25721 Investment Management Assignment Part I

Finance Discipline Group 
UTS Business School 

Question 1 (Asset returns and risk) - 5 marks)

Extreme volatility and falling share prices have been experienced in share markets across the globe since late February. This is a dramatic change from the rising share prices that occurred over the twelve months prior to February. Rooster Wealthy Investors Trust provides you with share prices for eight (8) companies listed on the Australian Securities Exchange (ASX). They ask you to write up an analysis of these companies. In the analysis you must:

• Briefly explain, in your own words, whether or not it would have been wise to trade on the ASX since the start of 2020. Note: Australian newspapers have regularly printed articles on this. (worth 1 mark)
• Identify the eight (8) companies in the EXCEL spreadsheet and in a table list their ASX industry group and describe, in your own words, two of their main products or services. The description for each company will require at least two sentences. (worth 1 mark)
• Graph the share prices of the companies and provide your own opinion, based on these graphs, whether it would be best to buy or short sell each of the companies. (worth 1 mark)
• Estimate the monthly average continuous returns and sample standard deviations of the monthly continuous returns for each of the companies and the ASX200 from July 2010 to July 2020. Summarise your estimations in a simple labelled table. (worth 0.5 mark)
• Estimate the sample correlation based on the monthly continuous returns for each pair of the eight (8) companies. Summarise your estimations in a simple labelled table and identify the pair that has the strongest relationship and the pair that has the weakest relationship. (worth 0.5 mark)
• Based on your estimations in (d) and (e) select four (4) companies that you consider would be the best to create a portfolio with. Provide a brief explanation of your decision. (worth 1 mark)

Question 2 (Mean-variance optimization - 5 marks)

The investors in Rooster Wealthy Investors Trust have a risk aversion factor of A = 4. Rooster Wealthy Investors Trust asks you to analyse a portfolio that consists of two risky assets and a risk-free asset. In the analysis you are required to

• Explain what a risk aversion factor of A = 4 implies about the investors who buy units in Rooster Wealthy Investors Trust. (worth 1 mark)
• The return and risk profile of investors in Rooster Wealthy Investors Trust can be described by the quadratic utility function covered in Lecture 2. Rank the eight companies from the one most preferred by the investors to the least preferred. Show and explain why the companies are ranked in this order. (worth 1 mark)

𝑼_𝒊(𝑬(𝒓), 𝝈) = 𝑬(𝒓) − 𝟏/2 𝑨_𝒊𝝈𝟐

• Construct a portfolio containing the two (2) companies that have the strongest relationship and a risk-free security. Use your estimations in Question 1 to calculate the percentage of funds that would be invested in each of the two companies and the riskfree asset. Assume the return on the risk-free security is the average cash rate. Do your calculations using trial and error (in a systematic way) in EXCEL and by using EXCEL’s Solver.
  1. List the percentage of wealth invested in each of the two companies and the risk-free asset and the return and risk of the two (2) companies; the risk-free interest rate security; the optimal risky asset portfolio and the optimal total portfolio (worth 0.5 marks)
  2. In a simple labelled table list the return, risk and utility of ten of the risky asset portfolios that lie near the optimal risky asset portfolio. Explain, in your own words, why these ten (10) portfolios are not the optimum risky asset portfolio

(worth 1 marks) iii. In a fully labelled mean-standard deviation diagram show the positions of the optimal total portfolio, the optimum risky asset portfolio, the risk-free interest rate security, the efficient frontier and capital allocation line. The diagram can be hand drawn. (worth 1 mark)

• Provide a recommendation, in your own words, to Rooster Wealthy Investors Trust on whether it would be better to invest in the optimum total portfolio; an ASX200 managed fund; or a risk-free interest rate security. (worth 0.5 marks)

Question 3 (Asset Pricing Theory - 5 marks)

Rooster Wealthy Investors Trust asks you analyse whether any of the eight (8) companies are mispriced. You decide to use the security market line (SML) to test for mispricing. The equation below summarises the single index model (SIM).

𝑅𝑖𝑡 = 𝛼𝑖 + 𝛽𝑖𝑀𝑅𝑀𝑡 + 𝜀𝑖𝑡

𝑅_𝑖𝑡 is the excess monthly return of stock i above the cash rate

𝑅_𝑀𝑡 the excess monthly return of the ASX200.

• In your own words explain how the SML can be used to test for mispricing and one weakness of using the SML to do this test. (worth 1 mark)
• Use the excess monthly share returns for the companies from July 2010 to July 2020 to estimate their 𝛼_𝑖 and 𝛽_𝑖. In a simple labelled table list 𝛼_𝑖 and 𝛽_𝑖 for each of the companies in alphabetical order of the company names. Note: The calculations that you will be using are discussed in Lectures 3 and 4. The calculations can easily be done in EXCEL using formula functions for “intercept” and “slope” or from a regression in

“Data Analysis” (the “Y-range” is the dependent variable, the column of excess stock return, and “X-range” is the independent variable, the column of excess ASX200 returns). (worth 0.25 marks)

• Under the assumptions of the SIM and using your estimations in (b), calculate the expected excess returns for each of the eight companies. List these in a simple labelled table. (worth 0.25 marks)
• You run the regression equation below to test whether any of the companies is mispriced:

𝑅̅_𝑖 = 𝛼 + 𝛾𝛽̂_𝑖 + 𝜀_𝑖

𝑅̅_𝑖 is the estimated expected excess return of each company

𝛽̂_𝑖is the beta coefficient of each company

Explain what your estimates for 𝛼 and 𝛾 as well as their p values and t statistics say about the relationship between 𝑅̅_𝑖 and 𝛽̂_𝑖. Note: The regression can be done in “Data Analysis” (the “Y-range” is the dependent variable, the column of expected excess stock returns and “X-range” is the independent variable, the column of betas). (worth 1.5 marks)

• Indicate whether any of the companies is mispriced by doing the following:

1. Plot the best-fitted line for the estimated 𝑅_𝑖’s and 𝛽_𝑖‘s and show the position of the companies on the graph. Note: This can be generated by selecting the “Line Fit Plots” option when doing the regression and in Design adding the Chart Element “Trendline (linear)” (worth 0.5 marks) ii. Calculate and explain the difference between the expected excess returns calculated in (c) and the 𝑅̅_𝑖 estimated using the 𝛼 and 𝛾 in (d) and beta in (b). (worth 0.5 mark)

• Identify whether the companies should be purchased or short sold. Explain why these trades would be profitable. (worth 1 mark)