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QUESTION
Show that the arithmetic return of a portfolio is a weighted sum of the arithmetic returns of the individual assets in the portfolio:
Show that the arithmetic return of a portfolio is a weighted sum of the arithmetic returns
of the individual assets in the portfolio:
r
v
1
=
I
∑
i
=1
π
(
i
)
r
(
i
)
1
where
I
∑
i
=1
π
(
i
)
= 1
What is the interpretation of the quantity
π
(
i
)
?
i) Let
E
[
r
n
] =
μ
and
V
[
r
n
] =
σ
2
for all values of
n
, and assume all returns are independent.
Compute
E
[
r
0
,N
] and
V
[
r
0
,N
].
ii) Let
E
[ ̃
r
n
] = ̃
μ
and
V
[ ̃
r
n
] = ̃
σ
2
for all values of
n
, and assume all returns are independent. Compute
E
[ ̃
r
0
,N
] and
V
[ ̃
r
0
,N
].
1
