F79PA Portfolio Theory & Asset Models

Prof Andrew CairnsDr Wei WeiDr Karamjeet Singh

Course co-ordinator(s): Prof Andrew Cairns (Edinburgh), Dr Wei Wei (Edinburgh), Dr Karamjeet Singh (Malaysia).


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, Malaysia.

Semester: 1.


  • 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: Due to covid, assessment methods for Academic Year 2021/22 may vary from those noted on the official course descriptor. Please see:
- Maths (F1) Course Weightings 2021/22
- Computer Science (F2) Course Weightings 2021/22
- AMS (F7) Course Weightings 2021/22

SCQF Level: 9.

Other Information

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

Canvas: further information and course materials are available on Canvas