Ending 7/12/2011
Chapter5
IntroductiontoRisk,Return,andtheHistoricalRecord
HoldingPeriodReturns
HPR price of a share Beginning price Cash dividend
Beginning price
$100
HPR
(5.10)
$120
120 100 0 20
0.20 20%
100
100
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HoldingPeriodReturns
HPR
Ending price of a share Beginning price Cash dividend
Beginning price
(5.10)
$10dividend
$100
HPR
$120
120 100 10 30
0.30 30%
100
100
PopulationParametersvs.SampleStatistics
PopulationParameters
Developtheory
Describestruedistribution
Possiblescenarios
Probabilities
SampleStatistics
Practice
Estimateofunderlyingdistribution
Observedscenarios
Observationsareequallyweighted
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PopulationParameters
Example
Twopossiblescenarios: s=1,p(1)=0.5
s=2,p(2)=0.5
StockA: r(1)=+0.05,r(2)=0.01
0.2
0.15
StockB:
0.2
0.1
0.05
0
0.05
0.1
0.15
0.2
0.1
0.15
0.2
r(1)=+0.20,r(2)=0.16
0.15
0.1
0.05
0
0.05
PopulationParameters
s possible scenario
p s probability of each scenario
of each scenario
r s return in each scenario
Expected(Mean)Return ameasureofcentrality
E r p s r s
(5.11)
s
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PopulationParameters
Example
Twopossiblescenarios: s=1,p(1)=0.5
s=2,p(2)=0.5
StockA: r(1)=+0.05,r(2)=0.01
E p r s r s 0.5 0.05 0.5 0.01 0.02
s
StockB:
r(1)=+0.20,r(2)=0.16
E r p s r s 0.5 0.20 0.5 0.16 0.02
s
PopulationParameters
Example
Twopossiblescenarios: s=1,p(1)=0.5
s=2,p(2)=0.5
StockA: r(1)=+0.05,r(2)=0.01 E(r)=0.02
0.2
0.15
StockB:
0.2
0.15
0.1
0.05
0
0.05
0.1
0.15
0.2
r(1)=+0.20,r(2)=0.16 E(r)=0.02
0.1
0.05
0
0.05
0.1
0.15
0.2
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PopulationParameters
VarianceofReturns ameasureofdispersion
2
2 p s r s E r
(5.12)
s
StandardDeviationofReturns:
2
StockA
0.2
0.15
0.1
0.05
0
0.05
0.1
0.15
0.2
0.15
0.1
0.05
0
0.05
0.1
0.15
0.2
StockB
0.2
PopulationParameters
StockA: r(1)=+0.05,r(2)=0.01
2
p s r s E r 0.50 0.05 0.02 0.50 0.01 0.02
2
2
2
s
0.0009
0.03
StockB: r(1)=+0.20,r(2)=0.16
2
p s r s E r 0.50 0.20 0.02 0.50 0.16 0.02
2
2
2
s
0.0324
0.18
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SampleStatistics
s observed scenario
r s return in observed scenario
SampleMean anestimateofthepopulationmean
r
1
n
n
r s
(5.13)
s 1
SampleStatistics
SampleVariance anestimateofpopulationvariance
2
1
n 1
n
r s r
2
(5.17)
s 1
SampleStandardDeviation:
2
6