Report: The Benefits of Diversification
The spreadsheet Report 1.xlsx contains monthly returns on ten Australian industry indices from February 2009 to February 2017. The industry abbreviations are in the table below.
Industry Abbreviations
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MATL
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FIN
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COND
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CONS
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UTIL
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|
Materials
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Financials
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Consumer Discretionary
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Consumer Staples
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Utilities
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|
TELE
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ENGY
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IT
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HC
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INDU
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Telecom
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Energy
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Information Technology
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Health Care
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Industrials
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Expected Industry Returns
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MATL
|
FIN
|
COND
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CONS
|
IT
|
TELE
|
ENGY
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UTIL
|
HC
|
INDU
|
|
0.40%
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0.45%
|
0.46%
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0.40%
|
0.41%
|
0.38%
|
0.40%
|
0.38%
|
0.39%
|
0.46%
|
Investor utility is represented by: U = E(R) - ½Aσ2. There are two investors with different risk aversion coefficients (A). Sheree has a risk aversion coefficient of 4 and Levi has a risk aversion coefficient of 2. Investors are able to short-sell each industry throughout the report. Unless otherwise stated, investors are unable to borrow or lend at the risk-free rate. The expected returns per month to be used throughout the report are in the following table.
You are required to use all of the historical data to estimate the covariance matrix so that you can construct the optimal risky portfolios for each investor using the Markowitz approach. Your report needs to address the following points:
1. Calculate the expected utility for both investors if they invested solely in each industry. Which industries does each investor prefer and why?
2. Consider the two industries that provide the highest and lowest utility to Levi (A=2). What is the optimal portfolio for both Levi and Sheree that contains these two industries? Discuss what happens to each investor's utility and portfolio risk. Will this conclusion always be reached or is specific to these two portfolios?
3. Calculate the optimal portfolio for both investors that consists of the following five industries: MATL, CONS, TELE, UTIL and HC. How does this compare to the one industry and two industry portfolios in terms of diversification benefits?
4. Calculate the optimal portfolio for both investors that consists of all ten industries. Compare this to the other portfolios in terms of diversification benefits. What do you notice?
5. Compare the differences in the benefits of diversification for the risk-averse investors to a risk-neutral investor. What explains the differences? Do you think it is a sensible approach for an investor to put all their wealth into one industry? You should discuss the difference between expected returns and actual returns in your response.
6. Now consider the case where both Levi and Sheree can invest in a risk-free asset. The risk-free rate is 0.15% per month. Compare the diversification benefit between the five industry optimal portfolio and the ten industry optimal portfolio. How does the existence of the risk-free rate affect your conclusion regarding diversification benefits? Are diversification benefits greater if the investors can borrow or lend at the risk-free rate?
7. Your report should conclude with a summary of your findings regarding differences in the benefits of diversification across investors and industries.
Your report will need to present the weights for each portfolio as well as the returns and standard deviation for each portfolio. Please set the initial weights to be equal weights when conducting your optimisation.
Marks will be approximately evenly allocated between calculations and discussion. There will be marks will be awarded for the clarity of your discussion, the structure of your report and how you present your findings. Please use graphs and/or tables to support your discussion but do not include the raw data in the appendix.
Attachment:- FE-REport-one-excel.xlsx