Hi, I'm struggling to get the same answer to part (ii) April 2013 Q4. I've used formula Var(rm) = E(rm^2)-[E(rm)]^2 For E(rm^2) I've calculated it using following method: E(rm^2) = Xa*Ea^2 + Xb*Eb^2 + Xc*Ec^2 + Xd*Ed^2 Where Xa = 10/100 Xb= 20/100 Xc= 40/100 Xd= 30/100 and Ea^2 = =3^2*(0.25) + 5^2*(0.5) +7^2*(0.25) Eb^2 = =3^2*(0.25) + 7^2*(0.5) +5^2*(0.25) Ec^2 = =3^2*(0.25) + 2^2*(0.5) +8^2*(0.25) Ed^2 = =3^2*(0.25) + 8^2*(0.5) +1^2*(0.25) My method is incorrect just would like to know why I can't do it this way. Thanks, Darragh
Hi rm is a random variable given by: rm = Xa*ra + Xb*rb + Xc*rc + Xd*rd but each of those separate returns (ra, rb, rc and rd) is also a random variable. Finding E[rm] is easy enough because of the linear nature of the expectation operator: E[rm] = Xa*E[ra] + Xb*E[rb] + Xc*E[rc] + Xd*E[rd] However, finding E[rm^2] from the underlying definition will require more terms than you've suggested: E[rm^2] = E[(Xa*ra + Xb*rb + Xc*rc + Xd*rd)^2] Hope you can see that it's easier to work with the return on the market under each of the four states.
