Question

You own a portfolio that has a total value of $175,000 and it is invested in Stock D with a beta of .89 and Stock E with a beta of 1.31. The beta of your portfolio is equal to the market beta. What is the dollar amount of your investment in Stock D?

Choices:

$40,104.17

$22,917.11

$34,375.22

$129,166.67

$45,833.33

Answer 1

Solution:

As per the information given in the question we have

Beta of stock D = 0.89     ;      Beta of Stock E = 1.31

Given that the Beta of the portfolio is equal to the market Beta = 1

Total value of investment in Portfolio = $ 175,000

To find dollar value of investment in Stock D

Let Proportion or weight of investment in Stock D be “ x “

Thus Proportion or weight of Investment in Stock E be “ 1 – x “

The formula for calculating the beta of the Portfolio is

β_P = [ ( W_D * β_D ) + ( W_E * β_E )]

where

β_P = Beta of the Portfolio = Market Beta = 1

WD = Proportion or Weight of Investment in Stock D = “ x “ ;     

β_D = Beta of the Stock D = 0.89    ;

W_E = Proportion or Weight of Investment in Stock E = “ 1 – x “ ;      

β_E = Beta of the Stock E = 1.31    ;

Applying the above values in the formula for calculating the beta of the portfolio we have

[ x * 0.89 ] + [ ( 1 – x) * 1.31 ] = 1

0.89x + 1.31 – 1.31 x = 1

0.89x – 1.31x = 1 – 1.31

- 0.42x = - 0.31

x = - 0.31 / - 0.42

x = 0.73809524

Thus proportion or weight of Investment in Stock D = 0.73809524 = 73.809524 %

Subsequently, we have the weight of investment in Stock E

= 1 – 0.73809524

= 0.26190476 = 26.190476 %

We know that the total value of the portfolio = $ 175,000

Proportion of investment in Stock D = 0.73809524 = 73.809524 %

Thus the Dollar amount of investment in Stock D is = Total value of portfolio * Proportion of investment in Stock D

= $ 175,000 * 73.809524 %

= $ 129,166.667

= $ 129,166.67 ( when rounded off to two decimal places )

The solution is Option 4 = $ 129,166.67