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

(

i

)

r

(

i

)

1

where

I

i

=1

(

i

)

= 1

What is the interpretation of the quantity

(

i

)

?

i) Let

E

[

r

n

] =

and

V

[

r

n

] =

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

] =

and

V

[

r

n

] =

2

for all values of

n

, and assume all returns are independent. Compute

E

[

r

0

,N

] and

V

[

r

0

,N

].

1