Question

You own a portfolio that has a total value of 235000 and it is invested in stock D with the Beta of .82 and stock E with a Beta of 1.43.the Beta of your portfolio equal to the market beta.what is the dollar amount of your investment in stock D

Answer 1

Solution:

Calculation of Portfolio Beta:

The formula for calculating the Portfolio Beta is

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

where

β_P = Portfolio Beta

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

W_E = Weight of Investment in Stock E ;       β_E = Beta of Stock E ;

As per the information given in the question we have

β_P = Portfolio Beta = Market Beta = 1 ;

Β_D = Beta of Stock D = 0.82    ; Β_E = Beta of Stock E = 1.43    ;

Let the Weight of Investment in Stock D = W_D = “ x “

Let the Weight of Investment in Stock E = W_E = “ 1 - x “

Applying the above vales in the formula we have

1 = ( x * 0.82 )   + ( ( 1 - x ) * 1.43 )

1 = ( 0.82x ) + ( 1.43 – 1.43x )

1 = 0.82x + 1.43 – 1.43x

1 = - 0.61x + 1.43

0.61x = 1.43 – 1

0.61x = 0.43

x = 0.43 / 0.61

x = 0.704918

x = 70.4918 %

Thus the Weight of investment in stock D = 70.4918 %

Calculation of dollar amount of investment in Stock D :

Total value of Investment in portfolio consisting of Stock D & Stock E = 235,000

Weight of investment in stock D = 70.4918 %

Thus the dollar amount of investment in Stock D = Total value of Investment in portfolio * Weight of investment in stock D

= $ 235,000 * 70.4918 %

= $ 165,655.7377

= $ 165,655.74 ( When rounded off to two decimal places )

= $ 165,656 ( when rounded off to the nearest dollar )

Thus the dollar amount of investment in Stock D = $ 165,656