applications programming for financial engineering
DEPARTMENT 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
DEPARTMENT 633

Spring 2012
IEOR 4500
Robust Arbitrage Model
Notation:
K = number of scenarios
0, 1, 2, . . . , n: indices for assets (cash is 0)
r = riskfree interest rate
kj = todays of the price for asset j ,
kj = expected value of kj , the price for asset j in scenario k 1
applications programming for financial engineering
DEPARTMENT 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
DEPARTMENT 633

Spring 2012
IEOR 4500  Realistic Portfolio Constraints
1. Long/short portfolios Here we consider portfolios where the assets can take long or short
positions. In addition, when we construct the portfolio we already have a vector of positions, xstart
which could incl
applications programming for financial engineering
DEPARTMENT 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
applications programming for financial engineering
DEPARTMENT 633

Spring 2012
Trade Execution and Dynamic Programming
Suppose we want to sell a large number N of shares of some stock.
Assume the current price of the stock is P0 is it reasonable to
expect that we will receive, from our trade, a cash flow of P0N?
The answer, in gener
applications programming for financial engineering
DEPARTMENT 633

Spring 2012
Notes on using cplex
1. From the command line, you run cplex simply by typing cplex, assuming it is in your PATH
2. Use to read les of extension .lp, as in read problem.lp, which can be shortened to:
r problem.lp
3. The rst line of an .lp le describes the