Mathematics of Portfolios

The details
Mathematics, Statistics and Actuarial Science (School of)
Colchester Campus
Postgraduate: Level 7
Thursday 03 October 2024
Friday 13 December 2024
05 January 2024


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,
MSC N32324 Actuarial Science,
MPHDN32348 Actuarial Science,
PHD N32348 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

No information available.

Module learning outcomes

By the end of the module, students will be expected to:

  1. Describe and discuss the application of utility theory to economic and financial problems.

  2. Discuss the advantages and disadvantages of different measures of investment risk.

  3. Describe and discuss the assumptions of mean-variance portfolio theory and find mean-variance optimal portfolios.

  4. Describe and discuss the properties of single and multifactor models of asset returns.

  5. Describe asset pricing models, perform calculations and appreciate the limitations of the models studied.

Module information

Indicative syllabus

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.

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.

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)

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.

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.

Learning and teaching methods

Teaching in the School will be delivered using a range of face to face lectures, classes and lab sessions as appropriate for each module. Modules may also include online only sessions where it is advantageous, for example for pedagogical reasons, to do so.


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 Coursework weighting
Exam  Main exam: In-Person, Open Book (Restricted), 120 minutes during Summer (Main Period) 
Exam  Reassessment Main exam: In-Person, Open Book (Restricted), 120 minutes during September (Reassessment Period) 

Exam format definitions

  • Remote, open book: Your exam will take place remotely via an online learning platform. You may refer to any physical or electronic materials during the exam.
  • In-person, open book: Your exam will take place on campus under invigilation. You may refer to any physical materials such as paper study notes or a textbook during the exam. Electronic devices may not be used in the exam.
  • In-person, open book (restricted): The exam will take place on campus under invigilation. You may refer only to specific physical materials such as a named textbook during the exam. Permitted materials will be specified by your department. Electronic devices may not be used in the exam.
  • In-person, closed book: The exam will take place on campus under invigilation. You may not refer to any physical materials or electronic devices during the exam. There may be times when a paper dictionary, for example, may be permitted in an otherwise closed book exam. Any exceptions will be specified by your department.

Your department will provide further guidance before your exams.

Overall assessment

Coursework Exam
30% 70%


Coursework Exam
30% 70%
Module supervisor and teaching staff
Dr Hirbod Assa, email:
Dr Hirbod Assa



External examiner

Dr Melania Nica
Available via Moodle
Of 47 hours, 45 (95.7%) hours available to students:
0 hours not recorded due to service coverage or fault;
2 hours not recorded due to opt-out by lecturer(s), module, or event type.


Further information

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