# 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.

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##### Solution Summary

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

##### 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 ...

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