You have just formed your portfolio by buying one share of Apple, which costs $$\frac{150}{?}$ share and a share of Microsoft, which costs $$\frac{250}{?}$ share. Over the next one year, you think the economy will be either good or bad with probability of $0\mathrm{.}5$ each. And the future return for each stock given the economic condition is as follows.

$\backslash$table$[[,$Apple,Microsoft$],[\backslash$table$[[$Economy is Good$],[($probability $=0\mathrm{.}5)]],0\mathrm{.}04,0\mathrm{.}10],[\backslash$table$[[$Economy is Bad $($pro$],[$bability $=0\mathrm{.}5)]],-0\mathrm{.}02,-0\mathrm{.}06]]$

$($a$)$ Find the expected return for the Apple stock and the Microsoft stock.

Note: Please write your answer in decimal form up to $2$ decimal places.

Apple:

Microsoft:

$($b$)$ Find the standard deviation of the future return for the Apple stock and the Microsoft stock.

Note: The value should be rounded to $4$ decimal places in the intermediate steps and $2$ decimal places on final result.

Apple:

Microsoft:

$($c$)$ Find the expected return of your portfolio.

Note: The value should be rounded to $4$ decimal places in the intermediate steps and five decimal places on final result.

The expected return of the portfolio:

$($d$)$ Find the correlation between these two stock returns.

Note: The value should be rounded to $4$ decimal places in the intermediate steps and a whole number on final result.

Corr$($RApple$,$ RMicrosoft