## Modules 2017–18

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UG code: MTH6156
Module name:
Description:

This module introduces the key ideas in financial economics and risk management. We begin by looking at various models of the long-term behaviour of security prices. Then we consider different measures of risk that are used by market practitioners. We next look at mean-variance portfolio theory, which is one important way of determining the risk and return of a portfolio, given the risk and return of the individual constituents. We now turn to various economics models that actually attempt to explain the returns of the various assets that trade in the market. Finally, you will learn how the theoretical notion of a utility function can be used to explain individual investors’ decisions when allocating their wealth between different investment opportunities.

Organiser: Dr Kathrin Glau
Details: Level |Semester B|15 credits
Subject area: Financial mathematics
Overlaps:
• MTH6120 Further Topics in Mathematical Finance
• ECN226 Capital Markets 1
Essential prerequisites:
• MTH5112 Linear Algebra I
• MTH5212 Applied Linear Algebra
• MTH5123 Differential Equations
• MTH6121 Introduction to Mathematical Finance
• MTH6154 Financial Mathematics I

MTH6155 Financial Mathematics II (can be taken concurrently)

Restrictions:

Not open to Associate Students.

Assessment:

#### Normal assessment

DescriptionDuration / LengthWeighting
Final examination 2 hours 100%

#### Reassessment

DescriptionDuration / LengthWeighting
Resit examination 2 hours 100%
Syllabus:
1. Efficient markets hypothesis (EMH)
1. Various forms of the EMH
2. Comparison and consequences of each form of the hypothesis
2. Stochastic models of long-term behaviour of security prices
1. Continuous-time log-normal model
2. Autoregressive models
3. Alternative models
4. Simple calculations
5. Parameter estimation
3. Investment risk and return
1. Measures of investment risk
2. Comparison of investment opportunities using different risk measures
3. Assessment of risk
4. More on value-at-risk
4. Mean-variance portfolio theory
1. Mean-variance portfolio theory (Markowitz)
2. Risk and return of portfolio of many assets
3. Benefits of diversification
4. The risk-free asset (Tobin)
5. Factor models of asset returns
1. Overview of multi-factor models
2. Single-index model
3. Types of risk
4. Calculations using various factor models
6. Pricing
1. Capital Asset Pricing Model (Sharpe and Lintner)
2. Arbitrage Pricing Theory (Ross)
7. Utility theory
1. Utility functions
2. Utility maximisation and the expected utility theorem
3. Simple investment allocation problems with finite number of possible outcomes
4. Portfolio optimisation problem
5. Stochastic dominance
8. Behavioural finance
1. Discussion of principal results
Learning outcomes:

This module covers:

• Efficient markets hypothesis
• Stochastic models of long-term behaviour of security prices
• Investment risk and return
• Mean-variance portfolio theory
• Factor models of asset returns
• Pricing models

#### Disciplinary Skills

At the end of this module, students should be able to:

• Understand the assumptions and limitations of the various forms of the efficient markets hypothesis
• Recognize methods of measuring risk
• Use portfolios for managing risk
• Find maxima of utility functions depending on several variables
• Effectively use the Capital Asset Pricing model
• Use the language of mathematical finance with confidence

#### Attributes

At the end of this module, students should have developed with respect to the following attributes:

• Acquire and apply knowledge in a rigorous way
• Connect information and ideas within their field of study
• Explain and argue clearly and concisely
• Apply analytical skills to investigate unfamiliar problems
• Acquire substantial bodies of new knowledge
• Identify information needs appropriate to different situations

#### Assessment Criteria

History:

Introduced in 2017–18 for G1N3 / G1N5 BSc in Mathematics with Actuarial Science / with Professional Placement and GN1H MSci in Financial Mathematics.