A money manager is holding the following portfolio: Stock Amount Invested Beta 1

Question

A money manager is holding the following portfolio:

Stock     Amount Invested            Beta

1            $300,000                           0.6

2            $300,000                           1.0

3            $500,000                           1.4

4            $500,000                           1.8

The risk free rate is 6 percent and the portfolio%u2019s required rate of return is 12.5 percent. The manager would like to sell all of her holdings of Stock 1 and use the proceeds to purchase more shares of Stock 4. What would be the portfolio%u2019s required rate of return following this change? PLEASE SHOW ALL WORK THANKS!!!!

Explanation / Answer

Total portfolio value = $1,600,000. Avg beta for portfolio = 0.6*300,000/1,600,000 + 1.0*300,000/1,600,000 + 1.4*500,000/1,600,000 + 1.8*500,000/1,600,000 = 1.3. So portfolio return = risk free rate + beta * risk premium = 6% +1.3*premium = 12.5%, which means market premium=5%. After moving money from stock 1 to stock 4, avg beta for portfolio = 1.0*300,000/1,600,000 + 1.4*500,000/1,600,000 + 1.8*800,000/1,600,000 = 1.525. So portfolio return = 6%+1.525*5% = 13.625%. Hope this helped. Let me know in case of queries.

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