The CCD portfolio has rates of return of 3.3333%, 4.00%, 4.6667%, and 4.00% in the four states. Demeaned, this is −0.6667%, 0%, 0.6667%, and 0%. Therefore, the variance of CCD is [(−0.6667%)2 +

(0%)2 + (0.6667%)2 + (0%)2]/4 ≈ 0.224%%, and its standard deviation is 0.47%. The de-meaned rates of return on M are −5%, −2%, 0, and 7%. The cross-products of the de-meaned CCD rates of return with the de-meaned M rates of return are therefore 3.3333%%, 0, 0, and 0. Therefore, the covariance of CCD and M is (3.3333%% + 0 . 3)/4 ≈ 0.8333%%. The variance of the market is 19.5%%. Therefore, the market beta of CCD is 0.833/19.5 ≈ 0.0427. This was the first method. Now the second method:

βCCD

= wC . βC

+ wD . βD

≈ 2/3 . (+1.128) + 1/3 . (−2.128) ≈ 0.0427.