Let's check that the beta combination formula is correct. Let me lead you along:
(a) Write down a table with the rate of return on the market and on portfolio CDD in each of the four possible states. (Hint: In scenario S1 [♣], the rate of return on CDD is 8.67%.) Then forget about C and D altogether. (In this question, you will work only with the market and CDD.)
(b) Compute the average rate of return on the market and on CDD.
(c) Write down a table with the de-meaned market rate of return and CDD rate of return in each of the four possible states. (The mean of the de-meaned returns must be zero.)
(d) Multiply the de-meaned rates of return in each scenario. This gives you four cross-products, each having units of %%. (Hint: In scenario S1 [♣], it is about -28.35%%.)
(e) Compute the average of these cross-products. This is the covariance between CDD and M.
(f) Divide the covariance between CDD and M by the variance of the market. Is it equal to the -1.04 from Formula 8.6?
(g) Which is faster-this route or Formula 8.6?
