$4.$ An investor wants to see the diversification benefit of having two stocks instead of one in his

portfolio, and the following table shows the characteristics of the two stocks.

Expected Return Standard

Stock X $0\mathrm{.}10\mathrm{.}2$

Stock Y $0\mathrm{.}30\mathrm{.}6$

a$)$ Assume different weights for the two stocks and the correlation between the two stocks is

$0\mathrm{.}1.$ Fill in the following blank space.

Weights Portfolio

Expected Return

Portfolio Standard

X Y Deviation

$10$

$0\mathrm{.}80\mathrm{.}2$

$0\mathrm{.}60\mathrm{.}4$

$0\mathrm{.}40\mathrm{.}6$

$0\mathrm{.}20\mathrm{.}8$

$01$

b$)$ Plot the two stocks X$,$ Y and the portfolios in part a$)$ onto a diagram with the standard

deviation on the X$-$axis and expected return on the Y$-$axis. Is it better to have two stocks

in the portfolio than having one stock?

c$)$ How will the diagram change if the correlation coefficient is $1?$ Show the diagram.

d$)$ If the correlation coefficient is $-1.$ What would be the weights of the two stocks in the

minimum variance portfolio? And what are the expected return and standard deviation of

the minimum variance portfolio?An investor wants to see the diversification benefit of having two stocks instead of one in his

portfolio, and the following table shows the characteristics of the two stocks.

a$)$ Assume different weights for the two stocks and the correlation between the two stocks is

$0\mathrm{.}1.$ Fill in the following blank space.

b$)$ Plot the two stocks $x,Y$ and the portfolios in part a$)$ onto a diagram with the standard

deviation on the $x-$axis and expected return on the $Y-$axis. Is it better to have two stocks

in the portfolio than having one stock?

c$)$ How will the diagram change if the correlation coefficient is $1?$ Show the diagram.

d$)$ If the correlation coefficient is $-1.$ What would be the weights of the two stocks in the

minimum variance portfolio? And what are the expected return and standard deviation of

the minimum variance portfolio?