Lily Qiu, Assistant Professor
Economics Department, Brown University
EC1710, Lecture 10, Spring 2010, page 1
Portfolio Risk and the MeanVariance Frontier
0. For stocks, we use their historical characteristics to indicate their future characteristics.
We assume that stock returns (rate of returns) are random variables which draw from
certain underlying distributions.
The past returns are a sample draw from the distribution,
and we work with that > we have no better choice.
1. Portfolio with two securities
Assume that you have $100 to invest, you put $20 into stock A and $80 into stock
B.
The past 3 monthly rate of returns are:
A
B
Portfolio
1,
0.03
0.08
0.2*0.03+0.8*0.08 = 0.07
2,
0.01
0.09
0.2*0.01+0.8*0.09 = 0.074
3,
0.02
0.10
0.2*0.02+0.8*0.10 = 0.084
Mean return(A) =
Mean return(B) =
When A’s return is 0.03 (3%) and B’s return is 0.08 (8%), what is the portfolio rate of
return?
Var(A) =
σ(A) =
Var(B) =
σ(B) =
Cov(A,B) =
Expected rate of return for the portfolio:
E(
p
r
~
) = E(
2
2
1
1
~
~
r
w
r
w
) =
1
w
E(
1
~
r
) +
2
w
E(
2
~
r
)
1
w
+
2
w
=1
For your portfolio:
1
w
=
,
2
w
=
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentLily Qiu, Assistant Professor
Economics Department, Brown University
EC1710, Lecture 10, Spring 2010, page 2
For your portfolio:
E(
p
r
~
) =
Variance for the portfolio:
σ
2
(
p
r
~
) =
n
s
p
p
s
r
E
s
r
1
2
))
~
(
)
(
(
Pr
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '10
 Qiu
 Standard Deviation, Variance, Probability theory, Modern portfolio theory

Click to edit the document details