Assume that the market index portfolio (RM) consists only of the following three stocks (stocks A, B and C). The data below shows the capitalization of each stock (the market value of outstanding shares), their average excess returns (or risk premium) E(Ri) and their standard deviation. Assume that all stocks satisfy the assumptions of the Single Index Model (as we discussed in class and as in the lecture notes). You also know that the standard deviation of the market index portfolio is σM = 25%. (Note: the capitalization of the market index is the total sum of capitalization of the three stocks. The index is build proportionally, i.e., each stock’s weight in the portfolio is proportional to its capitalization relative to the caputalization of the market portflio(index)).
Capitalization Beta Average Excess Standard
Returns Deviation
Stock A 3,000 1.0 10% 40%
Stock B 1,940 0.2 2% 30%
Stock C 1,360 1.7 17% 50%
a) What is the mean excess return of the index (market) portfolio (E(RM))?
b) Based on the SIM model, what is the covariance between Stock A and Stock B?
c) Based on the SIM model, what is the covariance between Stock B and the market index?
d) Break down the variance of Stock B into systematic and firm-specific components.