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PortfolioTheory
Abriefintroductionto
PortfolioTheory
forFinTech 510
3
PortfolioTheory
r
PortfolioTheory:amodelofthetradeoffbetween:
• risk(standarddeviation,)
• return(increaseinvalue,r)
Whenyouhavecompletedthesemodules,youwillunderstand:
• thetradeoffbetweenriskandreturn
• theimportanceofdiversificationforportfoliooptimization
Universeofall
possible
portfolios
“EfficientFrontier”of
optimalportfolios
5
InvestmentReturn&Risk
Investorslookattwokeystatisticswhenassessing
financialinvestments:
Therateofreturnoftheinvestment
Theriskinessoftheinvestment
Let’sexamineeachoftheseindetail.
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Step1:CalculatingtheRateofReturn
Anasset’srateofreturn:percentagechangeinthatasset’svalueovera
specifiedtimeperiod.
Rateofreturniscalculatedas:r
n+1
=
Where:P
n
= Priceattimeperiodn
P
n+1
=Priceattimeperiodn+1
r
n+1
=rateofreturnfromperiodntoperiodn+1
P
n+1
– P
n
P
n
Allelseequal,investorswould
liketheirrateofreturntobeas
highaspossible
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Today,youpurchase sharesinacompanyat$15/share.P
0
=15
Oneyearfromnow: P
1
=18
TheRateofReturnr
1
=
Twoyearsfromnow:P
2
=12
RateofReturnr
2
= – 33%
18–15
15
=20%
Step1:CalculatingtheRateofReturn
Example1
18/15 - 15/15 =
18/15 - 1
