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Constructing portfolios and efficient frontiers

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Assume the expected returns, standard deviations, and correlations for well-diversified portfolios of US stocks, US bonds, US real estate and international stocks are given as follows. The risk-free rate is 4%.

Expected Annual Return
Annual Standard Deviation
US Stocks
9%
19%
US Bonds
5.5%
11%
US Real Estate
6%
12%
International Value Stocks
10%
21%
Emerging Markets Equities
10.5%
26%
Annual Correlations are as follows:
US Stocks
US Bonds
US Real Estate
International Value Stocks
Emerging Markets
US Stocks
1
US Bonds
55%
1
US Real Estate
35%
30%
1
Int'l Value Stocks
50%
20%
25%
1
Emerging Markets
45%
25%
10%
40%
1

1) Derive the efficient frontier using US stocks, bonds, real estate, international value stocks, and emerging markets equities. (Hint: Use Solver. In setting the objective function and the constraints, do not permit short-sales, and recall that the goal is to choose the portfolio weights that minimize the level of portfolio risk, given some level of expected return. Start with the level of portfolio expected return equal to that of 5.5%, and then lower this constraint in 0.5% increments until you reach 10%)
2) Find the minimum variance portfolio. What are the expected return and standard deviation of this portfolio?
3) Find the market portfolio. What are the expected return and standard deviation of the market portfolio?
4) Chart the capital market line on the efficient frontier.

Solution Preview

Refer to the excel sheet for calculations

Step 1 lists all of the information you've provided.

Step 2

First of all, we have a correlation matrix and we need a covariance matrix for calculating portfolio variances, so we need to convert that using

cov(x,y) = cor(x,y)*sd(x)*sd(y)

You will see that I've computed the covariance matrix in step 2.

Step ...

Solution Summary

Constructing portfolios and efficient frontiers, calculating the returns/risks for each portfolio and finding the minimum variance portfolio using excel.

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