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.

$\backslash$table$[[,$Expected Return,Standard$],[$Stock X$,0\mathrm{.}1,0\mathrm{.}2],[$Stock Y$,0\mathrm{.}3,0\mathrm{.}6]]$

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.

$\backslash$table$[[$Weights$,\backslash$table$[[$Portfolio$],[$Expected Return$]],\backslash$table$[[$Portfolio Standard$],[$Deviation$]]],[x,Y,,],[1,0,,],[0\mathrm{.}8,0\mathrm{.}2,,],[0\mathrm{.}6,0\mathrm{.}4,,],[0\mathrm{.}4,0\mathrm{.}6,,],[0\mathrm{.}2,0\mathrm{.}8,,],[0,1,,]]$

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?