What is the minimum variance portfolio

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Reference no: EM132183784

Investments Assignment - Risk/Return Trade-off (Markowitz Efficient Frontier)

This is an INDIVIDUAL assignment designed to provide a better understanding of the concepts of diversification, risk and return trade-off, and the efficient frontier. It will also help you upgrade your Excel skills. You are required to use Excel in order to draw the efficient frontier for a set of given securities (stocks and bonds) and identify the minimum variance portfolio. You are also asked to discuss the different shapes of the frontier under different correlation scenarios.

Project Description - Assume the market is formed of only two securities (a bond fund and a stock fund). Use the following numbers in Excel:




Corr(B, S)

Bonds (B)




Stocks (S)




Take the following steps:

1. Consider alternative two-asset portfolios formed by varying the weights for the two funds provided above. That is, start with a portfolio that has 0% in the stock fund and 100% in the bond fund and calculate E(rP) and σP. Repeat the exercise by increment of 2% for the weight of the stock fund (i.e. recalculate E(rP) and σP for a portfolio that has 2% in stocks, then 4%, then 6% etc). Note that as long as you know the weight of the stock fund in the portfolio of two assets, the weight of the bond fund is also known (the two weights should add to 1).

2. Graph these data points - the resulting figure should be your investment opportunity set. What is your efficient frontier? Why?

3. The first question to ask at this point is what is the minimum variance portfolio? Is it among the ones you found in step 1 (this would be very unlikely)? How can you find the minimum variance portfolio? Determine its return and standard deviation. What are the weights for stocks and bonds in this portfolio?

4. Repeat steps 1 through 3 when the correlation between stocks is 0, and then with a correlation of -.9. How and why does the shape of your investment opportunity set change? What is the new minimum variance portfolio in each one of these cases? Explain!

5. What is the optimal portfolio for each one of the frontiers (i.e. the portfolio that optimizes your Sharpe ratio)? Assume that your particular degree of risk aversion dictates that you invest 35% of your wealth in the risk free asset and 65% in the optimum portfolio. Consider a risk free rate of 2%. Can you describe your overall allocation for each one of the three cases above?

Report Description - Keep in mind that this is an individual project! Your submitted report should include:

Your Excel Worksheet with your numbers (you will have three of them because of the three different correlation numbers). Identify the formulas you used for calculating E(rP) and σP.

Graph each of the investment opportunity sets separately and then put them together on the same graph.

Make sure your graphs identify the minimum variance portfolios. Describe the formulas you used for obtaining them.

Discuss each one of the questions identified in the project description.

Reference no: EM132183784

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Organize your Report - Make sure your report is professional and easy to read. Here are some suggestions on what you should include: Cover page (name, title, course name etc), Page Numbers, Discussion/Sections and Appendix - use some of the skills you learned working on your Portfolio Project! For example: Include your excel worksheet with your numbers in the Appendix and number them (there should be three of them, one for each correlation coefficient). Make sure each Appendix has a name. Use the appendix numbers to refer to in your discussion. Try to separate your discussion into sections to make it easy to follow (for example, you can use sections like "Investment Opportunity Sets"; "Minimum Variance Portfolio" etc) Make sure your discussion covers each one of the questions identified in the project description.

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