1.Consider the following stocks, all of which will pay a liquidating dividend in a year and nothing in the interim:
a. Calculate the expected return of each stock.
b. What is the sign of correlation between the expected return and market capitalization of the stocks?
2.In Problem 1, assume the risk-free rate is 3% and the market risk premium is 7%.
a. What does the CAPM predict the expected return for each stock should be?
b. Clearly, the CAPM predictions are not equal to the actual expected returns so the CAPM does not hold. You decide to investigate this further. To see what kind of mistakes the CAPM is making, you decide to regress the actual expected return onto the expected return predicted by the CAPM. What is the intercept and slope coefficient of this regression?
c. What are the residuals of the regression in (d)? That is, for each stock compute the difference between the actual expected return and the best fitting line given by the intercept and slope coefficient in (b).
d. What is the sign of the correlation between the residuals you calculated in (e) and market capitalization?
e. What can you conclude from your answers to part (b) of the previous problem and part (d) of this problem about the relation between firm size (market capitalization) and returns? (The results do not depend on the particular numbers in this problem. You are welcome to verify this for yourself by redoing the problems with another value for the market risk premium, and by picking the stock betas and market capitalizations randomly.)
3.Explain how to construct a positive-alpha trading strategy if stocks that have had relatively high returns in the past tend to have positive alphas and stocks that have had relatively low returns in the past tend to have negative alphas.
4.If you can use past returns to construct a trading strategy that makes money (has a positive alpha), it is evidence that market portfolio is not efficient. Explain why.