Question

A money manager is holding the following portfolio:

            Stock       Amount Invested        Beta

            1             $400,000           1.00

            2             600,000           0.85

            3             300,000           1.20

            4             500,000           0.50

            5             200,000           1.70

      The risk-free rate is 7 percent and the portfolio’s required rate of return is 13.975 percent. The manager would like to sell all of her holdings of Stock 4 and use half the proceeds to purchase more shares of Stock 5, and the other half of the proceeds to purchase more shares of Stock 3. (6 points)

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

a.
Current portfolio beta
Portfolio Beta	Weight of stock 1*Beta of stock 1 + Weight of stock 2*Beta of stock 2 + Weight of stock 3*Beta of stock 3 + Weight of stock 4*Beta of stock 4 + Weight of stock 5*Beta of stock 5
Calculation of weight for each stock
Stock	Amount invested	Weight
1	$400,000	0.20	400000/2000000
2	$600,000	0.30	600000/2000000
3	$300,000	0.15	300000/2000000
4	$500,000	0.25	500000/2000000
5	$200,000	0.10	200000/2000000
	$2,000,000
Portfolio Beta	(0.20*1)+(0.30*0.85)+(0.15*1.20)+(0.25*0.50)+(0.10*1.70)
Portfolio Beta	0.93
Calculation of new weight for each stock and new portfolio beta
Stock	Amount invested	Weight
1	$400,000	0.20	400000/2000000
2	$600,000	0.30	600000/2000000
3	$550,000	0.28	550000/2000000
5	$450,000	0.23	450000/2000000
	$2,000,000
The amount invested in stock 3 and 5 would increase by $250,000 (500,000/2)
New portfolio beta	(0.20*1)+(0.30*0.85)+(0.28*1.20)+(0.23*1.70)
New portfolio beta	1.18
The existing portfolio's required rate of return is 13.975% from this we can calculate the market risk premium using CAPM model and then calculate new required rate of return
Required rate of return = Risk free rate + Beta*(Market risk premium)
0.13975 = 0.07+(0.93*Market risk premium)
Market risk premium	(0.13975-0.07)/0.93
Market risk premium	7.50%
Calculation of required rate of return
Required rate of return = 0.07 + (1.18*0.075)
Required rate of return	15.87%
The required rate of return following the change would be 15.87%