Question

Lucas has a portfolio consist of stock Jay, and stock Hawk. Stock Jay accounts for 60% of his portfolio, and stock Hawk accounts for 40% of the portfolio. Below table shows the values of standard deviation of return of two stocks, and the variance of his portfolio.. Standard Deviation Variance of Portfolio Stock Jay 22% 0.046 Stock Hawk 28% What is the correlation coefficient (ρ) between the returns on stock Jay and stock Hawk? 0.342 0.046 0.542 0.442

Answer 1

formula to be used here

variance of returns of the portfolio = (W1*standard deviation of jay)^2 + (W2*standard deviation of hawk)^2 + 2*W1*W2*correlation coefficient*standard deviation of jay* standard deviation of hawk

where, variance of returns of the portfolio = 0.046

W1(jay) = 0.6

W2(hawk) = 0.4

standard deviation of jay = 0.22

standard deviation of hwak = 0.28

correlation coefficient (ρ) = ?

put all these values in above formula

0.046 = (0.6*0.22)^2 + (0.4*0.28)^2 + 2*0.6*0.4*0.22*0.28*ρ

0.046 = (0.0132)^2 + (0.112)^2 + 0.029568*ρ

0.046 = 0.017424 + 0.012544 + 0.029568*ρ

0.046 = 0.029968 + 0.029568*ρ

0.046 - 0.029968 = 0.029568*ρ

0.016032 = 0.029568*ρ

ρ = 0.016032/0.029568

= 0.542208

or 0.542

correlation coefficient (ρ) between the returns on stock Jay and stock Hawk = 0.542

option (c) should be the correct answer.

Please check with your answer and let me know.