Properties of portfolios: return 25
Multiple-asset portfolio
xj
= Dollar amount in of security
J bought (or sold short) / total
equity investment in the portfolio
... portfolio return is weighted average of individual securities’ returns
Weights are fractions of individual
securities in total portfolio value
Weights can be positive (long positi
on) or negative (short position)
Weights must add to 1
Expected value of a random variable
∑=
=
n j
j
j
P
r
x
r
1
Single-period random cash flows: Mean-variance portfolio theory
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()
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[
]
[
1
∑
∑
∫
=
∞ ∞−
=
⇒
=
=
n j
j
j
P
s
s
s
r
E
x
r
E
dx
x
xf
p
x
X
E