Microsoft PowerPoint - PoF.ppt

Properties of portfolios: riskƒ 26

We quantify risk in terms of statisti

cal measures, conventionally this is

done using the

variance / standard deviation (volatility)

ƒ

Variance of a random variable

ƒ

Covariance and correlation of two random variables

ƒ

Variance of a weighted sum

]²

[

²]

[

])²]

[

[(

]

[

2

Y E Y E Y E Y E Y V Y

− = − = = σ

Single-period random cash flows: Mean-variance portfolio theory

] [ ] [ ] [

])]

[

])(

[

[(

]

cov[

X

E

Y

E

YX

E X E X Y E Y E

YX

yx

− = − − = = σ

[]

]

cov[

2

]

[

]

[

2

2

2

YX

ab

X V b Y V a

bX

aY

V

bX

aY

+ + = + = + σ

1

1

,

,

,

,

≤

≤

−

=

X

Y

X

Y

X

Y

X

Y

ρ

σ

σ σ

ρ