a. Suppose Asset A has an expected return of 10% and a standard deviation of 20%. Asset B has an expected return of 16% and a standard deviation of 40%. If the correlation between A and B is 0.35, what are the expected return and standard deviation for a portfolio consisting of 30% Asset A and 70% Asset B?
b. Plot the attainable portfolios for a correlation of 0.35. Now plot the attainable portfolios for correlations of +1.0 and -1.0.
c. Suppose a risk-free asset has an expected return of 5%. 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.
d. Construct a plausible 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? Don't worry about specific values when constructing the graph - merely illustrate how things look with "reasonable" data.
e. 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? Add a second set of indifference curves that leads to the selection of a different optimal portfolio. Why do the two investors choose different portfolios?
f. What is the Capital Asset Pricing Model (CAPM)? What are the assumptions that underlie the model?
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 plotted 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 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.
j. 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?
k. Briefly explain the difference between the CAPM and the Arbitrage Pricing Theory (APT).
l. Suppose you are given the following information. The beta of a company, bi, is 0.9; the risk-free rate, rRF, is 6.8%; and the expected market premium, rm-rRF, is 6.3%. Because your company is larger than average and more successful than average (that is, it has a lower book-to-market ratio), you think the Fama-French three-factor model might be more appropriate than the CAPM. You estimate the additional coefficients from the Fama-French three-factor model: 'The coefficient for the size effect, ci, is -0.5, and the coefficient for the book-to-market effect, di, is -0.3. If the expected value of the size factor is 4% and the expected value of the book-to-market factor is 5%, then what is the required return using the Fama-French three-factor model? (Assume that ai = 0.0.) What is the required return using CAPM?