Course syllabus - Portfolio Theory I 7.5 credits

Portföljteori I

Course code: MAA314
Valid from: Autumn semester13
Level of education: First cycle
Subject: Mathematics
Main Field(s) of Study: Mathematics/Applied Mathematics, Business Administration, Economics,
In-Depth Level: G2F (First cycle, has at least 60 credits in first-cycle course/s as entry requirements), G2F (First cycle, has at least 60 credits in first-cycle course/s as entry requirements), G2F (First cycle, has at least 60 credits in first-cycle course/s as entry requirements),
School: UKK
Ratification date: 2013-02-01

Objectives

Given the fact that there is, hardly, no single asset that may be characterized as having the highest return combined with the lowest risk; actors in the financial markets, naturally, become managers of portfolios of assets. The students will construct optimal financial portfolios, across risky and risk-free assets, and also examine risk aversion (utility functions). The objective is to provide students with analytical tools and to increase the student's knowledge surrounding portfolio topics, especially if they plan to work as a fund manager, security analyst, allocation specialist, quant manager, product developer, trader, or riskcontroller.

Learning outcomes

At the end of the course the student is expected to be able to
- construct, build, an optimisation model in Excel via the Fisher Black or other method.
- via the Lagrange and/or other method derive the optimal weight vector.
- explain why the characteristics of portfolios are significantly different from single assets.
- estimate an adjusted correlation matrix either via the Blume or Vasicek, or other technique.
- explain the single-index model and multifactor models.
- produce orthogonal indexes and understand principal-component analysis.
- use the cut-off ratio to quickly determine optimal portfolios.
- derive the CAPM and the APT.

Course content

The course will present the fundamental issues of finance, such as single factor and multifactor models, in a portfolio theory context. Based on a mathematical and statistical setting; the course will explore the mechanics of portfolio theory via geometric and algebraic analysis. The focus is on the overall investment process with emphasis on summarizing and distilling the issues surrounding portfolio optimization (mean-variance optimization) of various assets, deriving the Capital Asset Pricing Model (CAPM) and the Arbitrage Pricing Theory (APT), and discussing the topic of portfolio evaluation through risk-adjusted performance attribution measures. Derivatives will be considered in investigating the effects on the investment opportunity set (Sharpe ratio). Regression analysis (single and multifactor), principal-component analysis, matrix algebra, and linear equations will set the framework for portfolio construction. At the end of the course students will approach current research in the field of finance; advanced methods such as dynamic portfolio theory, predictability and higher moments. The course will use Excel for the project.

Teaching methods

Lectures combined with exercises, two external lecturers and an optimisation project.

Specific entry requirements

At least 60 credits totally from these areas: technical, natural sciences, business administration or economics where Methods of Statistical Inference 7,5 credits or equivalent is included and a TOEFL test result, minimum score 173 (CBT), 500 (PBT) or 61 (iBT) or an IELTS test result with an overall band score of minimum 5,0 and no band score below 4,5. Exemption from the requirements of Swedish language proficiency will be made.

Examination

Seminar (SEM1), 1.5 credits, marks Pass (G)
Written examination (TEN1), 6 credits, marks Pass (G) or Pass with distinction (VG)

A student who has a certificate from MDH regarding a disability has the opportunity to submit a request for supportive measures during written examinations or other forms of examination, in accordance with the Rules and Regulations for Examinations at First-cycle and Second-cycle Level at Mälardalen University (2016/0601). It is the examiner who takes decisions on any supportive measures, based on what kind of certificate is issued, and in that case which measures are to be applied.

Suspicions of attempting to deceive in examinations (cheating) are reported to the Vice-Chancellor, in accordance with the Higher Education Ordinance, and are examined by the University’s Disciplinary Board. If the Disciplinary Board considers the student to be guilty of a disciplinary offence, the Board will take a decision on disciplinary action, which will be a warning or suspension.

Rules and regulations for examinations

Marks

Three-grade scale

Enviromental aspects

The course does not contain any specific environmental considerations.

Course literature is preliminary until 3 weeks before the course starts. Literature may be valid over several terms.

Valid from: Autumn semester13

Decision date: 2013-07-31

Last update: 2013-07-31

Books

Elton, Edwin J.; Gruber, Martin J.; Brown, Stephen J; Goetzmann, William N;

Modern portfolio theory and investment analysis

ISBN: 978-0-470-05082-8, 0-470-05082-9 LIBRIS-ID: 10454394

728 s.

Valid from: Autumn semester15

Decision date: 2015-06-23

Last update: 2015-06-23

Books

Elton, Edwin J.; Gruber, Martin Jay; Brown, Stephen J.; Goetzmann, William N.;

Modern portfolio theory and investment analysis

ISBN: 9781118469941 (pbk.) LIBRIS-ID: 16776214

xiv, 738 pages

Valid from: Autumn semester17

Decision date: 2017-10-13

Last update: 2017-10-17

Books

Elton, Edwin J.; Gruber, Martin Jay; Brown, Stephen J.; Goetzmann, William N.;

Modern portfolio theory and investment analysis

ISBN: 9781118469941 (pbk.) LIBRIS-ID: 16776214

xiv, 738 pages

9th Edition, (754 pages)