COMPG004 - Market Risk Measures and Portfolio Theory

This database contains 2017-18 versions of the syllabuses. For current versions please see here.

PrerequisitesKnowledge of linear algebra, probability and stochastic process theory. Introductory course in Financial Mathematics.
Taught ByCamilo Garcia Trillos (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.


Market Risk

  • Introduction: Abstract market mathematical modelling. Main assumptions. Risk.
  • Utility functions: properties, examples, related concepts
  • Risk measures: utility-based, tail-based, coherent, convex. Notable examples: value at risk, expected shortfall.
  • Risk treatment: avoidance, reduction (hedging, diversification), sharing (insurance, outsource), retention (capital).
  • Pricing rules

Portfolio choice

  • Consumption-investment problems
  • Performance measurement and efficient frontiers
  • Equilibrium pricing models: Example CAPM (*)

Practical aspects

  • Factor models
  • Risk measure estimation
  • Backtesting

Mathematical Tools

  • Probability and Markov chains in general states
  • optimisation

Numerical tools (Python)

  • structure
  • conditionals
  • loops and functions
  • Monte Carlo methods
  • Linear algebra operations
  • Data import
  • Plotting
  • Hypothesis testing
  • Optimisation routines

Method of Instruction

3 hours of lectures per week. 1 hour of demonstration lecture. Additional online material.


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%

Students will also have homework assignments and online tests to complete.


Reading list available via the UCL Library catalogue.