Question

Portfolio Beta and Required Return You hold the positions in the table below. A) What is the beta of your portfolio? B) If you expect the market to earn 14 percent and the risk-free rate is 3.0 percent, what is the required return of the portfolio?

Company                             Price                                      Shares                                   Beta

Texas, Inc.                           $30.00                                  200                                        2.8

Dollar Earned Stores       $20.00                                  600                                        2.2

Atomic, Inc.                        $70.00                                  400                                        1.4

Big Truck Corp                   $40.00                                  100                                        -0.6

This problem can be solved two different and equivalent ways. Both ways require the weights of the stocks in the portfolio. In one method, compute the required return for each stock and then use the weights to form the portfolio required return.

The other method uses the weights to compute the portfolio beta. This portfolio beta is used to compute the portfolio required return.

Answer 1

Total Value of a stock is calculated using the formula:

The total value of a stock = Price * Shares

Therefore, Total value of Texas Inc. = 30*200 = 6000

Similarly, Total value of other stocks are mentioned in the below table

Company	Price	Share	Value = Price*Share
Texas	30	200	6000
Dollar Earned Stores	20	600	12000
Atomic	70	400	28000
Big Truck Corp	40	100	4000

We need to calculate the weights of different company stocks in the portfolio

Total Value of the portfolio = 6000+12000+28000+4000 = 50000

Weight of Texas = W_T = Value of Texas/Total Value of Portfolio = 6000/50000 = 12%

Similarly, We can calculate the weights of other company's stocks in the portfolio and it is mentioned below in the table:

Company	Price	Share	Value = Price*Share	Weights
Texas	30	200	6000	12%
Dollar Earned Stores	20	600	12000	24%
Atomic	70	400	28000	56%
Big Truck Corp	40	100	4000	8%
		Total	50000

W_T = 12%, W_D = 24%, W_A = 56%, W_B = 8%

Beta of the Stocks are also given:

β_T = 2.8, β_D = 2.2, β_A = 1.4, β_B = -0.6

Note: We are using the second method (mentioned in the problem) to solve this problem

Beta of the portfolio can be calculated using the formula:

β_P = W_T*β_T + W_D*β_D +W_A*β_A +W_B*β_B = (12%*2.8) + (24%*2.2) + (56%*1.4) + (8%*(-0.6)) = 1.6

Required Rate on the portfolio can be calculated using CAPM Equation

R_P = R_F + β_P *(R_M - R_F)

Expected market return = R_M = 14%, Risk-free Rate = R_F = 3%

Therefore, R_P = 3%+1.6*(14%-3%) = 20.6%

Answer

Beta of the portfolio = 1.6

Portfolio return = 20.6%