Question

Hyacinth Macaw invests 55% of her funds in stock I and the balance in stock J. The standard deviation of returns on I is 16%, and on J it is 23%. (Use decimals, not percents, in your calculations.)

a. Calculate the variance of portfolio returns, assuming the correlation between the returns is 1. (Do not round intermediate calculations. Round your answer to 4 decimal places.)

Portfolio variance _______

b. Calculate the variance of portfolio returns, assuming the correlation is .6. (Do not round intermediate calculations. Round your answer to 4 decimal places.)

Portfolio variance ________

c. Calculate the variance of portfolio returns, assuming the correlation is 0. (Do not round intermediate calculations. Round your answer to 4 decimal places.)

Portfolio variance_________

Answer 1

Portfolio Variance = Weight of stock I^2 * Std. Deviation of Stock I^2 + Weight of Stock J^2 * Std.Deviation of Stock J^2 + 2*Weight of stock I *Weight of stock J * Correlation* Std.deviation of Stock I * Std.deviation of Stock J

a. Portfolio Variance = 0.55^2*0.16^2 +0.45^2*0.23^2 +2*0.55*0.45*1*0.16*0.23 = 0.0367

b. Portfolio Variance = 0.55^2*0.16^2 +0.45^2*0.23^2 +2*0.55*0.45*0.6*0.16*0.23 =0.0294

c. Portfolio Variance =  0.55^2*0.16^2 +0.45^2*0.23^2 +2*0.55*0.45*0*0.16*0.23 = 0.0185