# IE444 Operations Research in Finance Fall 2008

Instructor: M. C. Pinar
Room: 305
Office Hours:  Tuesdays 2-5 pm.

Reference Material:

General information

The course aims to familiarize students with basic quantitative tools used in modern finance. The student intending to take the course should have a background in optimization at the level of IE303 and elementary probability as well as familiarity with engineering economics concepts. There will be homework assignments requiring use of XPRESS-MP optimization package, and of MATLAB.  There is no textbook. The instructor will provide hand-outs in class.

Topics

1. Cash flow streams,  present value, bonds (1 week)
2. Bond price volatility, duration and convexity (2 weeks)
3. Bond portfolio analysis, cash flow matching and dedication: Nielsen's notes. (1 week)
4. Option basics (2 weeks)
Midterm examination
5. Arbitrage in option pricing (2 weeks) (chapter 2 of Zhang)
6. Option pricing models (2 weeks)(chapter 4 of Zhang)
7. Modern portfolio theory, Risk measures VaR and CVaR (2 weeks, reference: relevant parts of Tutuncu and Cornuejols' notes above and and section 1 of review paper by M. Steinbach)
8. Mortgage-backed securities (2 weeks)
Homeworks

• Homework Assignment 1: Exercises 3.4.2, 3.5.2, 3.5.3 and 3.5.4, Due date : 25.9.2008.
• Homework Assignment 2: Exercises 4.1.2, 4.1.3, 4.2.1, 4.2.3, 4.2.7 and 4.2.8, Due date : 9.10.2008.
• Homework Assignment 3: distributed in class, Due date : 23.10.2008.
• Homework Assignment 8: Due January 6, 2009. Select 20 stocks quoted at the IMKB30 national index. You will receive by e-mail a set of closing prices of these stocks corresponding to the last quarter of 2006.  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 for the same period 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.

Grading
 Homeworks: 30 % Midterm examination (date to be announced, in class, closed notes): 30 % Final: TBA 40 % Participation: 0 %