You have been hired at the investment firm of BETA FIRM. One of its clients does not understand the value of diversification or why stocks with the biggest standard deviation of returns do not always have the highest expected returns. Your assignment is to address the client’s concerns by showing the client how to answer the following questions.

a. Suppose Asset A has an expected return of 10 percent and a standard deviation of returns of 20 percent. Asset B has an expected return of 16 percent and a standard deviation of returns of 40 percent. If the correlation of returns between Asset A and Asset B is 0.35, what are the expected return and standard deviation for a portfolio comprised of 30 percent Asset A and 70 percent Asset B?

b. Create a table and find the expected return and standard deviation of a portfolio with different percentage (weights) invested in each asset. Vary the percentages at the interval of 10%.

c. Plot the attainable portfolios for a correlation of 0.35. Now plot the attainable portfolios for correlations of +1.0 and -1.0.

d. 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.

e. Construct a reasonable, but hypothetical, graph that 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? Do not worry about specific values when constructing the graph-merely illustrate how things look with "reasonable" data.

f. Now add a set of indifference curves to the graph created for part b. What do these curves represent? What is the optimal portfolio for this investor? Finally, add a second set of indifference curves which leads to the selection of a different optimal portfolio. Why do the two investors choose different portfolios?

g. Now add the risk-free asset. What impact does this have on the efficient frontier?

h. Write out the equation for the Capital Market Line (CML) and draw it on the graph. Interpret the CML. Now add a set of indifference curves and illustrate how an investor's optimal portfolio is some combination of the risky portfolio and the risk-free asset. What is the composition of the risky portfolio?

i. What is the Capital Asset Pricing Model (CAPM)? What are the assumptions that underlie the model? What is the Security Market Line?

j. What is a characteristic line? How is this line used to estimate a stock's beta coefficient? Write out and explain the formula that relates total risk, market risk, and diversifiable risk.

k. What are two potential tests that can be conducted to verify the CAPM? What are the results of such tests? What is Roll's critique of CAPM tests?

l. Briefly explain the difference between the CAPM and the Arbitrage Pricing Theory (APT).

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a If a portfolio is comprised of 30 Asset A and 70 Asset B the expected return of the portfolio is 134 and the standard deviation of the portfolio is 338 This can be calculated using the following equ... View the full answer