# COMPG004 - Market Risk Measures and Portfolio Theory

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

Code | COMPG004 |
---|---|

Year | MSc |

Prerequisites | Knowledge of linear algebra, probability and stochastic process theory. Introductory course in Financial Mathematics. |

Term | 1 |

Taught By | Camilo 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. |

# Content

### 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.

# Assessment

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.

# Resources

Reading list available via the UCL Library catalogue.