Question

Suppose that a portfolio consists of the following stocks:

Stock		Amount		Beta
Chevron		$25,000		0.65
General Electric		50,000		1.30
Whirlpool		25,000		1.55

The risk-free rate (rf) is 5 percent and the market risk premium (rm-rf) is 7.2 percent.

1. Determine the beta for the portfolio. Round your answer to two decimal places.
2. Determine how much General Electric stock one must sell and reinvest in Chevron stock in order to reduce the beta of the portfolio to 1.00. Do not round intermediate calculations. Round your answer to the nearest dollar.

3. Determine the expected return on the portfolio in parts a and b. Do not round intermediate calculations. Round your answers to two decimal places.

   Expected Return (Original portfolio):  

   Expected Return (Revised portfolio):

Answer 1

Answer a

The beta of a portfolio is the weighted average beta of the securities which constitute the porfolio

Stock	Amount	Weight	Beta	Weight*Beta
Chevron	25,000	0.25	0.65	0.16
General Electric	50,000	0.50	1.30	0.65
Whirlpool	25,000	0.25	1.55	0.39

Portfolio Beta =Weight*Beta

= .16+.65+.39

= 1.20

Answer b

Let X be the weight of Chevron.

Stock	Amount	Weight	Beta	Weight*Beta
Chevron	25,000	X	0.65	.65x
General Electric	50,000	0.50	1.30	0.65
Whirlpool	25,000	.5-X	1.55	(.5-x)*1.55

Portfolio Beta =Weight*Beta

1 = .65x+.65+.775-1.55x

= -.9x+1.425

.9x = 1.425-1

= .425

X = .425/.9

= .472222222

Revised investment in Chevron = Total investment*weight

= 100000*.472222

= 47,222.22

General Electric stock sold = 47222.22-250000

= 22,222.22

​​​​​​​Answer c

Using Capital Asset Pricing Model

Expected Rate of Return = Rf + b ( Rm – Rf )

Where,

Rf – Risk free return = 5%

b – Beta

Rm – Expected return on market portfolio

Rm-Rf – Market risk premium = 7.2%

Expected Return (Original portfolio) = 5+1.2*7.2

= 5+8.64

= 13.64%

Expected Return (Revised portfolio) = 5*1*7.2

= 5+7.2

= ​​​​​​​12.20%