Question

You own a portfolio that has a total value of $245,000 and it is invested in Stock D with a beta of .80 and Stock E with a beta of 1.45. The beta of your portfolio is equal to the market beta. What is the dollar amount of your investment in Stock D?

Answer 1

Solution:

As per the information given in the question we have

Beat of Stock D = 0.80

Beat of Stock E = 1.45

To find the portfolio weights so that the Beta of the total portfolio = Beta of the market

We know that Beta of the market = 1

Thus let the total weight of the portfolio = 1

Let " x " be the weight of Stock D and (1 - x ) be the weight of Stock E

We know that beta of a portfolio can be calculated using the formula :

β_P = ( β_D * W_D ) + ( β_E * W_E )

where

β_D = Beta of Stock D   ;     W_D = Weight of Stock D

β_E = Beta of Stock e    ;     W_E = Weight of Stock E

As per the information given we have

β_D = 0.80    ;       W_D = X   ;   β_E = 1.45       ;     W_E = ( 1 –X )

Applying the above values in the formula we have :

( 0.80 * x) + ( 1.45 * ( 1 - x) ) = 1

0.80 x + 1.45 - 1.45 x = 1

- 0.65 x = - 0.45

x = ( - 0.45 / - 0.65 ) = 0.692308

Thus weight of Stock D = x = 0.692308

Weight of Stock E = ( 1 - x ) = ( 1 - 0.6923 ) = 0.307692

We know that the total dollar value of the portfolio = $ 245,000

Thus the Dollar value of Investment in Stock D = $ 245,000 * 0.692308

= $ 169,615.38

= $ 169,615 ( When rounded off to the nearest whole number )

Thus the Dollar value of Investment in Stock E = $ 245,000 * 0.307692

= $ 75,384.62

= $ 75,385 ( When rounded off to the nearest whole number )

Thus the Dollar amount of Investment in Stock D = $ 169,615

Thus the Dollar amount of Investment in Stock E = $ 75,385