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Chapter05-RiskandReturn:PastandPrologue
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5-PAGE1
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CHAPTER05
RISKANDRETURN:PASTANDPROLOGUE
The1%VaRwillbelessthan–30%.Aspercentileorprobabilityofareturndeclinessodoesthemagnitudeofthatreturn.Thus,a1percentileprobabilitywillproduceasmallerVaRthana5percentileprobability.
Thegeometricreturnrepresentsacompoundinggrowthnumberandwillartificiallyinflatetheannualperformanceoftheportfolio.
No.Sinceallitemsarepresentedinnominalfigures,theinputshouldalsousenominaldata.
Decrease.Typically,standarddeviationexceedsreturn.Thus,anunderestimationof4%ineachwillartificiallydecreasethereturnperunitofrisk.Toreturntotheproperriskreturnrelationshiptheportfoliowillneedtodecreasetheamountofriskfreeinvestments.
UsingEquation5.6,wecancalculatethemeanoftheHPRas:
E(r)=QUOTEs=1Sp(s)r(s)s=1Sp(s)
UsingEquation5.7,wecancalculatethevarianceas:
Var(r)=?2=QUOTEs=1Sp(s)[r(s)s=1Sp(s)
=[0.3?(0.44–0.14)2]+[0.4?(0.14–0.14)2]+[0.3?(–0.16–0.14)2]
=0.054
Takingthesquarerootofthevariance,wegetSD(r)=?=QUOTEVar(r)Var(r)=QUOTE0.0540.054=0.2324or23.24%
Weusethebelowequationtocalculatetheholdingperiodreturnofeachscenario:
HPR=QUOTEEndingPrice－BeginningPrice+CashDividendBeginningPrice
Theholdingperiodreturnsforthethreescenariosare:
Boom: (50–40+2)/40=0.30=30%
Normal: (43–40+1)/40=0.10=10%
Recession: (34–40+0.50)/40=–0.1375=–13.75%
E(HPR)=QUOTEs=1Sp(s)
=[(1/3)?0.30]+[(1/3)?0.10]+[(1/3)?(–0.1375)]
=0.0875or8.75%
Var(HPR)=QUOTEs=1S
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