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1、ExamFMReviewPart2IntroductionJeffreyBaer3BActuarialScienceWorktermsatManulifeandTowersWatsonWaterlooSOSPresident,May2009–Aug2010Stat231andActSci231Tutorthisterm!Outline1.StockPricing2.FinancialAnalysis3.StockPositions4.ForwardContracts5.CallandPutOptions6.Put-CallParityandOptionCombinations7.He
2、dging8.Prepays,Futures,andSwapsStockPricingSharePrice=PVofFutureDividendsIfdividendsareconstantforever,withfirstdividendpaidatperiod-end,effectiveinterestifortheperiod:Price=Dividend/i(levelperpetuity)Ifdividendsareincreasinggeometricallybyafactorof(1+k)eachperiod,effectiveinterestiforeachperio
3、d,withfirstdividend=Dividend1paidatthefirstperiod-end:Price=Dividend1/(i-k)(increasingperpetuity)Example1Manulife’sstockiscurrentlysellingfor$28.50.Itsnextdividend,payableoneyearfromnow,isexpectedtobe$0.50/share.Analystsforecastalong-rundividendgrowthrateof7.5%forManulife.Tomorrow,thelong-rundi
4、videndgrowthrateestimatechangesto7%.Calculatethenewstockpricethatwouldresult.FinancialAnalysisSpotRate(rt):Annualeffectiveyieldrateforaninvestmentoflengthtyearsmadeatt0(e.g.zero-couponbond)i.e.if3-yearspotrateis6%,caninvest$1attime0at6%effective/yearandreceive1.063attime3ForwardRate(ftorft,t+1)
5、Annualeffectiveyieldrateearnedonaninvestmentmadetyearsfromnowintheperiodt->t+1,withtheinvestmentlockedinattime0ft=(1+rt+1)t+1/(1+rt)t–1i.e.if5-yearforwardrateis6%,wecanmakeaninvestment5yearsfromnowthatwillearn6%fromtime5totime6Example2Theyieldtomaturityonthree5%annualcouponbondsmaturingat$1000p
6、ar,eachwithdifferentterm,isgivenbelow.Determinethe1,2,and3yearspotratesandthe2-yearforwardrate.Term1year2years3yearsYieldtoMaturity6%6.5%7%FinancialAnalysisMacaulayDurationRepresentsaveragetimingofanasset’scashflowsweightedbythePVofeachcashflow(-d/dδ(ln(Price))MacD=[Σ(Ct*vt*t)]/[Σ(Ct*vt)]=[Σ(Ct
7、*vt*t)]/(PriceofAsset)SingleCashFlowattimen:MacD=nLevelannuityimmediate:MacD=(Ia)n¯
8、/an¯
9、ModifiedDuration(akaVolatility)-d/di(ln(Price))ModD=v(MacD)FinancialAnalysisDurationofaPortfolioIfaportfoliocontainsmultipleassetswithknowndu
