Question

.  A money manager is holding the following portfolio:

            Stock       Amount Invested        Beta

              1             $400,000            0.5

              2             400,000            0.8

              3             600,000            1.2

              4             600,000            1.6

   The risk-free rate is 5 percent and the portfolio’s required rate of return is 11.6 percent.  The manager would like to sell all of her holdings of Stock 2 and use the proceeds to purchase more shares of Stock 3.

1. What is the beta of the current portfolio?
2. What is the beta of the new portfolio?
3. What would be the portfolio’s required rate of return following this change?

Answer 1

Beta of Portfolio = Weighted Avg beta of Securities in portfolio

Stock	Investment	Weight	Beta	Portfolio Beta
1	$ 4,00,000.00	0.2	0.5	0.1
2	$ 4,00,000.00	0.2	0.8	0.16
3	$ 6,00,000.00	0.3	1.2	0.36
4	$ 6,00,000.00	0.3	1.6	0.48
Portfolio Beta				1.1

Required ret = Rf + Beta ( Risk Premium)

11.6% = 5% + 1.1 (Risk Premium)

1.1 Risk Premium = 11.6% - 5 %

= 6.6%

Risk Premium = 6.6% / 1.1

= 6%

Beta of New portfolio:

Stock	Investment	Weight	Beta	Portfolio Beta
1	$   4,00,000.00	0.2	0.5	0.1
2	$                     -	0	0.8	0
3	$ 10,00,000.00	0.5	1.2	0.6
4	$   6,00,000.00	0.3	1.6	0.48
Portfolio Beta				1.18

New Required Ret

= Rf + Beta ( Risk Premium )

= 5% + 1.18 ( 6%)

= 5% + 7.08%

= 12.08%