ECF6102 QUANTITATIVE SKILLS FOR BUSINESS
ECF6102 QUANTITATIVE SKILLS FOR BUSINESS
SEMESTER 1, 2019
MAJOR GROUP* ASSIGNMENT
– Due dates:
- Part A on week 9,
pm on Sunday 5th
May 2019 (AWST)
- Part B on week 12, 11:59 pm on Sunday 26th May 2019 (AWST)
- The assignment needs to be submitted electronically via Blackboard
(two-step process. More information will be provided on Blackboard)
- Your submission should include the ECU assignment cover page (provided on our Bb website). Please note that if an assignment cover sheet is not included’ your assignment will not be graded.
- The ECU assignment cover page must include:
- Names of all author(s)
- Students’ ID number(s)
- Allocated group number (if applicable)
- The assignment must be submitted as one document by one group member
- (*) Student working in groups should complete and submit electronically only the first page of the assignment contract (this document is provided on our Blackboard website)
* This score contributes 20% to your final grade
- This is a group assignment. Students may form groups of no more than 2 members
- Every group MUST complete and sign a group contract (document provided on our Blackboard website)
- The assignment must be prepared on A4 paper using a word processor. Make sure you choose a legible font face and size (e.g. Times New Roman 12 or Arial 11) and double- spaced the lines. Handwritten assignments will not be accepted.
- All equations should be typed in and graphs drawn with the aid of a suitable software tool or package.
- Answer all parts of the questions by applying the methodology of statistics.
- For full marks, ALL sections are to be completed.
- ALL answers must be justified with sufficient logical workings to gain maximum marks in the presentation allocation for each section.
- Time extensions will NOT be granted for work-related difficulties or computer/printer malfunctions and/or lost data.
Extensions will only be granted on medical grounds, and where supported by documentation
- Full Presentation marks are awarded only for a fully word processed assignment, including all diagrams and formulae.
This assignment is to be completed in two (2) parts:
Part A Uses the data set called ‘TOP 45 ASX’ from the Blackboard site in the Assignment folder. You are required to answer a number of questions concerning the data set.
This part Involves you to perform the manual calculation for questions using the data set ‘TOP 45 ASX’. You should use your calculator, appropriate formulae and statistical methodology to answer the questions. All the steps and working must be shown here as would be required in a final examination answer. (Use as much accuracy as is necessary and generally up to 4 decimal places).
You are also required to substantiate several of the solutions found manually using the software PhStat/Excel software. Provide a separate printout of your results where applicable.
Part B This part requires you to undertake further statistical analysis using the data set ‘TOP 45 ASX’. Requirements are as above.
This part requires you to undertake regression analysis using the data set ‘STOCK PRICES 2018’.
INTRODUCTION TO THE DATA SETS:
TOP 45 ASX
The file Top 45 ASX contains a list of top 45 listed companies, extracted from Eikon on 19.02.2019. The following variables are included:
- Ticker: The Australian Stock Exchange allocated company three-letter code;
- Market Cap [bill]: the value of the company in $ billions;
- Tang Assets [bill]: Net tangible assets – the total assets of a company less total liability and not including intangible items such as goodwill;
- Div Yld [%]: Dividend Yield – this is the dividend in cents divided by the share price;
- P/E ratio: Price to Earnings ratio – a stock’s price divided by its historic earnings per share.
STOCK PRICES 2018
The file Stock Prices 2018 contains 2018 weekly data for the ASX ALL ORDINARIES and three
extracted from Eikon on 1.03.2019. The following variables are included:
- DATE – week beginning on the date given;
- ALL ORD – weekly closing value for the ASX ALL ORDINARIES index;
- ANZ – weekly closing stock price for AUST AND NZ BANKING GROUP;
- IAG – weekly closing stock price for INSURANCE AUSTRALIA GROUP;
- QAN – weekly closing stock price for QANTAS AIRWAYS LTD.
Part A – Statistical Analysis
Using the sample data attached, calculate the sample mean and standard deviation for the variables: –
- P/E ratio (2 marks)
- Did yld (2 marks)
- Tangible Assets (2 marks)
Check for normality for ALL variables in the data set. Are there any variables that could be considered NOT approximately normally distributed? Use PhStat to determine your answer here. Include your printouts from PhStat supporting your reasoning.
Write a summary on descriptive statistical findings, referring to Questions 1 and 2.
Using the sample data, calculate the sample proportion of companies whose P/E ratio exceeds 20, and its corresponding standard deviation.
Set up and interpret the following confidence intervals:
- a 95% confidence interval for the true population mean P/E ratio. (4 marks)
- a 99% confidence interval for the true population mean Did yld. (4 marks)
- a 90% confidence interval for the true population proportion of all companies whose P/E Ratio is better than 20. (4 marks)
A follow-up study will provide a point estimate of the population proportion of companies with a P/E ratio that exceeds 23. The study must provide 90% confidence that the point estimate is within 0.07 of the population proportion. If no previous proportion estimate is available (do not refer to the calculation in Question 4 above), how large a sample would you recommend for this study? Explain your answer.
Part B – Statistical Analysis (cont)
A stock market analysts claimed that on average the P/E ratio of all companies in the ASX 50 is more than 24. Do the data provide significant support for this claim?
Use a 5% significance level to test this claim. You should use both the critical value approach and the p-value approach to justify your answer. The relevant PhStat printout should be also provided.
Comment on your findings.
The Australian Financial Review has claimed that less than 35% of all companies in the ASX 50 have a dividend yield (%) that is 6% or more. How much evidence does the data providers need to support this claim?
Use a 0.05 level of significance to test this claim. You should use both the critical value approach and the p-value approach to justify your answer. The relevant PhStat printout should also be provided.
Comment on your findings.
Part B – Regression Analysis
The volatility of a stock is often measured by its beta value. You can estimate the beta value of a stock by developing a simple linear regression model, using the percentage weekly change in the stock as the dependent variable and the percentage weekly change in a market index as the independent variable. The ASX ALL ORDINARIES index is a common index to use. For example, if you wanted to estimate the beta value for ABC Company, you could use the following model, which is sometimes referred to as a market model:
(% 𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤 𝑐𝑐ℎ𝑎𝑎𝑎𝑎𝑎𝑎𝑤𝑤 𝑖𝑖𝑎𝑎 𝐴𝐴𝐴𝐴𝐴𝐴 𝐴𝐴𝐶𝐶𝐶𝐶𝐶𝐶𝑎𝑎𝑎𝑎𝑤𝑤)
= 𝛽𝛽0 + 𝛽𝛽1(% 𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤 𝑐𝑐ℎ𝑎𝑎𝑎𝑎𝑎𝑎𝑤𝑤 𝑖𝑖𝑎𝑎 𝐴𝐴𝐴𝐴𝐴𝐴 𝐴𝐴𝐴𝐴𝐴𝐴 𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝐴𝐴𝑂𝑂𝑂𝑂𝑂𝑂𝐴𝐴 𝑖𝑖𝑎𝑎𝑖𝑖𝑤𝑤𝑖𝑖) + 𝜀𝜀
The least-squared regression estimate of the slope b1 is the estimate of the beta value for ABC Company. A stock with a beta value of 1.0 tends to move the same as the overall market. A stock with a beta value of 1.5 tends to move 50% more than the overall market, and a stock with a beta value of 0.6 tends to move only 60% as much as the overall market. Stocks with negative beta values tend to move in the opposite direction of the overall market.
The ASX ALL ORDINARIES index tracks the overall movement of the
stock market by considering the stock prices of all listed corporations on ASX.
Using the given data set ‘Stocks Prices 2018’ AND simple ordinary least squares regression based solutions (Computer printout is sufficient solution here), answer the following:
HINT: Calculate Use the percentage change in the ASX ALL ORDINARIES index as the independent variable and the percentage change in a company’s stock price as the dependent variable)
Estimate the market model for ANZ, IAG and QAN.
Write a brief summary of your findings.
Which company has the best estimated market model? Explain your reasons here.
For each of the three companies, interpret the beta value. How can investors use the beta value as a guide for investing?