# 2011 sample exam q6

#### the_tank

##### New Member
I am not sure if anyone had the same question before. I cannot find the formula in the answer. It's regarding calculating covariance of two market using factor beta in different markets and covariance of the factors. It's not in chapter 16 of madden portfolio theory and investment analysis..

#### the_tank

##### New Member
Don't have access but thanks anyway

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
from source question forum:
It uses property of covariance, see http://en.wikipedia.org/wiki/Covariance

R(A) = 0.75*E + 0.20*Bond
R(B) = 0.45*E + 0.65*Bond

Cov[R(A),R(A)] = Cov [0.75*E + 0.20*Bond, 0.45*E + 0.65*Bond] = 0.75*0.45*Cov(E,E) + 0.20*0.65*Cov(Bond,Bond) + 0.20*0.45*Cov(E,Bond) + 0.65*0.75*Cov(Bond,E)

= 0.75*0.45*variance(E) + 0.20*0.65*variance(Bond)+ (0.75*0.65)*Cov(E,Bond) + Cov(Bond,E)*[0.20*0.45 + 0.65*0.75]

Thanks, David

#### the_tank

##### New Member
I got it. I guess I wouldn't be able to figure out R(A)=0.75E + 0.2Bond. The factor beta(equity and bond payoff) seems obtained from univariate regression from the question. But this is definitely what GARP try to test. Many thanks.