The Mathematics of Financial Modelingand Investment Management

16-Port Selection Mean Var Page 475 Wednesday, February 4, 2004 1:09 PM

Portfolio Selection Using Mean-Variance Analysis 475

EXHIBIT 16.2 Feasible and Markowitz Efficient Portfoliosa

a The picture is for illustrative purposes only. The actual shape of the feasible region

depends on the returns and risks of the assets chosen and the correlation among

them.

tor of expected returns μμμμ= {μi} and an N×N variance-covariance matrix

Σ = {σij}. Under these assumptions, the return of a portfolio a with

weights wa = {wi}a is a random variable, which is the sum of normally

distributed random variables. Therefore, it is a normally distributed

random variable with the following mean and variance:

μa = wa ′μμμμ

σ

2

a = wa′ΣΣΣΣwa

For instance, if there are only two assets with weights wa ′ = {wa 1 wa 2 },

then the portfolios expected return is

μa = wa 1 μ 1 + wa 2 μ 2