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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?




CAPM of Changed Portfoliosantosh 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 Betaabdollah 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
B1+b2+..+b19=21.1
Now the new portfolio beta is: 1/20* 21.1+1/20*1.4=1.125. 


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