You are thinking about irvesting your money in the stock market. You have the

following two stocks in mind: stock A and stock B$.$ You know that the economy

can either go in recession or it wil boom. Being an optimistic investor, you

believe the likelihood of observing an economic boom is two times as high as

observing an economic depression. You also know the following about your two

stocks:

$($a$)$ Calculate the expected retum for stock A and stock $B$

$($b$)$ Calculate the total risk $($variance and standard deviation$)$ for stock A and for

stock B

$($c$)$ Calculate the expected retum on a portfolio consisting of equal proportions

in both stocks.

$($d$)$ Calculate the expected return on a portfolio consisting of $10\%$ invested in

stock A and the remainder in stock $B.$

$($e$)$ Calculate the covariance between stock A and stock B$.$

$($i$)$ Calculate the correlation coeff cient between stock A and stock $B.$

$($g$)$ Calculate the variance of the portfolio with equal proportions in both stocks

using the covariance from answer $e.$

$($h$)$ Calculate the variance of the portfolio with equal proportions in both stocks

using the portfolio returns and expected portfolio returns from answer $c.$