## Practical Financial Optimization

### PhD School at the Faculty of SCIENCE at University of Copenhagen

**Content**

**Week One**

Day 1: Introduction to GAMS using mean variance/ mean standard deviation optimization.

Day 2: Continued introduction to GAMS. Adding practical constraints such as fixed costs, size constraints and gearing to the mean variance model. Analysing the results in Excel.

Day 3: Continued introduction to GAMS. Introducing classical concepts in fixed income modelling and management: yield curve generation, portfolio dedication and immunization.

Day 4 and 5: Project work. The participants will be asked to formulate, solve and analyse a GAMS model based on a given problem formulation. The results should be presented at the end of week 1.

**Week Two**

Day 1: Scenario generation and optimization. Case: index tracking and regret minimization.

Day 2: Scenario optimization continued. Case: Value at Risk and Conditional Value at Risk.

Day 3: Stochastic programming. Case: Mortgage loan refinancing.

Day 4: The final project will be introduced. We will work together on developing a back-testing framework for use in the final project.

Day 5: We will work on the final project in the class. By the end of this day the students should be able to perform independent work on the project.

**Learning outcome**

**Competencies**

The course gives an introduction to the domain of practical financial risk and portfolio management. Participants will work with problem areas that can be attacked using optimization models.

**Skills**

Participants will be trained in quantitative evaluation of risk-return trade-offs, and learn how to model, solve, and document large, practical problems.

The course also gives an introduction to the programming language GAMS (General Algebraic Modelling Systems), which will be used extensively in all the cases and examples.

Participants who have followed the course will be able to formulate and solve optimization problems in GAMS in particular within the following areas:

- Measuring and managing return and risk trade offs

- Adding practical constraints to financial optimization problems

- Immunization and dedication of a bond portfolio

- Modelling Value at Risk and Conditional Value at Risk

- Back-testing results of ex-ante optimization

**Knowledge**

See course contents above.

**Literature**

Reading material will be sent out in July.

Example of course literature:

“A GAMS Tutorial”: http:/?/?www.gams.com/?dd/?docs/?gams/?Tutorial.pdf

Zenios, Stavros A. (2008), "Practical Financial Optimization: Decision Making for Financial Engineers", Blackwell.

**Teaching and learning methods**

3 hours of lectures and 3 hours of tutorials on each of the 10 (week)days August 2 to 13.

After that (or: during the 2nd week) students are given an assigment to which they must (before the regular teaching block begins) hand in written answers (a report).

**Remarks**

Week 1 and 2: Lectures, tutorials, and supervised project work

Week 3: Unsupervised project work and report writing

A report-based oral exam is held in week 4.

On-campus attendance is required only for the first two weeks (i.e. *not* for the exam).