashmarket,hewillneedtobeshortinthefuturesmarkettohedgetheportfolio.Sincethevalueofeachone-pointmovement(knownasatick)intheLIFFEFTSE100contractisworth10,thefundmanagerwillneedtosellfuturescontractsaccordingtothefollowingformula:,11,.,Hedgedportfoliowillhaveavalueon30Junedeterminedby:,12,.,9.2.2Hedgingwithbondfutures,Bondfuturescontracts(suchasthelonggiltcontractonLIFFE)canbeusedtohedgethesystematicriskortheinterest-rateriskfromholdingbondportfolios.Bondfuturescontractsarepricedoffthecheapest-to-deliver(CTD)bondfromtherangeofdeliverablebonds.TherelationshipbetweenchangesinthefuturespriceandthepriceoftheCTDbond(see,forexample,Blake,2000,Chapter8)isgivenby:wherechangeinthepriceofthelonggiltfuture;changeinthepriceoftheCTDbond;price(orconversion)factorfortheCTDbond.,13,.,Supposethaton1Aprilapensionfundmanagerisexpectingacashinflowofabout1.20mintwomonthstime,whichheintendsinvestingintheCTDbond(whichwesupposetobeTreasury10.5%202325withapricefactorof1.3032131andcurrentlytradingat118per100nominal).Heisconcernedthatyieldswillfallandgiltpriceswillriseagainsthim.Becauseheisshortcash,hedecidestohedgehisexposurebypurchasinglonggiltfuturescontractsonLIFFE.TodothishebuysJunecontractsaccordingtothefollowingformula:,14,.,15,.,16,.,Exampleofduration.A10%annualcouponbondistradingatparwiththreeyearstomaturity,soPd=B=100,d=10,rm=10%,T=3years.Therefore,durationisgivenby:Thepresentvalueequationforanannualcouponbondisgivenby:,17,.,Differentiatingthisequationwithrespectto(1+rm)gives:Multiplyingbothsidesofby(1+rm)/Pdgivesthefollowingrelationshipbetweenabondsprice,itsyieldtomaturityanditsdurationholds:,18,.,SupposethatthebondtobehedgedistheTreasury11.5%2023(denotedbythesubscriptHbelow),thenthedurationhedgeratioisgivenby:Thisratiocanbesimplifiedifweassumeparallelyield-curvemovementsItcanbesimplifiedevenfurtherifweassumeparallelpercentage-yield-curvemovements,19,.,assumingthatPH=126.25,DCTD=11.6yearsandDH=13years,then:Intermsofduration,theTreasury11.5%,2023bondisequivalentto1.2CTDbonds,inthesensethatitisabout20%morevolatilethantheCTDbond.Thissuggeststhattheappropriatenumberofcontractsrequiredtohedgethisbondisgivenby:,20,.,thatis(assumingagainanominalexposureof1000000):Intermsofhedgingbondportfolios,againitispossibletouseduration-basedhedging.Supposethatthedurationoftheportfoliois14.2yearsandtheweightedaverageprice(per100nominal)ofthebondsintheportfoliois110.125.Thentheappropriatedurationhedgeratiofortheportfoliois:whereDP=durationoftheportfolio;PP=weightedaveragepriceofthebondsintheportfolio;thatis:,21,.,Thenumberoffuturescontractsnecessarytohedgea10mbondport-folioisgivenby,22,.,9.2.3Hedgingwithcurrencyfutures,TohedgeagainstthisriskthefundmanagerdecidestobuysterlingcurrencyfuturescontractsontheChicagoMercantileExchange(CME),whichhaveacontractsizeof62500tradedagainstthedollar.Supposethaton1Aprilthespotexchangerateis$1.75per,andtheJuneCMEfuturespriceis$1.77.Atthespotexchangerate,thedividendpaymentsarevaluedat1714285.71(i.e.$3000000/$1.75),23,.,9.3HEDGINGWITHOPTIONS,9.3.1HedgingwithindividualstockoptionsSupposethaton1April,withABCtradingat115p,theJune115pcallistradingat12pandtheJune115pputat10p.Therisklessrateofinterestis10%andABChasannualdividendsof6%(assumequarterlydividendsarepaidattheendofeachquarter).Wecanconsiderthetwohedgingalternatives.,24,.,ThefirstalternativeinvolvesholdingontoABC,earningthedividends,andbuyingtheputoption.ThesecondalternativeinvolvessellingABCandinvestingtheproceedsat10%andbuyingthecalloption.,25,.,26,.,So,wehavethefollowingsimplerulesforhedgingwithoptions:ifthecashpositionisadverselyaffectedbyfallingprices,thenbuyputsorsellcalls;ifthecashpositionisadverselyaffectedbyrisingprices,thensellputsorbuycalls.Butwhenshouldoptionsbeusedinpreferencetofutures?Theanswerdepends(a)onwhethertheexposureintermsofamountortimingiscertainoruncertain,and(b)onwhethertheexposureissymmetricalorasymmetrical.,27,.,Onceanoptionshedgehasbeenchosen,thenextstepistodecidewhethertouseafixedhedgeoraratiohedge.Afixedhedgeisaoneoffoptionshedgedesignedtolimitthemaximumlossonthehedgedposition,buttobenefitfromanyupsidepotential.Inotherwords,afixedoptionshedgeisratherlikeaninsurancepolicy:inreturnforapremium,theminimumvalueofacashpositionisguaranteed.Aratio(ordelta-neutral)hedgeisdesignedtoestablishandpreserveacombinedcash-and-optionspositionthatisdelta-neutralovertime.Thedeltaofanoptionmeasurestheresponsivenessoftheoptionprice(P0)tochangesinthepriceoftheunderlyingsecurity(PS):,28,.,WeknowfromEquation(9.3)thatthehedgeratioisdeterminedbyThenumberofputoptioncontractsnecessarytohedgetheABCsharesisdeterminedasfollows:ifthedeltaoftheputoptionusedtohedge30000ABCsharesis0.75,thenthenumberofputoptionsrequiredtoconstructtheratiohedgeisgivenby:,29,.,30,.,9.3.2Hedgingwithstock-indexoptions,Theaimofhedgingwithindividualstockoptionsistohedgethespecific(ornonsystematic)risksofindividualshares.Theaimofhedgingwithstock-indexoptions,ontheotherhand,istohedgethesystematic(ormarket)riskofaportfolioofshares.Wemust,therefore,takeintoaccountthebetaoftheportfoliobeinghedged.Thenumberofcontractsneededtohedgeaportfolioofsharesisdeterminedasfollows.Forafixedhedge:,31,.,Foraratiohedge:Toillustrate,wewillsupposethaton15Julyapensionfundmanagerhasa5mportfoliowithabetaof1.15,whichheintendstohedgebybuyingLIFFENovember1850putoptionsontheFTSE100index(whichhaveatickvalueof10).Theclosingindexon15Julyis1825.00andthefundmanagerintendsemployingafixedhedge.Thenumberofcontractstohedgetheportfolioisfoundusing,32,.,9.3.3Hedgingwithbondoptions,Itispossibletohedgelong-terminterest-rateriskusingoptionsonbondfutures.Thefollowingrulesapply:calculatethebestfutureshedge;forafixedhedge,replacethefutureshedgewiththesamenumberofoptionscontracts;foraratiohedge:,33,.,9.3.4Hedgingwithcurrencyoptions,Aswithothertypesofoptionshedges,hedgingwithcurrencyoptionsisusefulwhenthehedgerwantstoinsureagainstdownsideexchangeraterisk,butwantstopreservesomeofthebenefitsoffavourableexchange-ratemovements.Toillustrate,wewillconsideraUKpensionfundmanagerwithaUSportfoliovaluedat$1mon1April,whenthecurrentexchangerateis$1.59andthethree-monthforwardrateis$1.65per.Supposethathedecidestohedgehalftheportfolioagainstariseinsterlingoverthenextthreemonths.,34,.,9.4HEDGINGWITHSWAPS,Supposethatthepensionfundmanagerholds50mnominalofbondstradingatparwithacouponof10per100nominal.Heexecutesanassetswapwithabankwherebyheretainsownershipofthebondsbutmakesfixed-ratepaymentstothebankof9.75%on50mandinreturnreceivesfloating-ratepaymentsfromthebankequaltoLIBOR(theLondonInter-BankOfferRate).Thecashflowsinvolvedinthistransactionfromthepensionfundspointofviewareasfollows.Thepensionfund:,35,.,If,atthetimeoftheswap,LIBORwas9.50%,thenthesyntheticFRNswouldyield9.75%,whichislessthantheyieldonthefixed-couponbonds.If,however,immediatelyaftertheswaphadtakenplaceLIBORroseto10.50%,thenthesyntheticFRNswouldyield10.75%.Thisisayieldof0.75%higherthanthatonthefixed-couponbonds,equivalentto375000perannumon50m.,36,.,9.5HEDGINGLONGEVITYRISK,buttheyarecurrentlyunabletohedgetheaggregatelongevityriskthattheyface,sincemortality-linkedhedginginstrumentsarenotcurrentlywidelyavailable.ConsideranindividualwhowillliveforexactlyTadditionalyears.Thisindividualcouldusealumpsumtopurchaseanannuityfromaninsurancecompanyorbuyanannuitybonddirectlyfromthefinancialmarkets;ThemarketpriceofaT-yearannuitybondis,37,.,Inreality,Tisarandomvariable,notafixedparameter.Annuitybondswithrandommaturitiesarecurrentlynottradedonfinancialmarkets,butinsurancecompaniesstillprovidelifeannuitieswithuncertainT.Wedenotetheconditionalprobabilityofdyingatagexhavingsurvivedtoagex1(thehazardrate)byqx.Supposethattheinsurancecompanyforecastslongevityincreasesbyadjustingdatafromanactuarialtablebymultiplyingbyanexponentialadjustmentfactor,wherex0isthecurrentageoftheannuitantandfisascalarIntermsoftheqx,theunconditionalprobabilityofdyingafterT0periods(conditionalonhavinglivedtoagex0)is,38,.,ThisunconditionalprobabilityisusedincomputingtheexpectedvalueinEquation(9.25),soEquation(9.25)isequivalenttoErrorsintheadjustmentfactorfcanhavealargeimpactonEquation.Historicalevidenceonlongevityforecastssuggeststhatforecasterrorsof1520%infforintervalsoftenormoreyearsaheadarenotuncommon(c.f.Table18.7inMacDonald,1996).,39,.,Anotherindicatorofthedifficultyinforecastinglongevityincreasesisthathistoricalvaluesoftheseadjustmentfactorsarenotconstants:theydifferconsiderablybetweenmenandwomen,acrossagesandtypesofpensioners.Todeterminetheeffectsoftheseforecasterrorsonannuityyields,weuseEquation(9.25)tosolvefortheannuityyieldd/P:,40,.,Tocomputetheactuariallyfairyield(i.e.withzerocostloading),wesubstitutesurvivalprobabilitiesdeterminedfromstandardmortalitytablesintoEquation(9.27).Foramaleaged65,adiscountrateofr=7%anda20-yearadjustmentfactorof0.80,thePMA80tablesandEquation(9.27)leadtoanactuariallyfairannuityyieldof10.6%,butforecasterrorssuggestitl