Mathematics of Portfolios

The details
Mathematical Sciences
Colchester Campus
Postgraduate: Level 7
Monday 13 January 2020
Friday 20 March 2020
01 October 2019


Requisites for this module



Key module for

DIP GN1309 Mathematics and Finance,
MSC GN1312 Mathematics and Finance,
MSC GN1324 Mathematics and Finance,
DIP N32309 Actuarial Science,
MSC N32312 Actuarial Science

Module description

The module introduces modern financial economic theories and methods on portfolio management to construct asset models to assist risk management of financial services firms.

Module aims


1. Utility Theory and Investment Risk
Utility function, expected utility theorem, measures of investment risk – variance of return, downside semi-variance of return, shortfall probabilities and Value-at-Risk (VAR) / Tail VaR.
2. Mean Variance Portfolio Theory
Short sales and portfolios of assets, diversification, the Markowitz model, the two-fund theorem, inclusion of a risk-free asset, the one-fund theorem.
3. The Capital Asset Pricing Model (CAPM)
Capital asset pricing model, betas and CAPM for portfolios, security market line, CAPM as a pricing formula, the Efficient Market Hypothesis (EMH)
4. Factor Models
Single factor models, multi-factor models, construction of the different types of multifactor models and perform calculations using both single and multi-factor models.
5. Arbitrage Pricing Theory
Simple APT, compatibility of APT with CAPM, More on compatibility of APT with CAPM, two-factor model, diversifying the portfolio, arbitrage pricing on the diversified portfolio

Module learning outcomes

On completion of the module students should be able to:
- Describe and discuss the application of utility theory to economic and financial problems.
- Discuss the advantages and disadvantages of different measures of investment risk.
- Describe and discuss the assumptions of mean-variance portfolio theory and find mean-variance optimal portfolios.
- Describe and discuss the properties of single and multifactor models of asset returns.
- Describe asset pricing models, perform calculations and appreciate the limitations of the models studied.

Module information

No additional information available.

Learning and teaching methods

This module has 30 lectures and 5 classes in the autumn term. There are 3 revision hours in the summer term.


This module does not appear to have any essential texts. To see non-essential items, please refer to the module's reading list.

Assessment items, weightings and deadlines

Coursework / exam Description Deadline Weighting
Coursework Homework 1 12/02/2020
Written Exam Test
Exam 120 minutes during Summer (Main Period) (Main)

Overall assessment

Coursework Exam
20% 80%


Coursework Exam
0% 100%
Module supervisor and teaching staff
Dr Haslifah Hasim (



External examiner

Dr Dimitrina Dimitrova
Cass Business School, City, University of London
Senior Lecturer
Available via Moodle
Of 40 hours, 33 (82.5%) hours available to students:
7 hours not recorded due to service coverage or fault;
0 hours not recorded due to opt-out by lecturer(s).


Further information
Mathematical Sciences

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