Charles invests in a price-weighted portfolio of two shares,ABC and XYZ.His funds manager sends him a statement of his performance at the end of each year for his tax return.Unfortunately,some of the form was illegible,and all he could discern was that the price-weighted portfolio return was 10%,the returns on ABC and XYZ were 8% and 16%,respectively and that the purchase price of ABC was $10.Given this information,at what price did Charles purchase the shares in company XYZ?
A) $\$ 2.50$
B) $\$3.33$
C) $\$ 3.75$
D) $\$ 4.25$

Question

Charles invests in a price-weighted portfolio of two shares,ABC and XYZ.His funds manager sends him a statement of his performance at the end of each year for his tax return.Unfortunately,some of the form was illegible,and all he could discern was that the price-weighted portfolio return was 10%,the returns on ABC and XYZ were 8% and 16%,respectively and that the purchase price of ABC was $10.Given this information,at what price did Charles purchase the shares in company XYZ?
A) $\$ 2.50$ 
B) $\$3.33$
C) $\$ 3.75$
D) $\$ 4.25$

Quizplus · Accepted Answer

Given that there are only two shares in the portfolio,the weights in each asset must sum to unity.That is,if we define the (unknown)price weight in asset B as w_b,then the weight in asset A is 1 - w_b.Using equation 1.16,page 23,we know the price-weighted return on the portfolio is 10%,which can be expressed as 0.10 = (1 - w_b)(8%)+ w_b(16%).Solving yields w_b = 25%.We can now solve for the selling price of asset B.We know that the price-weight of asset B is calculated as the purchase price of asset B divided by the combined purchase prices of both assets A and B,and that the weight must be 25%.Hence if we denote the purchase price of asset A as P,we know that P/(10 + P)= 0.25.Hence,P = 2.5 + 0.25P,which can be solved to yield P = 3.33.To verify the answer is correct,we now know that the price of assets A and B are $10 and $3.33 (and hence a combined cost (16%)= 10.0% as required.

Charles Invests in a Price-Weighted Portfolio of Two Shares,ABC and XYZ.His