Question

Suppose that a portfolio consists of the following stocks: Stock Amount Beta Chevron $20,000 0.55 General Electric 55,000 1.40 Whirlpool 25,000 1.20 The risk-free rate ( ) is 6 percent and the market risk premium ( ) is 8.4 percent.

Determine the beta for the portfolio. Round your answer to two decimal places.

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. $

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 :

(i) Calculation of Beta of Portfolio :

Total Investment = 20000 + 55000 + 25000 = 100,000

Weight of Cheron = 20000 / 100000 = 0.20

Weight of General Electric = 55000 / 100000 = 0.55

Weight of Whirlpool = 25000 / 100000 = 0.25

Beta of Portfolio = Sum of (Beta * Weights)

= [0.55 * 0.20] + [1.4 * 0.55] + [1.2 * 0.25]

= 0.11 + 0.77 + 0.3

= 1.18

(ii) Determination of Amount to reduce the portfolio beta to 1

Let x be the amount sold from general electric and reinvested in Chevron

Total Investment will be 100000 only

Weight of Cheron = [(20000 + x) / 100000 ]

Weight of General Electric = [(55000 - x) / 100000 ]

Weight of Whirlpool = 25000 / 100000 = 0.25

Beta of Portfolio = Sum of (Beta * Weights)

1 = {0.55 * [(20000 + x) / 100000 ]} + {1.4  * [(55000 - x) / 100000 ]} + [1.2 * 0.25]

1 = {(11000 + 0.55x) / 100000} + {[77000 - 1.4x] /100000]  + 0.3

1 - 0.3 = 0.11 + 0.0000055x + 0.77 - 0.000014x

0.7 - 0.11 - 0.77 = -0.0000085x

-0.18 = - 0.0000085x

==x = (-0.18) / (-0.0000085)

= $21176.47 or $211,76

(iii) Original Expected Return of Portfolio(for part a.) = Risk free rate + (Beta * Market Risk Premium)

= 6% + (1.18 * 8.4%)

= 15.912% or 15.91%

Revised Expected Return of Portfolio(for part b.) = Risk free rate + (Beta * Market Risk Premium)

= 6% + (1 * 8.4%)

= 14.4%