Your friend is interested in investing in Stock A and Stock B$.$ He knows that you are currently taking Financial Management and has sought your help in analyzing the investment opportunity. You have been provided the following forecast:

State of Economy

Probability of Occurrence

Stock A Expected Return

Stock B Expected Return

Expansion

$20\%$

$25\%$

$35\%$

Stable

$50\%$

$15\%$

$25\%$

Recession

$30\%$

$-5\%$

$-15\%$

$($i$)$ Given the above forecast, your friend wants to know what the expected returr the portfolio would be if he were to invest $$1,500$ in Stock A and $$4,500$ in Stock

$(5$ marks$)$

$($il$).$ Calculate the correlation coefficient between the two stocks. $(9$ marks$)$

$($iii$)$ What is the standard deviation of the portfolio?

$(2$ marks$)$

$($iv$)$ If your friend wishes to have an expected return of $18$ percent on the portfolio, how much of the money should be invested in stock A and how much in stock B$?$

$(4$ marks$)$