Applications Programming for Financial Engineering
INDUSTRIAL 633

Spring 2012
IEOR 4500
Quick Review of the Principal Components Method
Suppose Q is the covariance matrix for the returns of n assets. Then Q is symmetric
(qij = qji for all indices i, j ) and positivesemidenite (v T Qv 0 for any vector v Rn
this is denoted Q 0). We
Applications Programming for Financial Engineering
INDUSTRIAL 633

Spring 2012
IEOR 4500
Maximizing the Sharpe ratio
Suppose we have the setting for a meanvariance portfolio optimization problem:
,
the vector of mean returns
Q,
the covariance matrix
xj = 1, (proportions add to 1)
(1)
(2)
(3)
Ax b, (other linear constraints).
0 x.
(
Applications Programming for Financial Engineering
INDUSTRIAL 633

Spring 2012
How to solve simple QPs The problem we discussed in class had the following general structure: Minimize
i 2 i x2 + 2 i i<j
ij xi xj

i
i xi , (*)
Subject to the constraints:
i
xi = 1, and
li xi ui , for all i. The method we discussed in class consisted
Applications Programming for Financial Engineering
INDUSTRIAL 633

Spring 2012
IEOR 4500
Factor models
Suppose we have a collection of n assets. A factor model for the asset returns is a statistical
model of the form:
r = +
+ V Tf
(1)
where
is the nvector of expected returns (computed from historical data),
r is the nvector of r