Mini-Case: Portfolio Theory

Chapter 5

Risk and Return: Portfolio Theory and Asset Pricing Models

MNI CASE

To begin, briefly review the Chapter 4 Mini Case. Then, extend your knowledge of risk and return by answering the following questions.

a. Suppose asset A has an expected return of 10 percent and a standard deviation of 20 percent. Asset B has an expected return of 16 percent and a standard deviation of 40 percent. If the correlation between A and B is 0.4, what are the expected return and standard deviation for a portfolio comprised of 30 percent asset A and 70 percent asset B?

Answer:

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b. Plot the attainable portfolios for a correlation of 0.4. Now plot the attainable portfolios for correlations of +1.0 and -1.0.

Answer:

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c. Suppose a risk-free asset has an expected return of 5 percent. By definition, its standard deviation is zero, and its correlation with any other asset is also zero. Using only asset A and the risk-free asset, plot the attainable portfolios.

Answer:

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d. Construct a reasonable, but hypothetical, graph which shows risk, as measured by portfolio standard deviation, on the x axis and expected rate of return on the y axis. Now add an illustrative feasible (or attainable) set of portfolios, and show what portion of the feasible set is efficient. What makes a particular portfolio efficient? Don't worry about specific values when constructing the graph—merely illustrate how things look with "reasonable" data.

Answer:

The figure above shows the feasible set of portfolios. The points B, C, D, and E represent single securities (or portfolios containing only one security). All the other points in the shaded area, including its boundaries, represent portfolios of two or more securities. The shaded area is called the feasible, or attainable, set.

The boundary AB defines the efficient set of portfolios, which is also called the efficient frontier. Portfolios to the...