QUESTION
Suppose you hold a diversified portfolio consisting of a $7,500 investment in each of 20 different common stocks. The portfolios beta is 0.65. Now, suppose you sell one of the stocks with a beta of 1.0 for $7,500 and use the proceeds to buy another stock whose beta is 1.35. Calculate your portf
Solution: Portfolio beta = w1b1 + w2b2 + . + w19b19 + w20b20 Since investment in each stock = $7500, Weights of each stock in a portfolio is same = 1/20 Hence, 1.12 = 1/20 ( b1 + b2 + + b19 + b20) 22.4 = b1 + b2 + . + b19 + 1 So, b1 +
2 + .+ b19 = 21.4 Now, Beta of new stock added = b20 = 1.75 New portfolios beta = 1/20 * (21.4 + 1.75) = 1/20 * 23.15 = 1.1575 Portfolios new beta = 1.1575
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