An investor is considering investing one-half of his wealth in Asset A and one-half in Asset B.He is not sure how the two assets are correlated.The correlation might be r = +1 or it might be r = -1.If it is r = + 1,then the portfolio standard deviation is 15%.Calculate the portfolio standard deviation if the correlation is r = -1.What is the difference between the standard deviations of Scenario 1 and Scenario 2? (Scenario 1 - Scenario 2)

A) 2.5%
B) 5.0%
C) 7.5%
D) 10.0%
E) 15.0%

Question

An investor is considering investing one-half of his wealth in Asset A and one-half in Asset B.He is not sure how the two assets are correlated.The correlation might be r = +1 or it might be r = -1.If it is r = + 1,then the portfolio standard deviation is 15%.Calculate the portfolio standard deviation if the correlation is r = -1.What is the difference between the standard deviations of Scenario 1 and Scenario 2? (Scenario 1 - Scenario 2)

A) 2.5% 
B) 5.0% 
C) 7.5% 
D) 10.0% 
E) 15.0%

Quizplus · Accepted Answer

Apply the equation for the standard deviation of a 2 asset portfolio to each scenario, and find the difference between the two standard deviations. Scenario 1: σ_p = 11ea7fdb_fc05_6a63_a768_9dac0d107d4e_TB2902_11 σ_p = 11ea7fdb_fc05_6a64_a768_1b5b7a128127_TB2902_11 σ_p = 11ea7fdb_fc05_6a65_a768_5d64bf1b2bdb_TB2902_11 σ_p = 11ea7fdb_fc05_9176_a768_9b0f83aa44ee_TB2902_11 = 0.15 or 15% Scenario 2: σ_p = 11ea7fdb_fc05_9177_a768_97c13a8fbfd3_TB2902_11 σ_p = 11ea7fdb_fc05_9178_a768_0b844cb7d347_TB2902_11 σ_p = 11ea7fdb_fc05_9179_a768_77964ad9c26e_TB2902_11 = 0.05 or 5% Difference = 0.15 - 0.05 = 0.10 or 10%

An Investor Is Considering Investing One-Half of His Wealth in Asset