Question

Your investment portfolio has 10,000 shares of Fairfax Paint, which has an expected return of 10.56 percent and a price of 6.8 dollars per share, and 30,000 shares of Litchfield Design, which has a price of 4 dollars per share. If your portfolio has an expected return of 14.64 percent, then what is the expected return for Litchfield Design? Answer as a rate in decimal format so that 12.34% would be entered as .1234 and 0.98% would be entered as .0098.

Answer 1

Solution:

Calculation of Expected Return of a portfolio:

The formula for calculation of Expected Return of a portfolio is

E(R_P) = ( R_A * W_A )+ ( R_B * W_B )

Where

E(R_P) = Expected return on a portfolio

R_A = Expected Return of Fairfax Paint    W_A = Weight of Investment in Fairfax Paint

R_B = Expected Return of Litchfield Design    W_B = Weight of Investment in Litchfield Design

Calculation of Total Investment in Fairfax Paint :

As per the information given in the question we have

No. of shares of Fairfax Paint = 10,000

Price per share of Fairfax Paint = $ 6.8

This implies Total of Investment in Fairfax Paint = No. of shares * Price per share

= 10,000 * $ 6.8 = $ 68,000  

Calculation of Total Investment in Litchfield Design :

No. of shares of Litchfield Design = 30,000

Price per share of Litchfield Design = $ 4

This implies Total of Investment in Litchfield Design = No. of shares * Price per share

= 30,000 * $ 4 = $ 120,000  

Thus total Investment in the portfolio = Total Investment in Fairfax Paint + Total Investment in Litchfield design

= $ 68,000 + $ 120,000 = $ 188,000

Thus the Weight of Investment in Fairfax Paint = Total of Investment in Fairfax Paint / Total Investment in the portfolio

= $ 68,000 / $ 188,000 = 0.3617

W_A = Weight of Investment in Fairfax Paint = 0.3617

Thus the Weight of Investment in Litchfield Design = Total of Investment in Litchfield Design / Total Investment in the portfolio

= $ 68,000 / $ 188,000 = 0.6383

W_B = Weight of Investment in Litchfield Design = 0.6383

As per the information available in the question and the calculations above :

E(R_P) = 14.64 % = 0.1464   ; R_A = 10.56 % = 0.1056 ; W_A = 0.3617   ; W_B = 0.6383 ; R_B = To find   

Applying the values in the formula we have

14.64 = ( 10.56 % * 0.3617 ) + (R_B * 0.6383 )

14.64 % = 3.8196 % + (R_B * 0.6383 )

14.64 % - 3.8196 % = (R_B * 0.6383 )

10.8204 % = (R_B * 0.6383 )

(R_B * 0.6383 ) = 10.8204 %

R_B = 10.2804 % / 0.6383

R_B = 16.9520 %

R_B = 0.169520

R_B = 0.1695 ( in decimal format )

Thus the expected return of the Litchfield design = 0.1695