Loredana has invested equal amounts in each of the shares of company A,company B and company C,which she purchased one year ago at prices of $10,$2 and $1,respectively.Loredana has recently sold her shares in company B for $2.50 and in company C for $1.15.If Loredana wishes to earn a continuously compounded return of 20% for the year,on her equally weighted portfolio,at what price will she need to sell her shares in company A?
A) $\$ 11.55$
B) $\$ 12.26$
C) $\$ 12.67$
D)$\$ 13.34$

Question

Loredana has invested equal amounts in each of the shares of company A,company B and company C,which she purchased one year ago at prices of $10,$2 and $1,respectively.Loredana has recently sold her shares in company B for $2.50 and in company C for $1.15.If Loredana wishes to earn a continuously compounded return of 20% for the year,on her equally weighted portfolio,at what price will she need to sell her shares in company A?
A) $\$ 11.55$ 
B) $\$ 12.26$
C) $\$ 12.67$
D)$\$ 13.34$

Quizplus · Accepted Answer

Using equation 1.5,page 14,the continuously compounded return for asset B is ln(2.5/2)= 0.223,and for asset C is ln(1.15/1)= 0.140.If we denote x as the return Loredana needs to earn on asset A,and she wishes to earn 20% on the equally weighted portfolio,then using equation 1.15,page 23,we know that the equally weighted portfolio return is: (1/3)(x)+ (1/3)(0.223)+ (1/3)(0.140)= 0.20.Solving the equation for x yields an answer of x = 23.7%.Therefore,Loredana must earn a return on asset A of 23.7%.Denoting P as the selling price,then using equation 1.5,ln(P/$10)= 0.237.Hence,P = 10e^0.237,which equals $12.67.As a check,using equation 1.5,ln(12.67/10)= 23.7.

Loredana Has Invested Equal Amounts in Each of the Shares $11.55\$ 11.55$11.55

Loredana Has Invested Equal Amounts in Each of the Shares $\$ 11.55$