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: E( r ) ( r )

Corr(B,S) 0.10 Bonds (B) 0.04 0.15 Stocks (S) 0.11 0.30

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 () and P. Repeat the exercise by increment of 2% for the weight of the stock fund (i.e. recalculate E(rP) and P for a portfolio that has 2% in stock and 98% in the bond, then 4%, in the stock and 96% in the bond, and then 6% in the stock and 94% in the bond, 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). When you are done with this step you should have 51 pairs of data points for (E(rP), P), which should be organized in a table similar to Spreadsheet 6.6 in your textbook. 2. Graph these data points the resulting figure should be your investment opportunity set (your graph should be similar to Figure 6.3 in your textbook). 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? (hint: Look at the bottom part of the Spreadsheet 6.6 in your textbook) 4. Repeat steps 1 through 3 when the correlation between stocks is 0, and then with a correlation of -.90. 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!