You hold a diversified portfolio of a $10,000 investment in each of the differen

Question

You hold a diversified portfolio of a $10,000 investment in each of the different common stocks (I.e, your total investment is$150,000). The portfolio beta is equal to 1.0, you have decided to sell one of your stocks which has a beta equal to 1.8 for $10,000. You plan to use the proceeds to purchase another stock which has a beta equal to 0.7. What will be the beta of the new portfolio? Show your answer to 2 decimal places You hold a diversified portfolio of a $10,000 investment in each of the different common stocks (I.e, your total investment is$150,000). The portfolio beta is equal to 1.0, you have decided to sell one of your stocks which has a beta equal to 1.8 for $10,000. You plan to use the proceeds to purchase another stock which has a beta equal to 0.7. What will be the beta of the new portfolio? Show your answer to 2 decimal places

Explanation / Answer

No of stocks = 15, with each stock value = $10,000
Total investment = $150,000

Portfolio beta = weighted average of the individual betas.

Let the average beta of 14 stocks be x

then, 1 = 10000/150000 * 1.8 + 140000/150000 * x

1 = 1.8/15 + 14x/15

1.8 + 14x = 15
x = 13.2/14 = 0.9428

Portfolio beta including the new stock = 10000 * 0.7/150000 + 140000 * 0.9428 /150000

= (7000 + 132000)/150000 = 139000/150000 = 139/150 = 0.9267 ~ 0.93

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