## 1. Draw A Properly Labeled Graph Of The Markowitz Efficient Frontier. Describe The Efficient Frontier In Exact Terms. Discuss The Concept Of Dominant Portfolios And Show An Example Of One On Your Graph.

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Questions 1. Why do most investors hold diversified portfolios?

2. What is covariance, and why is it important in portfolio theory?

3. Why do most assets of the same type show positive covariances of returns with each other? Would you expect positive covariances of returns between different types of assets such as returns on Treasury bills, General Electric common stock, and commercial real estate? Why or why not?

4. What is the relationship between covariance and the correlation coefficient?

### 5. Explain the shape of the efficient frontier.

6. Draw a properly labeled graph of the Markowitz efficient frontier. Describe the efficient frontier in exact terms. Discuss the concept of dominant portfolios and show an example of one on your graph.

7. Assume you want to run a computer program to derive the efficient frontier for your feasible set of stocks. What information must you input to the program?

8. Why are investors' utility curves important in portfolio theory?

9. Explain how a given investor chooses an optimal portfolio. Will this choice always be a diversified portfolio, or could it be a single asset? Explain your answer.

10. Assume that you and a business associate develop an efficient frontier for a set of investments. Why might the two of you select different portfolios on the frontier?

11. Draw a hypothetical graph of an efficient frontier of U.S. common stocks. On the same graph, draw an efficient frontier assuming the inclusion of U.S. bonds as well. Finally, on the same graph, draw an efficient frontier that includes U.S. common stocks, U.S. bonds, and stocks and bonds from around the world. Discuss the differences in these frontiers.

12. Stocks K, L, and M each have the same expected return and standard deviation. The correlation coefficients between each pair of these stocks are:

K and L correlation coefficient = +0.8

K and M correlation coefficient = +0.2

L and M correlation coefficient = -0.4

Given these correlations, a portfolio constructed of which pair of stocks will have the lowest standard deviation? Explain.

Problems 1. Considering the world economic outlook for the coming year and estimates of sales and earnings for the pharmaceutical industry, you expect the rate of return for Lauren Labs common stock to range between -20 percent and +40 percent with the following probabilities:

Probability 