This is an exam question. I know that to find beta I need the covariance between the portfolio and asset A but don't know how to find it.

The Question


Investor I: market portfolio is consisting of 75% of asset A and 25% of asset B, i.p $r_m=3/4r_a+1/4r_b$ $\Rightarrow $ cov($r_a,r_m$)$=$cov($r_a,3/4r_a+1/4r_b$)=$3/4V(r_a)$.

Investor J: market portfolio is consisting of 50% of asset A and 50% of asset B, i.p $r_m=1/2r_a+1/2r_b$ $\Rightarrow $ cov($r_a,r_m$)$=$cov($r_a,1/2r_a+1/2r_b$)=$1/2V(r_a)$.

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  • $\begingroup$ Isn't it: $Cov(r_a,3/4r_a+1/4r_b)=3/4V(r_a)+1/4Cov(r_a,r_b)$ ? $\endgroup$ – Alex C Apr 21 '18 at 20:19
  • $\begingroup$ yeah but cov is 0 in the example $\endgroup$ – Andrew Apr 21 '18 at 21:27

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