Instructor: M. C. Pinar

Room: 305

Office Hours: Wednesdays 15:30-17:15

Textbook and Reference Material:

- Optimization in Finance (will be made available to the students) by Reha Tutuncu
- Optimization Methods in Finance (will be made available to the students) by Gerard Cornuejols
- Investment Science, by D.G.
Luenberger, Oxford University Press, 1998 (recommended only)

Topics: A more detailed syllabus in pdf format is here.

Homework 4: Due, April 5, 2004. Download the MS EXCEL file data.xls here. The file contains monthly historical

returns between January 1986 and December 1995 for 29 of the 30 companies listed in the Dow-Jones Index.

Use the Excel data analysis tool to compute the mean vector and covariance matrix for the data. Then

1. Compute and plot the MV efficient frontier using the XPRESS-MP solver in MOSEL and any graphics program

of your choice.

2. Assume there is also a risk free asset with annual return R=0.33 percent (this is the average annual return

on US T-Bills between 1950 and 1969 multiplied by 1/12). How does the composition of the efficient portfolios

change? Report your observations along with a discussion.

3. Assume you currently own the following portfolio: x0(i)=0.20 for i=1,...,5 and x0(i) =0 for i=6,...,29. Reoptimize the

portfolio (without using the riskless asset) considereing transaction costs for buying and selling. Solve for a fixed level

of expected return and three different transaction costs (0.2 %, 0.5 % and 2 %). Comment on your results.

1. Using the MS EXCEL file data.xls of HW 4, compute a minimum CVaR portfolio at 95 %. Assume all historical

returns (mu) equally likely in approximating the CVaR. The set of feasible portfolios is described by the following constraints:

0 <= x(i) <= 0.1 for all i, e' x =1, sum(i,x(i)*mu(i)) >= mutarget, where mutarget=5 %. Remember that you have to use LP.

2. Assume you currently own the following portfolio: x0(i)=0.20 for i=1,...,5 and x0(i) =0 for i=6,...,29. Reoptimize the

portfolio considering transaction costs for buying and selling. Solve for three different transaction costs (0.2 %, 0.5 % and 1 %).

Midterm Examination: April 7, 2004, 13:40--15:30.

Final Examination: May 24, 2004, Monday, 12:15--15:30 BZ--08.

Grading

Homeworks: 20 %

Midterm examination: 30 %

Final: 50 %

Participation: 0 %