# 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.

## closed as off-topic by Helin, Bob Jansen♦Apr 21 '18 at 20:00

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• "Basic financial questions are off-topic as they are assumed to be common knowledge for those studying or working in the field of quantitative finance." – Helin, Bob Jansen
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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