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12.01.09

Course consists of two interrelated parts

- Portfolio optimization and risk management

- Econometric techniques in finance

Course organization

Place and Time:

Lectures: Monday, 12.15-15.00, EL4 Exercises: Friday, 15.15-17.00, EL4 Exercise rules

Contents

1. Portfolio optimization and risk management

1. Portfolio selection and risk management in finance and insurance using modern optimization and simulation methodology

2. Modern approaches to risk management based on Value at Risk

3. Decision support for management of portfolios of industrial projects and risk management using modern financial and investment methodology in different branches of industry like energy, telecom and others.

4. Optimization and simulation methodology and commercial software for optimal financial decisions and industrial risk management

Portfolio Optimization and risk management part of the course

Lectures	Topics	Material	Exercises	Solutions
*Lecture 1*	1. Introduction to mean-variance analysis	1. [2], pp.119-125 Powerpoint slides: Introduction to financial optimization and risk management Mean-variance analysis, part 1 Data set Simplest Excel implementation of mean-variance model using only Excel functions	Exercise 1	Solution
*Lecture 2*	1. Mean-variance analysis, continued	1. [2], pp. 126-144 Powerpoint slides 1 2 Matlab files for computation of mean-variance efficient frontier Matlab files for experiments with one factor model	Exercise 2	Solution
*Lecture 3*	1. Introduction to fixed income portfolio models 2. Risk measurement for fixed income portfolios 3. Fixed income portfolio models	1. [2], pp. 147-158, Powerpoint slides 2. [2] pp. 80-92 3. [2], pp.159-170 Powerpoint slides Data set with indexes of Norwegian government bills and bonds of different maturities	Exercise 3	Solution
*Lecture 4*	1. Scenario optimization. Mean-absolute deviation models. Regret models. Introduction to Value-at-Risk	1. [2], pp. 100-103, 173-184 Powerpoint slides	Exercise 4	Solution
*Lecture 5*	1. Introduction to dynamic portfolio strategies 2. Introduction to optimization under uncertainty	1. [2], pp 209-219 2. [2], pp. 220-233 Powerpoint slides
*Lecture 6*	Guest lecture of Professor Sjur Flåm	Material to the lecture 1 2 3
*Lecture 7*	1. Scenario optimization. VAR and Conditional Value at Risk (CVAR) efficient portfolios. Put/call efficient frontiers 2. Dynamic portfolio and risk management: 2.1 Asset and Liability management model 2.2 Constant mix strategies	1. [2], pp. 184-192 Powerpoint slides 1 2 2.1. [2], pp. 233-244, Powerpoint slides 2.2. Formulation of optimization problem for finding constant mix weights Example how constant mix strategy works Computation of optimal constant mix weights	Exercise 5

Recommended literature

1. Alexei A. Gaivoronski. On-Line lecture notes on financial optimization, material placed on this page

2. Stavros Zenios, Financial Optimization, book draft, 2005. Note. This draft is a courtesy of Stavros Zenios. No other use is permitted except for this course. When asked for password type guest. Only part of this book will be "pensum".

3. Selection of papers on financial optimization and risk management placed on the course page

Examples of exam exercises, financial optimization and risk management part

Exercises Solutions More exercises More solutions

Attention!!! These exercises are from previous exams in the full course on Financial Optimization and Risk Management. For this reason they may use material which was not taught during this course. Only those exercises which are based fully on material taught during this semester is relevant for you.

Exam 2009

Exercises Solutions