Calculating Beta of Portfolio after Portfolio Change

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Calculating Beta of Portfolio after Portfolio Change
Charles Raphael, Member
Please help me to solve this question:
You have $2 million portfolio consisting of a $100,000 investment in each of 20 different stock. The portfolio has a beta equal to 1.1. You are considering selling $100,000 worth of one stock which has a beta equal to 0.9 and using the proceeds buy another stock which has beta equal to 1.4. What will be the new beta of your portfolio following this transaction?

I Would Calculate the Weighted Average Beta of the Portfolio
I calculate the weighted average and obtain a new beta of 1.1250.

CAPM of Changed Portfolio
Please calculate the weighted beta of remaining 19 stocks using 19/20 as their weight and 1/20 as the weight of stock to be removed.
Use as equation: 19/20*b +1/20*0.9 = 1.1. Determine the value of b which is the weighted beta of 19 stocks.
Then again calculate the weighted beta of 20 stocks portfolio as 19/20*b +1/20*1.4.

Portfolio Beta
The beta of your portfolio is: (100'000/2'000'000)*b1+(1/20)b2+...+(1/20) 0.9=1.1
So 1.1=1/20*(b1+b2...+b19)+1/20*.09
Now the new portfolio beta is: 1/20* 21.1+1/20*1.4=1.125.


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