Question

Your grandfather gives your $10,000 to invest and you must invest every penny. He wants you to have an expected return of 12.40% for your portfolio. You can chose between stock J with an expected return of 13% and stock L with an expected return of 8%.

How much should you invest in stock J to achieve these results?

Answer 1

Solution:

The formula for calculation of Expected Return of a portfolio is

E(R_P) = ( R_J * W_J ) + ( R_L * W_L )

Where

E(R_P) = Expected return on a portfolio

R_J = Return of Stock J   ;   W_J = Weight of Stock J ;

R_L = Return of Stock L  ; W_L = Weight of Stock L ;

As per the information given in the question we have

R_J = 13 %  = 0.13 ; R_L = 8 % = 0.08   ;    E(R_P) = 12.40 % = 0.1240 ;

Let the weight of Stock J be “ x “ . Thus W_J = x    ;   

Let the weight of Stock L be ( 1 – x) . Thus W_L = ( 1 – x )   ;

Applying the values in the formula for expected return on a portfolio we have

0.1240 = ( 0.13 * x ) + ( 0.08 * ( 1 – x ) )

0.1240 = 0.13x + 0.08 – 0.08x

0.1240 – 0.08 = 0.13x – 0.08x

0.0440 = 0.05x

0.05x = 0.0440

x = 0.0440 / 0.05

x = 0.88

x = 88 %

Thus the weight of Stock J i.e., proportion of Investment in Stock J = 88 %

We know that the total amount to be invested in the portfolio = $ 10,000

Thus the amount to be invested in the portfolio = Total amount to be invested in the portfolio * Weight of Stock J

= $ 10,000 * 88 %

= $ 8,800

The amount to be invested in stock J is $ 8,800 to achieve an expected portfolio return of 12.40 %.