Question

Hyacinth Macaw invests 62% of her funds in stock and the balance in stock J. The standard deviation of returns on I is 14%, and on Jit is 26%. (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 This is a numeric cell, so please enter numbers only. b. Calculate the variance of portfolio returns, assuming the correlation is 0.4. (Do not round intermediate calculations. Round your answer to 4 decimal places.) Portfolio variance ſ 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

Weight of stock I in the portfolio = w_I = 0.62

Weight of stock J in the portfolio = w_J = 1-0.62 = 0.38

Standard Deviation of stock I = σ_I = 14%

Standard deviation of stock J = σ_J = 26%

Variance of the portfolio is calculated using the formula:

Variance of portfolio = σ_P² = w_I²*σ_I² + w_J²*σ_J² + 2*ρ*w_I*w_J*σ_I*σ_J

where ρ is the correlation between returns of stock I and stock J

Part a

Correlation between the return is 1

ρ = 1

σ_P² = (0.62)²*(14%)² + (0.38)²*(26%)² + 2*1*0.62*0.38*14%*26% = 0.00753424+0.00976144+0.01715168 = 0.03444736

Answer a -> Portfolio variance when ρ is 1 = 0.0344

Part b

Correlation between the return is 0.4

ρ = 0.4

σ_P² = (0.62)²*(14%)² + (0.38)²*(26%)² + 2*0.4*0.62*0.38*14%*26% = 0.00753424+0.00976144+0.006860672 = 0.024156352

Answer b -> Portfolio variance when ρ is 0.4 = 0.0242

Part c

Correlation between the return is 0

ρ = 0

σ_P² = (0.62)²*(14%)² + (0.38)²*(26%)² + 2*0*0.62*0.38*14%*26% = 0.00753424+0.00976144+0 = 0.01729568

Answer c -> Portfolio variance when ρ is 1 = 0.0173