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FIN 6275 (PARTI)

INVESTMENTANALYSIS AND GLOBAL PORTFOLIO MANAGEMENT

Spring 2022

HOMEWORK 2: PORTFOLIO MANAGEMENT

Homework Objectives:

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

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

Submit through Blackboard)

For this homework use the ETF return data from January 1999 to December 2019 (months 1 to 252 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.

Throughout the homework,

if at least one of the last names in the group starts with A-J,

assume an investor with a risk aversion A=2 and the risk free rate is 0.001 per month

Please keep building on the same graph throughout questions I and II, so you can see how the changing investment options keep changing your utility (use ‘hold on’ to keep plotting on the same graph).

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. Ifthe investor can allocate his money between the risk-free rate and one ofthe 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).

Note: I’m lookingfor the numerical solutions/answers in questions III andIV.

You don’t need to calculate anything by hand,just locate the answer in the matrices/vectors.

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 utilityfor all portfolios along thefrontier: you have the risk and return of all portfolios. Thenfind 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.

(The graph needs to show all ETFs, the efficientfrontier, and the indifference curve!)

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

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

(Start a new graph, stop holding on to old one in section III. The graph needs to show all ETFs). (Hint: all answersfor ii. to v. can befound in the output of portalloc)