Investments and Portfolio Management Report: Diversification
In this report you are asked to construct and discuss optimal portfolios for three investors, Angela, Benjamin and Casey. For all investors, their utility is represented by: U = E(R) - ½Aσ2. However, they have different risk aversion coefficients (A), as summarised in the table below:
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Investor Risk Aversion Coefficients
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Investor
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Angela
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Benjamin
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Casey
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Risk aversion coefficient (A)
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4
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2
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0
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Unless otherwise stated, investors are unable to short-sell any asset, nor are they able to borrow or lend at the risk-free rate. The expected returns and variance-covariance matrix you are required to use are contained in the spreadsheet 'Report 1 2017S2 - data.xlsx'. The data is calculated from monthly average spot prices for four precious metals - gold, silver, platinum and palladium - as well as end of month values for an equities index, specifically the S&P/ASX200 index. You are required to use the estimates provided in order to construct the optimal risky portfolios for each investor using the Markowitz approach.
Specifically, your report needs to address the following points:
1. Assume each investor is restricted to investing in a single precious metal at a time. Which precious metal does each investor prefer and why? Present all possible expected utility outcomes for each investor in your answer.
2. Assume each investor can now choose to construct a portfolio of gold and palladium. Report on the optimal portfolio each investor would construct. Discuss the differences in each investor's utility and portfolio characteristics. Discuss whether investors would prefer to hold the portfolio or the single precious metal as calculated in (1).
3. Construct the optimal portfolio for each investor that contains (a) all four precious metals; and (b) all four precious metals and the S&P/ASX200 equities index. How do these compare in terms of diversification benefits? Comment on the differences in utility from your answer in (2).
4. Consider Casey specifically. How would you describe their attitude to risk? Do you think their optimal strategy is a sensible approach? You should discuss the difference between expected returns and actual returns in your response.
5. Now consider the case where Angela and Benjamin can borrow and invest in a risk-free asset. The risk-free rate is 0.15% per month. How does the ability to borrow or lend at the risk-free rate change the characteristics of these two investor's optimal risky portfolio and optimal combined portfolio? Assume for this question investors are able to invest in all four precious metals and the equities index.
6. Assume that the risk-free asset in (5) is only available to Angela, and Benjamin is restricted to a retail risk-free borrowing and lending asset. Specifically, Benjamin can invest at a risk-free rate of 0.105% per month but is charged 0.20% per month to borrow. How does this affect Benjamin's optimal investment strategy? Comment on what (if any) changes occur to Benjamin's utility and the characteristics of his utility-maximising portfolio.
7. Your report should conclude with a summary of your findings regarding differences in the benefits of diversification across investors and asset classes.
Your report will need to present the weights for each portfolio you calculate as well as the returns and standard deviation for each portfolio. Please set the initial weights to be equal weights when conducting your optimisation. Address the requirements of each question clearly.