MA311-6-AU-CO:
Mathematics of Portfolios
2025/26
Mathematics, Statistics and Actuarial Science (School of)
Colchester Campus
Autumn
Undergraduate: Level 6
Current
Thursday 02 October 2025
Friday 12 December 2025
15
03 May 2024
Requisites for this module
MA126
(none)
(none)
(none)
(none)
BSC N233 Actuarial Science (Including Placement Year),
BSC N233DT Actuarial Science (Including Placement Year),
BSC N323 Actuarial Science,
BSC N323DF Actuarial Science,
BSC N323DT Actuarial Science,
BSC N324 Actuarial Science (Including Year Abroad),
BSC N325 Actuarial Science (Including Foundation Year),
BSC L1G2 Economics and Mathematics (Including Placement Year),
BSC LG11 Economics and Mathematics,
BSC LG18 Economics and Mathematics (Including Foundation Year),
BSC LG1C Economics and Mathematics (Including Year Abroad),
BSC GN13 Finance and Mathematics,
BSC GN15 Finance and Mathematics (Including Placement Year),
BSC GN18 Finance and Mathematics (Including Foundation Year),
BSC GN1H Finance and Mathematics (Including Year Abroad),
MSCIN399 Actuarial Science and Data Science,
BSC N333 Actuarial Studies,
BSC N333DT Actuarial Studies,
BSC N334 Actuarial Studies (Including Placement Year),
BSC N334DT Actuarial Studies (Including Placement Year),
BSC N335 Actuarial Studies (Including Year Abroad)
The module introduces modern financial economic theories and methods on portfolio management to construct asset models to assist risk management of financial services firms.
The aims of this module are:
- To cover part of the syllabus of CM2 published by the Institute and Faculty of Actuaries (IFoA)
- To provide a grounding in the principles of modelling with a focus on risk management.
By the end of the module, students will be expected 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.
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.
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 a published bibliography for this year.
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
Reassessment
Module supervisor and teaching staff
Dr Daniel Ahelegbey, email: d.f.ahelegbey@essex.ac.uk.
Dr Daniel Ahelegbey , Dr Jianya Lu
maths@essex.ac.uk
Yes
Yes
No
Available via Moodle
Of 2 hours, 2 (100%) hours available to students:
0 hours not recorded due to service coverage or fault;
0 hours not recorded due to opt-out by lecturer(s), module, or event type.
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