Okay.
Method 1:
a * .12 + (1-A)*.16 = .20
A = -1
r(combined) = -1*r(1) + 2*r2 = .2
= -1 * (rf + ß1*MRP) + 2 * (rf + ß2*MRP)
= rf + MRP*( -ß1 + 2ß2)
(rcombined – rf)/MRP = ßcombined = 2 ß2 – ß1 = 1.7
This results in a beta that is lower than Portfolio 3, and is correct.
Method 2, however, results in the two betas being the same which is wrong:
r(combined) = r(3) (as it says in the problem)
[r(combined) - r(f)]/MRP = [r(3) - r(f)] / MRP
which means
ß(combined) = ß(3) which is not the case.
This in fact would suggest that any two portfolios with the same expected rate of return have the same ß which is not the case. I hope you can tell me why this method is wrong so that I can correct any misunderstanding.
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