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Group Report: Principles of Diversification
Due Date: 5pm Monday 13 May
Weight: 30%
Word Limit: 2500 words
The spreadsheet Group Report Data.xlsx contains monthly returns on the eleven Australian GICS industry portfolios from January 2018 to March 2024. The industry abbreviations are in the table below.
You need to estimate a number of portfolios for two different investors and discuss the implications for diversification. Key information on portfolio construction is as follows:
. Investor utility is based on monthly values and is represented by: U = E(R) – ½Aσ2. There are two investors with different risk aversion coefficients (A). Taylor has a risk aversion coefficient of 5 and Travis has a risk aversion coefficient of 10.
. The expected returns per month to be used throughout the report are in the following table. Do not use historical average returns as expected returns.
. The covariance matrix needs to be estimated using all of the historical data provided to construct portfolios for each investor using the Markowitz approach.
. Both investors are able to short-sell each industry throughout the report (i.e. they can have a negative portfolio weight).
. Investors are unable to borrow or lend at the risk-free rate except for part 5 of the report.
. Set the initial weights to be equal weights when conducting your optimisation (i.e. weights = 9.09%).
|
Industry |
Abbreviation |
Expected Return (per month) |
|
Consumer Discretionary |
COND |
1.40% |
|
Consumer Staples |
CONS |
0.95% |
|
Energy |
ENGY |
1.70% |
|
Financials |
FIN |
1.35% |
|
Health Care |
HC |
1.00% |
|
Industrials |
INDU |
1.35% |
|
Information Technology |
IT |
1.50% |
|
Materials |
MATL |
1.15% |
|
Utilities |
UTIL |
1.10% |
|
Real Estate |
RE |
1.60% |
|
Telecoms |
TELE |
1.05% |
Your report will need to undertake the following analysis:
1. Calculate the expected utility for both investors if they invest 100% of their wealth solely in each industry. Which industry does each investor prefer? What are the reasons for their preference? (15 marks)
2. Consider the ENGY and HC industries. What is the optimal portfolio for both Taylor and Travis that contains these two industries? Discuss what happens to each investor’s utility and portfolio risk for this portfolio compared to holding these two industries individually. Will you always reach this conclusion or is specific to these two portfolios? (15 marks)
3. Calculate the optimal portfolio for both investors that consists of the following five industries: ENGY, HC, IT, MATL and RE. How does this portfolio compare to the one industry and two industry portfolios in terms of diversification benefits to each investor? (15 marks)
4. Calculate the optimal portfolio for both investors that consists of all eleven industries. Compare this to the other portfolios you have already estimated in terms of diversification benefits. What do you observe? Contrast the differences in what you observe between the two investors. (15 marks)
5. Now consider the case where both Taylor and Travis can lend at the risk-free rate but cannot borrow at the risk-free rate. The risk-free rate is 0.45% per month. Estimate the optimal combined portfolio for each investor using the five industries in part 3 and then estimate the optimal combined portfolio for each investor using all eleven industries. How does the existence of the risk-free rate affect your conclusion regarding diversification benefits? Are diversification benefits increased or reduced if the investors can lend at the risk-free rate? (20 marks)
6. Your report should conclude with a summary of your findings regarding differences in the benefits of diversification across investors, industries and portfolio size. (10 marks)
Other information
. 10 marks will be awarded for the clarity of your discussion, the structure of your report and how you present your findings. Please use tables and charts to summarise your results.
. Please use graphs and/or tables to support your discussion but do not include the raw data in the appendix. All tables and charts need to be displayed in your written report.
. Your report will need to present the correlation matrix for the industries, portfolio weights, portfolio returns and portfolio standard deviation.
. Please use 12pt font with 2cm margins and include any references in a bibliography. You do not need to reference any lecture notes or tutorial material.
. Written reports should be submitted via Turnitin on Moodle.
. Excel spreadsheets need to be submitted via the link on Moodle. The spreadsheet will not be graded but it can assist in understanding your method if you make any mistakes in your calculations.
. Please review the excel recording from Week 3 on Moodle as that will be extremely helpful for using Excel to complete the report.
. Please post any clarifying questions on the report to the discussion forum on Moodle.
Individual Reflection Report
Each student will need to submit an individual reflection report via Moodle. This report should detail any issues you had working in the group, what were the positive and negatives of working with your group members. The report should be a minimum of one paragraph and a maximum of one page. If group members do not make a fair contribution to the group report, then their assessment mark could be adjusted.