**FIN 6275: Investment Analysis and Global Portfolio Management**

1. Doing this homework, you will learn how to choose among different investment options.

2. You will appreciate how your utility will change as the investment restrictions are relaxed and you have more and more options to choose from.

3. You will further develop your programming and quantitative skills (great resume builder).

**Submit through Blackboard:**

Both results and programs should be submitted through Blackboard. Only one team member should upload the homework. This homework uses the data you obtained for the first homework.

For this homework use the ETF return data from January 1999 to December 2017 (months 1 to 228 if your return data starts in January 1999). I am saving the last 20 months of data for Homework 3 where you will evaluate how the portfolio you create now will do relative to a benchmark.

**I. You can only invest in one ETF:**

i. Plot all portfolios in a Mean-Variance framework (i.e. average return – standard-deviation graph). Note: Plot all portfolios in the same graph, include labels so the portfolios can be identified. ‘hold on’ to this graph so you can plot additional things on it later.

ii. What is the utility of the investor from holding each industry portfolio separately? (9 utilities)

iii. Which portfolio would this investor prefer?

iv. Plot the investor’s indifference curve across his preferred portfolio (you still need to show the other industry portfolios on the graph, these portfolios lie below this curve).

**II. You can invest in one ETF and the risk-free rate**

i. If the investor can allocate his money between the risk-free rate and one of the ETFs, which ETF would he choose and why?

ii. Plot the best capital allocation line of this chosen ETF (the graph needs to include all previous steps).

iii. How much should this investor allocate to the risk-free asset and how much to the preferred ETF to maximize his utility? (Assume the borrowing rate is the risk-free rate.)

iv. What is his utility at this optimal allocation? Has his utility improved due to the existence of a risk-free rate?

v. Plot the investor’s new best indifference curve (the graph needs to include all previous steps).

**III. Combining all ETFs: Efficient Frontier of RISKY assets (WITHOUT the risk-free rate)**

No Short Selling or Leverage Allowed (this is the default, all risky weights are between 0 and 1).

i. Plot the efficient frontier based on all ETFs.

ii. Find (numerically) the optimal portfolio for the investor (the one with the highest utility) and report its weights. (Hint: Calculate the utility for all portfolios along the frontier: you have the risk and return of all portfolios. Then find the maximum utility point and see what its weights are.)

iii. What is the utility of the investor at this optimal portfolio?

iv. Plot the indifference curve across the optimal portfolio.

**IV. All Risky and Risk-free assets: Optimal OVERALL portfolio: combining the risk-free asset with the optimal RISKY portfolio**

i. Plot the new efficient frontier with the risk-free rate based on the portfolios.

ii. What are the weights of the different industries in the optimal “RISKY” portfolio?

iii. What are the return and standard deviation of the optimal RISKY portfolio?

iv. What is the asset-allocation (i.e. the weight of the risky asset) in this investor’s optimal “OVERALL” portfolio?

v. What are the risk and standard deviation of the investor’s optimal OVERALL portfolio?

vi. What is the utility of the investor at this optimal overall portfolio? (Hint: use the return and standard deviation of that optimal portfolio).

vii. Summary: Now compare the utility that the investor had under the following investments:

1. Just one ETF

2. Just one ETF combined with the risk-free rate

3. A portfolio of all ETFs only

4. A portfolio of all ETFs with the risk of free

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