MA311-6-SP-CO:
Mathematics of Portfolios
2020/21
Mathematics, Statistics and Actuarial Science (School of)
Colchester Campus
Spring
Undergraduate: Level 6
Current
Sunday 17 January 2021
Friday 26 March 2021
15
15 July 2020
Requisites for this module
MA126
(none)
(none)
(none)
(none)
BSC N233 Actuarial Science (Including Placement Year),
BSC N323 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
The module introduces modern financial economic theories and methods on portfolio management to construct asset models to assist risk management of financial services firms.
No information available.
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.
Syllabus
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.
Teaching will be delivered in a way that blends face-to-face classes, for those students that can be present on campus, with a range of online lectures, teaching, learning and collaborative support.
- Elton, Edwin J.; Gruber, Martin Jay; Brown, Stephen J.; Goetzmann, William N. (2014) Modern portfolio theory and investment analysis, Hoboken, NJ: Wiley.
- Luenberger, David G. (c2014) Investment science, Oxford: Oxford University Press.
- Dobbins, Richard; Witt, Stephen F.; Fielding, John. (1996) Portfolio theory and investment management, Oxford: Blackwell Business.
The above list is indicative of the essential reading for the course. The library makes provision for all reading list items, with digital provision where possible, and these resources are shared between students. Further reading can be obtained from this module's reading list.
Assessment items, weightings and deadlines
| Coursework / exam |
Description |
Deadline |
Coursework weighting |
| Coursework |
Test |
|
|
| Exam |
Main exam: 180 minutes during Summer (Main 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
Prof Spyridon Vrontos, email: svrontos@essex.ac.uk.
Dr Spyros Vrontos & Dr Peng Liu
Dr Spyros Vrontos (svrontos@essex.ac.uk), Dr Peng Liu (peng.liu@essex.ac.uk)
Yes
Yes
No
Dr Dimitrina Dimitrova
Cass Business School, City, University of London
Senior Lecturer
Available via Moodle
Of 2523 hours, 0 (0%) hours available to students:
2523 hours not recorded due to service coverage or fault;
0 hours not recorded due to opt-out by lecturer(s).
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