# How to find beta from the information given? [closed]

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.

## 1 Answer

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($r_a,1/2r_a+1/2r_b$)=$1/2V(r_a)$.

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