股票外汇技术分析英文版(14)

ExamFMReviewPart2IntroductionJeffreyBaer3BActuarialScienceWorktermsatManulifeandTowersWatsonWaterlooSOSPresident,May2009–Aug2010Stat231andActSci231Tutorthisterm!Outline1.StockPricing2.FinancialAnalysis3.StockPositions4.ForwardContracts5.CallandPutOptions6.Put-CallParityandOptionCombinations7.Hedging8.Prepays,Futures,andSwapsStockPricingSharePrice=PVofFutureDividendsIfdividendsareconstantforever,withfirstdividendpaidatperiod-end,effectiveinterestifortheperiod:Price=Dividend/i(levelperpetuity)Ifdividendsareincreasinggeometricallybyafactorof(1+k)eachperiod,effectiveinterestiforeachperiod,withfirstdividend=Dividend1paidatthefirstperiod-end:Price=Dividend1/(i-k)(increasingperpetuity)Example1Manulife’sstockiscurrentlysellingfor$28.50.Itsnextdividend,payableoneyearfromnow,isexpectedtobe$0.50/share.Analystsforecastalong-rundividendgrowthrateof7.5%forManulife.Tomorrow,thelong-rundividendgrowthrateestimatechangesto7%.Calculatethenewstockpricethatwouldresult.FinancialAnalysisSpotRate(rt):Annualeffectiveyieldrateforaninvestmentoflengthtyearsmadeatt0(e.g.zero-couponbond)i.e.if3-yearspotrateis6%,caninvest$1attime0at6%effective/yearandreceive1.063attime3ForwardRate(ftorft,t+1)Annualeffectiveyieldrateearnedonaninvestmentmadetyearsfromnowintheperiodt-t+1,withtheinvestmentlockedinattime0ft=(1+rt+1)t+1/(1+rt)t–1i.e.if5-yearforwardrateis6%,wecanmakeaninvestment5yearsfromnowthatwillearn6%fromtime5totime6Example2Theyieldtomaturityonthree5%annualcouponbondsmaturingat$1000par,eachwithdifferentterm,isgivenbelow.Determinethe1,2,and3yearspotratesandthe2-yearforwardrate.Term1year2years3yearsYieldtoMaturity6%6.5%7%FinancialAnalysisMacaulayDurationRepresentsaveragetimingofanasset’scashflowsweightedbythePVofeachcashflow(-d/dδ(ln(Price))MacD=[Σ(Ct*vt*t)]/[Σ(Ct*vt)]=[Σ(Ct*vt*t)]/(PriceofAsset)SingleCashFlowattimen:MacD=nLevelannuityimmediate:MacD=(Ia)n¯|/an¯|ModifiedDuration(akaVolatility)-d/di(ln(Price))ModD=v(MacD)FinancialAnalysisDurationofaPortfolioIfaportfoliocontainsmultipleassetswithknowndurationsandpresentvalues:Portfolioduration=Σ(Assetduration)*(PVasset)/(PVportfolio)Convexityd2/di2(ln(Price))Convexity=[ΣCt(vt+2)(t)(t+1)]/PricePriceSensitivityChangeinpriceofassetduetochangeininterestrateiΔP=-(ModD)(OriginalPrice)(Δi)+0.5(Convexity)(OriginalPrice)(Δi)2Higherduration→MorePriceSensitiveFinancialAnalysisRedingtonImmunizationProtectsagainstsmallchangesininterestrateGivenaportfolioofassetsandliabilities,immunizedif:1.PVAssets=PVLiabilities2.DurationofAssets=DurationofLiabilities3.ConvexityofassetsConvexityofLiabilitiesFullImmunizationProtectsagainstanychangeininterestrateDifferent3rdcondition:exactlyoneliabilitycashoutflowbetweentwoassetcashinflowsExample3Manulifebuysa2-yearzerocouponbondthatwillmaturefor$10,000.Itplanstousethisassettomaketwopaymentstoacustomer,thefirstinoneyearandthesecondin10years.DeterminetheamountsofthepaymentsinordertosatisfyRedingtonimmunizationiftheeffectiveinterestrateis8%.StockPositionsBuyingastockgivesyoualongpositioninthatstockTwodifferentstockpricesexistatanygiventimeBidprice:priceforsellingstockAskprice:priceforbuyingstockAskpricebidprice(Askprice–Bidprice=bid-askspread)Brokerswillalsochargecommissiononthepurchaseand/orsaleofstocks(flatfeeor%ofpurchase/sale)Ifarisk-freeinterestrateisgiven,theprofitonastocktransactionshouldconsidertheopportunitycostofbuyingstock(notbeingabletoinvestthatmoneyattherisk-freeinterestrate)StockPositionsShort-sellingastockgivesyouashortpositioninthatstockToshort-sell,borrowthestockfromsomeoneelse,selltheborrowedshares,andbuythembacklaterwithhopesthatthestockpricehasdecreasedTerminology:Proceeds:moneyreceivedfromsaleofborrowedshares,aftercommission(heldbythelender)Haircut:investmentbytheborrowergiventothelenderascollateralincasetheborrowerdoesnotreturnthesharesBorrowerstillretainsinterestthataccumulatesonthehaircutwhilethehaircutisinthelender’spossessionNeithertheborrowernorthelenderownsthestockformostofthetransactionThus,anydividendspaidduringthetransaction,whichwouldnormallyhavebeenpaidtothelender,mustbecoveredbytheborrowerExample4Thebidandaskpricesforacertainstockaregivenbelow.JeffreyentersintoashortsaleonFebruary25for100shares.HecovershisshortpositiononAugust25.Thebroker’scommissionis$10/transaction.Jeffreymustdepositahaircutequalto50%oftheproceedsreceivedonthesaleofthestock.Themarketrateofinterestisanominalrateof8%compoundedsemi-annually,buttheinterestrateearnedonthehaircutisonly5%compoundedsemi-annually.Adividendof$0.90/sharewaspayableonMarch31(ignoreinterestondividend).WhatisJeffrey’sprofit/lossonthisshortsale?February25August25Bid$35.22$39.65Ask$35.37$39.8ForwardContractsContractthatobligatesonepartytobuyandanothertosellaspecifiedquantityofanunderlyingassetonacertainexpirationdateContractspecifiesprice(forwardprice)tobepaid,regardlessofasset(spot)priceatexpirationNopaymentsaremadepriortotheexpirationdateLongposition:futurebuyerShortposition:futuresellerForwardContractsPayoff:valueoftheforwardcontracttoonepart