### Calculate the expected utility for both investors

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##### Reference no: EM131455000

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

 MATL FIN COND CONS UTIL Materials Financials Consumer Discretionary Consumer Staples Utilities TELE ENGY IT HC INDU Telecom Energy Information Technology Health Care Industrials

Expected Industry Returns

 MATL FIN COND CONS IT TELE ENGY UTIL HC INDU 0.40% 0.45% 0.46% 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

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The given reports relates to concepts of portfolio management. A portfolio is nothing but a combination or a bundle of individual securities. Portfolio management is related to management of investment in securities effectively and efficiently. The process of portfolio management includes selection of securities from numerous securities having different returns and risks with a view that the investors yield maximum for a given level of risk and minimum risk for a given level of return.

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### Reviews

#### inf1455000

4/21/2017 5:48:46 AM

Much obliged to you such a great amount for all the offer assistance. A debt of gratitude is in order for helping me with each task. Without you my work wouldn't be as great. It was exceptionally amusing to adjust my work with you! Much appreciated once more!

#### inf1455000

4/21/2017 5:46:42 AM

Hello the report looks to be headed in the right direction. It does need to go into more depth on answering the 7 questions. However I am concerned about the excel as there should be calculations done their. I have attached some documents to show how the calculations should sort of look.

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