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

Question

A money manager is holding the following portfolio : Stock Amount Invested Beta 1 $300,000 0.6 2 $300,000 1 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?   SHOW ALL WORK!! A money manager is holding the following portfolio : Stock Amount Invested Beta 1 $300,000 0.6 2 $300,000 1 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?   SHOW ALL WORK!! Stock Amount Invested Beta 1 $300,000 0.6 2 $300,000 1 3 $500,000 1.4 4 $500,000 1.8

Explanation / Answer

Hi,

Please find the answer as follows:

Current Scenario:

Portfolio Beta = 1.3

Required Rate of Return = Rf + B*(Rm - Rf)

12.5 = 6 + 1.3*(Rm - 6)

Rm = (12.5 - 6 + 7.8)/1.3 = 11%

Revised Scenario

Portfolio Beta = 1.525

Required Rate of Return (Changed) = Rf + B*(Rm - Rf)

Required Rate of Return (Changed) = 6 + 1.525*(11 - 6) = 13.625%

Answer is 13.625 or 13.63%

Thanks,

Stock Amount Invested Weight Beta Weight*Beta
1 3,00,000 0.1875 0.6 0.1125 2 3,00,000 0.1875 1 0.1875 3 5,00,000 0.3125 1.4 0.4375 4 5,00,000 0.3125 1.8 0.5625 Total 16,00,000 1
1.3

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