The University of Southampton
Courses

# MATH6017 Financial Portfolio Theory

## Module Overview

The module aims to introduce the students to the basics of portfolio theory. Beginning with a summary of the reasons why both private investors and large institutional investors might wish to own share portfolios, the module progresses to consider how risk and return vary as share prices move and introduces the student to the basics of Markowitz portfolio theory. Illustrative two-asset cases will then be considered before the risk/reward diagram for an N asset portfolio is examined. The notions of short selling and riskless assets will then be introduced to the student and incorporated into the theory. Finally, the student will learn how to solve the general Markowitz portfolio problem to determine the Optimum portfolio, the Capital Market Line and the Market Price of Risk. If time permits, discussion will also take place of more advanced models of portfolio theory.

### Aims and Objectives

#### Learning Outcomes

##### Knowledge and Understanding

Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:

• Demonstrate knowledge and understanding of basic principals in optimal portfolio construction.
• Demonstrate knowledge and understanding of some of the most common models in constructing optimal portfolio and how they can be solved, including closed-form solutions and iterative algorithms.
• Understanding various ways in generalizing the basic portfolio optimization models to more complex situations.
##### Subject Specific Intellectual and Research Skills

Having successfully completed this module you will be able to:

• Develop general portfolio construction for a range of practical (and small) problems.
• Appreciate the power of using mathematical optimization and analytical skills relevant to financial portfolio construction.

### Syllabus

• Investment in shares from the point of view of private investors, speculators and large investment companies. • The role of investment in pension funds. • Definitions of mean and variance. • The mean and variance for sums of variables. • How shares move relative to each other: covariance and correlation co-efficients. • The advantages of portfolio diversification. • The differences between negative, zero and positive correlation and examples of shares that display these properties. • Risk and reward for shares, definition of the risk/reward diagram. • Drawing risk/reward diagrams for portfolios with a small number of assets. • Particular two-asset cases. • Generalisation to portfolios with N assets. • The effect of short selling in risk/reward diagrams. Including riskless assets in the analysis. • Generation of portfolio possibilities region. • Analysis of a combination of risky and riskless assets: arbitrage. • The general Markowitz portfolio problem. • Finding the CML, MPOR and optimal portfolio. • (If time permits) asset risk and reward in the presence of uncertainty, strong and weak efficient market hypotheses

### Learning and Teaching

#### Teaching and learning methods

Two 4-hour lectures Two 2-hour computer sessions Two 2-hour lectures

TypeHours
Independent Study150
Total study time150

Elton EJ & Gruber MJ. Modern Portfolio Theory and Investment Analysis.

Merton RC. Continuous Time Finance.

Blake D. Financial Market Analysis.

### Assessment

#### Summative

MethodPercentage contribution
Closed book Examination 100%

#### Repeat

MethodPercentage contribution
Examination 100%

#### Referral

MethodPercentage contribution
Examination 100%

#### Repeat Information

Repeat type: Internal & External