IE444 Operations Research in Finance Fall 2005

Instructor: M. C. Pinar
Room: 305
Office Hours:  Monday 15:30-17:00, Wednesday 14:30-17:00
Textbook and Reference Material:
          General information

The course aims to familiarize students with basic operations research tools used in modern finance. The emphasis is on optimization models. The student intending to take the course should have a background in optimization at the level of IE303 and in engineering economics concepts. There will be homework assignments requiring use of XPRESS-MP optimization package.


          1. Cash flow streams,  present value, fixed-income instruments
          2. Linear programming models in finance: cash flow matching and dedication: sections 2.1 and 2.2 of Nielsen's notes.
          3. Fundamental theorem of asset pricing (chapter 2 of Zhang)
          4. Risk-neutral pricing and arbitrage detection in single period models, pricing options (chapter 4 of Zhang)
          5. Arbitrage in multiperiod investments: stochastic linear programming and binomial trees (based on a paper by A.J.King)
          6. Introduction to quadratic programming
          7. Mean-Variance Markowitz portfolio optimization (based on notes by Zhang, and a review paper by M. Steinbach)
          8. Multiperiod and other extensions of Markowitz portfolio optimization (based on M. Steinbach)
          9. Integer programming in finance: constructing an index fund (from G. Cornuéjols' notes)
         10. Risk measures in finance and their minimization: VaR and CVaR (based on Cornuéjols and Tűtűncű)
         11. Credit risky bonds and optimization (based on the paper by Bertsimas and Pachamanova)
         12. Robust portfolio selection (based on the paper by Bertsimas and Sim, and section 4 of the paper by Ben-Tal and Nemirovski)         The third homework is here.        Homework 8: Due December 6, 2005. Select 20 stocks quoted at the IMKB. Record 90 days of closing prices of these stocks starting from January 2, 2005.  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. Use the bank deposit as a risk free asset (find  the average  return on bank deposits for the same period).  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,...,20. Reoptimize the portfolio (without using the riskless asset) considering 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.