考文垂大学 商科课程 机构投资 课件2.docx

考文垂大学 商科课程 机构投资 课件2.docx

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考文垂大学商科课程机构投资课件2

PENSIONS

INMANYCOUNTRIES,PENSIONFUNDSARETHEDOMINANTFORMOFINSTITUTIONALINVESTMENT.THESEFUNDSAREBUILTUPDURINGTHEWORKINGLIFEOFTHEINVESTORANDTHENUSEDTOFINANCEANINCOMEDURINGRETIREMENT.

THEYMAYBEOPERATEDBYTHECOMPANYFORWHICHTHEPERSONWORKS.THECOMPANYINVESTSOVERTIMETOBUILDUPAFUNDTHATISUSEDTOPROVIDEARETIREMENTINCOMEFORITSEMPLOYEES.

ALTERNATIVELYTHEEMPLOYEESINVESTINAFUNDOFTHEIRCHOOSINGWITHAVIEWTOBUILDINGUPASUMOFMONEYTHATCANBEUSEDTOBUYANANNUITY（GUARANTEEDSTREAMOFINCOME）ATRETIREMENT.

THEMOSTIMPORTANTASSETSWITHINTHEPORTFOLIOSOFPENSIONFUNDSTENDTOBESTOCKMARKETINVESTMENTSINTHEFORMOFSHARESANDBONDS.BUTOTHERASSETSAREOFTENHELD,SUCHASDEPOSITSANDPROPERTY.

THEIMPORTANCEOFFUNDEDPENSIONSVARIESCONSIDERABLYBETWEENCOUNTRIES.IFSL（INTERNATIONALFINANCIALSERVICES,LONDON）ESTIMATEDTHATIN2004THEUKHAD$1,464BILLIONINPENSIONFUNDS,GERMANYHAD$268BILLIONANDFRANCE$164BILLION.

HOWEVERTHEIMPORTANCEOFPENSIONFUNDSINGERMANYANDFRANCESEEMEDTOBEINCREASINGRAPIDLYSINCEPENSIONFUNDSINBOTHHADMORETHANDOUBLEDINTHEPREVIOUSTHREEYEARS.

PENSIONSCHEMESCANBEDIVIDEDINTODEFINEDBENEFITANDDEFINEDCONTRIBUTIONSCHEMES.

DEFINEDBENEFITSCHEMESAREVIRTUALLYALWAYSPENSIONSPROVIDEDBYEMPLOYERSFORTHEIREMPLOYEES.THEYSTIPULATEAPARTICULARLEVELOFINCOMEINRETIREMENT,NORMALLYBASEDONFINALSALARYANDLENGTHOFSERVICE.

DEFINEDCONTRIBUTIONPENSIONSCHEMESDONOTINVOLVEAPRESCRIBEDINCOMEINRETIREMENT.INSTEADTHEYPRESCRIBELEVELSOFCONTRIBUTIONTOTHEFUNDPRIORTORETIREMENT.

THEPENSIONOBTAINEDTHROUGHADEFINEDCONTRIBUTIONSCHEMEDEPENDSUPONTHEGROWTHRATEOFTHEFUNDANDANNUITYRATESATTHETIMEOFRETIREMENT.

MOSTOFTHEMONEYINPENSIONFUNDSISINVESTEDINSTOCKMARKETS.INCONSEQUENCETHEREISAHIGHDEGREEOFUNCERTAINTYCONCERNINGTHEFUTUREVALUEOFAPENSIONFUND.

INTHECASEOFMONEY-PURCHASESCHEMES,ITISTHERECIPIENTOFTHEPENSIONWHOBEARSTHISRISK.THERECIPIENTALSOBEARSTHERISKTHATANNUITYRATES,ANDHENCETHERETIREMENTINCOMETHATCANBEPURCHASED,WILLBELOWATRETIREMENT.

SINCEANNUITIESAREBASEDONGOVERNMENTBONDS（GILTS）,THISRISKRELATESTOTHEPOSSIBILITYTHATRATESOFYIELDONGOVERNMENTBONDSWILLBELOWATTHETIMEOFRETIREMENT.

INTHECASEOFFINAL-SALARYSCHEMES,THEEMPLOYERBEARSTHERISKS.ACOMBINATIONOFPOORINVESTMENTPERFORMANCE,LOWBONDYIELDS,ANDHIGHRATESOFSALARYGROWTHCANRESULTINPENSIONFUNDSBEINGINSUFFICIENTTOMEETTHEPENSIONCOMMITMENTS.INSUCHACASETHEEMPLOYERMUSTREPLENISHTHEPENSIONFUNDOUTOFTHATEMPLOYER’SBUSINESSREVENUES.

UNTIL1999MOSTCOMPANYPENSIONSCHEMESWEREDEFINEDBENEFITSCHEMES（PENSIONBASEDONSALARYANDYEARSOFSERVICE）.SINCE1999MANYCOMPANIESHAVEBEENCLOSINGDEFINEDBENEFITSCHEMESTONEWEMPLOYEESANDREPLACINGTHEMWITHDEFINEDCONTRIBUTIONSCHEMES（PENSIONBASEDONANACCUMULATEDPENSIONFUND）.

THISHASBEENPARTLYDUETOTHERISKSTHATDEFINEDBENEFITSCHEMESIMPOSEONEMPLOYERS.THESERISKSTAKESEVERALFORMS.THEREISTHERISKOFSTOCKMARKETSPERFORMINGPOORLYWITHTHEEFFECTTHATTHEEMPLOYERHASTOMAKELARGEADDITIONALCONTRIBUTIONSTOTHEPENSIONFUND.

ANOTHERMAJORFORMOFRISKARISESFROMCHANGESINLONGEVITY;IFPENSIONERSLIVELONGERTHEYDRAWMOREFROMTHEPENSIONFUND.

FALLINGBONDYIELDSANDUNEXPECTEDLYFASTSALARYINCREASESCANEXACERBATETHESERISKS.

ANNUITIES

ANNUITIESAREGUARANTEEDINCOMES.THEYAREOFTENUSEDFORPENSIONPURPOSES.UPONRETIREMENTAPERSONWOULDBUYANANNUITYANDTHEREBYGUARANTEEARETIREMENTINCOMEPAYABLEUNTILDEATH.

ONCETHEANNUITYISTAKENOUTITCANNOTBECHANGED.THEBUYEROFTHEANNUITYALSONEEDSTOBEAWARETHATTHEMONEYUSEDTOBUYTHEANNUITYISNOTUSUALLYREFUNDABLE.

IFSOMEONEDIESIMMEDIATELYAFTERBUYINGANANNUITY,THEMONEYUSEDTOBUYTHEANNUITYISNORMALLYLOST.

ANNUITIESCANBELOOKEDUPONASAFORMOFINSURANCE.ANNUITIESTHATPAYANINCOMEFORTHERESTOFAPERSON’SLIFEINSURETHEINDIVIDUALAGAINSTTHEPOSSIBILITYOFOUTLIVINGTHEMONEYSETASIDEFORRETIREMENT.

ASWITHOTHERFORMSOFINSURANCE,RISKISPOOLEDSOTHATTHEREAREBOTHGAINERSANDLOSERS.THEPOOLINGMECHANISMUSESTHEFUNDSOFTHOSEWHODIEEARLYTOSUBSIDISETHEINCOMEOFTHOSEWHOLIVELONGERTHANAVERAGE.THISISA‘MORTALITYCROSS-SUBSIDY’WHEREBYTHOSEWHODIEYOUNGSUBSIDISETHOSEWHOLIVELONGLIVES.

ANNUITIESNORMALLYINVESTINGOVERNMENTBONDS（GILTS）.THEANNUITYPAYMENTSTOTHEPENSIONERARISEPARTLYFROMTHEYIELDONTHEGOVERNMENTBONDS,ANDPARTLYFROMTHEREPAYMENTOFTHEINITIALPURCHASEPRICEOFTHEANNUITY.

THECOSTOFTHEANNUITYISRETURNEDTOTHEPENSIONEROVERTIMEATARATETHATWOULDRETURNTHEENTIRESUMBYTHEEXPECTEDDATEOFDEATH.INSURANCECOMPANYSTATISTICIANS（ACTUARIES）DETERMINETHEEXPECTEDDATEOFDEATH.

SINCEANNUITYPAYMENTSDEPENDONTHEYIELDSONGOVERNMENTBONDS,PENSIONERSFACEAHIGHDEGREEOFUNCERTAINTY.YIELDSONGOVERNMENTBONDSVARYOVERTIME.

INCONSEQUENCEANNUITYRATESCANCHANGESUBSTANTIALLYFROMYEARTOYEAR.IFAPERSONRETIRESINAYEARINWHICHANNUITYRATESARERELATIVELYLOW,THATPERSONSUFFERSALOWPENSIONFORTHERESTOFHIS,ORHER,LIFE.

THESYSTEMOFOBTAININGAPENSIONBYBUYINGANANNUITYATRETIREMENTINVOLVESACONSIDERABLEAMOUNTOFRISK.THESIZEOFTHEPENSIONDEPENDSUPONWHENTHISOCCURS.

RETIREMENTATATIMEWHENSHAREPRICES（ANDHENCEPENSIONFUNDVALUES）ARELOWANDGOVERNMENTBONDYIELDSARELOWRESULTSINALOWPENSION.ASMALLFUNDWOULDBEINVESTEDATALOWRATEOFYIELD.

THEENDOWMENTEQUATION

THEEQUATIONFORESTIMATINGTHESUMTOBEACCUMULATEDFROMREGULARINVESTMENTIS:

M=p[（1+y）T-1]/y

WHERE:

M=SUMTOBEACCUMULATED

P=PERIODICPAYMENT

Y=RATEOFRETURNONTHE

ENDOWMENTFUND（PERPERIOD）

T=NUMBEROFPERIODS（e.g.MONTHS）

Exercise

If£100permonthweretobeinvestedover25yearsinafundwithanexpectedaveragerateofreturnof6%p.a.（netofcharges）whatfundvalue,attheendofthe25years,wouldbeexpected?

Answer

M=p[（1+y）T-1]/y

M=1200[（1.06）25–1]/0.06

M=£65,837.41

Exercise

Someoneisplanningtoaccumulate£250,000over40years.Whatistherequiredannualcontributiontotheendowmentfundiftherateofreturnonthefundis5%p.a.?

Answer

M=p[（1+y）T-1]/y

250,000=p[（1.05）40-1]/0.05

250,000=px120.8

p=250,000/120.8=2069.54

Therequiredannualcontributionis£2,069.54

Exercise265

（a）Pensioncontributionsaretax-deductibleandyourmarginalrateoftaxis40%.Youplantoinvestanetsumof£150permonthinapensionfundfor（i）30years,and（ii）50years.Whatsumwouldyouexpecttoaccumulateatanaverageannualgrowthrateof6%withazeroannualmanagementcharge?

（b）Howwouldtheanswerschangeiftherewerea2%p.a.managementcharge?

Answer

（a）Anetmonthlycontributionof£150amountstoagrosscontributionof£250permonth（£250x0.6=£150）.

Theendowmentequationis:

M=p.[（1+y）T-1]/y

（i）Using0.5%permonth（6%/12）

M=250.[（1.005）360–1]/0.005

M=£251,128.76

（ii）M=250.[（1.005）600–1]/0.005

M=£946,797.77

（b）Anannualmanagementchargeof2%wouldreducetheannualgrowthrateto4%（6%-2%）.

（i）Using0.333%permonth（4%/12）

M=250.[（1.00333）360–1]/0.00333

M=£173,388.69

（ii）M=250.[（1.00333）600–1]/0.00333

M=£476,715.90