COMPG004 - Market Risk Measures and Portfolio Theory

Note: Whilst every effort is made to keep the syllabus and assessment records correct, the precise details must be checked with the lecturer(s).

PrerequisitesKnowledge of probability and stochastic process theory. Introductory course in Financial Mathematics.
Taught ByJohannes Ruf (100%)
Aims/Learning Outcomes

The module aims to familiarise students with key concepts and models in general asset pricing, portfolio theory, and risk measurement. Those concepts and models include risk aversion, utility functions as a representation of preferences, efficient frontiers, Markowitz Portfolio theory, the Capital Asset Pricing model, Value at Risk, and Expected Shortfall.
Students will be able to apply the standard models in asset pricing, portfolio theory, and risk measurement. Students will be aware of the statistical and numerical limitations of these models and know about modern approaches to tackle those issues.


Utility functions and risk aversion models; equilibrium pricing and efficiency, arbitrage and pricing kernels; risk measurement, value at risk and coherent risk measures; portfolio choice and optimization, mean-variance analysis, beta pricing; consumption and terminal wealth optimization; dynamic financial markets and capital asset pricing in continuous time; statistical and numerical issues.

Method of Instruction

3 hour lectures per week.


The course has the following assessment component:

  • Written examination (2.5 hours, 100%)

To pass this course, students must:

  •  Obtain an overall pass mark of 50% 


Recommended texts

Back, K., Asset Pricing and Portfolio Choice Theory, Oxford University Press, 2010.

Cochrane, J. H., Asset Pricing, Princeton University Press, 2005.

Duffie, D., Dynamic Asset Pricing Theory, Princeton University Press, 2001.

Hans Föllmer, Alexander Schied, Stochastic Finance: An Introduction in Discrete Time, Walter de Gruyter, 2011

McNeil, Frey, Embrechts, Quantitative Risk Management: Concepts, Techniques and Tools, Princeton University Press, 2015