TI4317 Quantitative and Empirical Methods in Finance

Professor Alexei A. Gaivoronski and Associate Professor Sjur Westgaard

Course organization    Contents     Recommended literature    Exam    





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


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






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


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



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


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


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 Flm

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