Risks, Values and Prices in Finance, Lecture Notes by S. Zhang,
(will be made available for lectures below).
Investment Science, by D.G.
Luenberger, Oxford University Press (recommended only)
The course aims to familiarize students with basic operations research
tools used in modern finance. The emphasis is on optimization models.
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
requiring use of XPRESS-MP optimization package.
1. Cash flow
streams, present value, fixed-income instruments
programming models in finance: cash flow matching and dedication:
sections 2.1 and 2.2
of Nielsen's notes.
theorem of asset pricing (chapter
2 of Zhang)
pricing and arbitrage detection in single period models, pricing
4 of Zhang)
5. Arbitrage in
multiperiod investments: stochastic linear programming and binomial
trees (based on a paper
to quadratic programming
Markowitz portfolio optimization
(based on notes
by Zhang, and a review paper
by M. Steinbach)
and other extensions of Markowitz portfolio optimization (based on M.
programming in finance: constructing an index fund (from G.
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)
portfolio selection (based on the paper
by Bertsimas and Sim, and section 4 of the paper
by Ben-Tal and Nemirovski)
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 returnon bank deposits for the same
period). How does
the composition of the efficient portfolioschange? 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.
examination (25.10.2005, in class, closed notes):