Question

Hyacinth Macaw invests 48% of her funds in stock I and the balance in stock J. The standard deviation of returns on I is 15%, and on J it is 29%. (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 .7. (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

ωA = weight of asset I or Asset 1 in the portfolio;

ωB = weight of asset J or Asset 2

σA = standard deviation of asset I or Asset 1;

σB = standard deviation of asset J or Asset 2; and

ρAB = correlation coefficient between returns on asset I and asset J.

Variance = (σA ^2* ωA ^2 + σB ^2* ωB ^2 + 2* ρAB * σA * ωA* σB * ωB )                            

a.

Variance = (0.15^2*0.48^2 + 0.29^2*0.52^2 + 2*1*0.15*0.48*0.29*0.52)^0.5

Variance = 0.0496

b.

Variance = (0.15^2*0.48^2 + 0.29^2*0.52^2 + 2*0.7*0.15*0.48*0.29*0.52)                            

Variance = 0.0431

c.

Variance = (0.15^2*0.48^2 + 0.29^2*0.52^2 + 2*0*0.15*0.48*0.29*0.52)                            

Variance = 0.0279