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

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) $$\begin{array} { | c | c | c | c | c | c | } \hline & \text { ASSET A } & \text { ASSET A } & \text { ASSET B } & \text { ASSET B } & \text { Correlation } \\\hline \text { Scenario } & \begin{array} { c } \text { Expected } \\\text { Return }\end{array} & \begin{array} { c } \text { Standard } \\\text { Deviation }\end{array} & \begin{array} { c } \text { Expected } \\\text { Return }\end{array} & \begin{array} { c } \text { Standard } \\\text { Deviation }\end{array} & \begin{array} { c } \text { Correlation of } \\\text { A and B }\end{array} \\\hline 1 & 10 \% & 20 \% & 5 \% & 10 \% & + 1 \\\hline 2 & 10 \% & 20 \% & 5 \% & 10 \% & - 1 \\\hline\end{array}$$

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