FINC3017 Investments and Portfolio Management

Report 1: Diversification (Precious Metals Portfolio)

Due: 4pm, 4th September 2017

Word limit: 1,500

Weight: 16.5%

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:

Investor Risk Aversion Coefficients

Investor Angela Benjamin Casey

Risk aversion coefficient (A) 4 2 0

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.

Marks will be approximately evenly allocated between calculations and discussion. 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 your written report. Please

use 12pt font with 2cm margins and include all references, if required, in a bibliography. You need to also

submit your workings as an Excel spreadsheet via the ‘Report 1 – Excel Spreadsheet’ link in Blackboard.

Written reports must be submitted via the Turnitin link labelled ‘Report 1’. Please ensure you receive an

email receipt from Turnitin that you have successfully submitted your report otherwise you could lose

all your marks from a late submission penalty.

## FINC3017 Investments and Portfolio Management

07
Sep