Cinderella plans to form a portfolio with two securities: Jaq and Gus.The correlation between the two securities is -1.Given the following forecasts,what are the weights in Jaq and Gus that will set the standard deviation of the portfolio equal to zero?

A) Portfolio weights in Jaq and Gus are 74.37% and 25.63%, respectively
B) Portfolio weights in Jaq and Gus are 25.63% and 74.37%, respectively
C) Portfolio weights in Jaq and Gus are 60.51% and 39.49%, respectively
D) Portfolio weights in Jaq and Gus are 39.49% and 60.51% respectively

Question

Cinderella plans to form a portfolio with two securities: Jaq and Gus.The correlation between the two securities is -1.Given the following forecasts,what are the weights in Jaq and Gus that will set the standard deviation of the portfolio equal to zero?
  
A) Portfolio weights in Jaq and Gus are 74.37% and 25.63%, respectively 
B) Portfolio weights in Jaq and Gus are 25.63% and 74.37%, respectively 
C) Portfolio weights in Jaq and Gus are 60.51% and 39.49%, respectively 
D) Portfolio weights in Jaq and Gus are 39.49% and 60.51% respectively

Quizplus · Accepted Answer

Expected return on Jaq,E(R_J)= 25%*15% + 13%*30% + (-5%)*55% = 4.9% Expected return on Gus,E(R_G)= (-10%)*15% + 8%*30% + 12%*55% = 7.5% ₃ σ_J = √[∑Pr_i(r_i-4.9%)²] = √(0.00606+0.001968+0.005391)= 11.584% ⁱ⁼¹ ₃ σ_G = √[∑Pr_i(r_i-7.5%)²] = √(0.00459375+0.0000075+0.00111375)= 7.5598% ⁱ⁼¹ The portfolio weight in Jaq is: w_J = σ_G/ (σ_G+ σ_J)= 7.5598%/(11.584%+7.5598%)= 39.49% The portfolio weight in Gus is 1- weight in Jaq = 60.51%

Cinderella Plans to Form a Portfolio with Two Securities: Jaq