Financial Data Analysis
Professor S. Kou, Department of IEOR, Columbia University
Lecture 1.b Review of Mean Variance Analysis
1
Review of The Mean Variance Analysis
Consider a one period economy as before with
N
risky assets, and a money market account
with the riskfree rate
r >
0
being a °xed constant. The trading strategy is denoted by
°
=
(
°
0
,
°
1
, ...,
°
N
), where
°
0
is the number of shares invested in the money market account, and
°
n
is
the number of shares invested in the
n
th risky asset. Let
R
be the return of such a strategy
°
at time 1.
The meanvariance analysis assumes that an investor attempts to solve the following prob
lem:
min
°
V ar
[
R
]
subject to
E
[
R
]
=
±; ± > r:
The intuition is that for the same return, the investor prefers a portfolio with a smaller variance.
Note that the mean variance problem does not take consideration of any distribution properties
(e.g. skewness, kurtosis etc.) other than the mean and variance. This is a signi°cant drawback
of the mean variance analysis.
Let
w
n
=
°
n
S
n
(0)
=V
(0)
,
w
= (
w
1
; :::; w
n
)
>
, where
S
n
(0)
is the values of the
n
th risky asset
at time 0 and
V
(0)
is the total initial amount of money at time 0. In other words,
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 Fall '10
 StevenKou
 Variance, Financial Engineering, Professor S. Kou, mean variance problem

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