# F79PA Portfolio Theory & Asset Models

Course co-ordinator(s): Professor Gareth Peters (Edinburgh), Hamidreza Farhadi ().

Aims:

To introduce asset pricing and portfolio selection models. This course covers the first half of the material in Subject CT8 of the Institute/Faculty of Actuaries examinations.

## Detailed Information

Course Description: Link to Official Course Descriptor.

Pre-requisite course(s): F78PA Probability and Statistics A & F78AB Actuarial and Financial Mathematics B .

Location: Edinburgh.

Semester: 1.

Syllabus:

• Utility theory
• Stochastic dominance
• Measures of investment risk
• Portfolio theory
• Single-period models of asset returns
• Capital asset pricing model
• Arbitrage pricing theory
• Efficient market hypothesis (optional)

Learning Outcomes: Subject Mastery

At the end of studying this course, students should be able to:

• Derive the properties of a utility function. Calculate an investor’s expected utility of an investment.
• State the conditions for absolute dominance, first and second order stochastic dominance. Show how first and second order stochastic dominance are related to utility theory. Demonstrate whether investments have dominance over each other.
• Calculate the following measures of risk: variance, semi-variance, shortfall probability, mean shortfall and Value at Risk.
• Calculate the mean and variance of return on a portfolio of assets. Describe the purpose and calculation of the following: opportunity set, efficient frontier, indifference curves, lagrangian function and separation theorem.
• Describe the properties of single factor and multi factor models. Show how to fit a single index model using historic data.
• Discuss the assumptions and uses of the Capital Asset Pricing Model and Arbitrage Pricing Theory. Derive the capital market line and security market line.

Reading list:

• Joshi & Paterson
Introduction to Mathematical Portfolio Theory, 1st edition.
Cambridge University Press
• Elton, E., Gruber, M., Brown, S. & Goetzmann, W.
Modern Portfolio Theory and Investment Analysis, 8th edition.
Wiley, New Jersey. (older versions are also useful)

Assessment Methods:

There are 2-hour exam (80%) at the end of the 1st semester, a midterm test (10%) and two assignments (10%).

SCQF Level: 9.

## Other Information

Help: If you have any problems or questions regarding the course, you are encouraged to contact the lecturer

VISION: further information and course materials are available on VISION