Reference no: EM132166851

Learning Outcomes

This assessment assesses the following Unit Learning Outcomes (ULO) and related Graduate Learning Outcomes (GLO):

Unit Learning Outcome (ULO)
ULO1 - assessed through student ability to apply knowledge of multivariate functions, data transformations and data distributions to summarise data sets.
ULO2 - assessed through the student ability to analyse datasets by interpreting summary statistics, model and function parameters.
ULO4 - assessed through student ability to develop software codes to solve computational problems for real world analytics.
ULO5 - assessed through student ability to demonstrate professional ethics and responsibility for working with real world data

Purpose
The aim of this assignment is to analyse the behaviour and performance of share prices of one company, from the listed five companies below, using historic data and the stochastic model given below. You can use statistical data analysis and features you have been learning in R.

Instructions
The work is individual. Solutions and answers to the assignment must be explained carefully in a concise manner and presented carefully. Use of books, articles and/or online resources on share price related to SIT718 Real World Analytics is allowed. Students are expected to refer to the suitable literature where appropriate.

Assessment Task: Problem solving task 1

The aim of this assignment is to analyse the behaviour and performance of share prices of one company, from the listed five companies below, using historic data and the stochastic model given below.

Let W be a Brownian motion. A stochastic process S has both a Newtonian term based on dt, where t is the time, and a Brownian term based on dW_t, the infinitesimal increment of W.

A stochastic process S can be defined as a continuous process (S_t, t ≥ 0) such that

dSt/St = μ_tdt + σ_tdW_t

It can be shown by using the It's formula that when σ_t = σ and μ_t = μ are both constants the solution for S_t is,

S_t = S₀exp[(μ - σ²/2)t + σW_t],

assuming that at t = 0, S₀; Wo = 0

1. Explain the meaning of σ_t and μ_t. Could these quantities be considered constant with time?

You are encouraged to research the information about stochastic modelling of share prices, Itô's calculus online or in books, research articles. State clearly ANY assumptions you have made.

2. Select ONE company on the stock market from the FIVE companies listed below. You can use Yahoo Finance to download the historic data

Companies:

- Australia and New Zealand Banking Group ANZ.AX
- National Australian Bank Limited (NAB.AX)
- Medibank Private Limited (MPL.AX)
- British Petrolium p.l.c. (BP)
- GlaxSmithKline plc (GSK)

Collect the closing share price data for this company for each trading day for 3 consecutive months, from 1 August 2018 to 31 October 2018 inclusive.

3. State the condition that share prices have to satisfy in order to be represented by a geometric Brownian motion? Does your data satisfy this condition? Check using appropriate statistical test and present your evidence in a suitable tabular format.

4. Compute σ and μ for your data assuming that they are both constant. You are encouraged to research the literature about σ and μ and find appropriate formulas to compute their values from the three months historic data.

5. Find information publicly available for your company, e.g. report and news releases.

Using this information about the company, critically appraise the computed values of σ and μ.

6. Estimate the expected value of the share price on 16 November 2016 and compare with published data.

7. In the light of your findings, state the possible restrictions of your model.

Write a short report (up to 250 words) about your company using your research, model and results.

8. Presentation

Presentation will be assessed for style and grammar, presentation of mathematics, graphs, tables and references. You should not exceed the 7 A4 sides page limit (including figures, tables, appendices and references).