Consider the returns for the following stocks:

State Probability Apple Microsoft Market

Boom $\mathrm{.}218\%16\%12\%$

Normal $\mathrm{.}69\%8\%6\%$

Recession $\mathrm{.}22\%4\%2\%$

i$)$ Find the Expected Return and Standard Deviation for each stock $($Apple & Microsoft$)$

ii$)$ Find the covariance and correlation between the two stocks $($Apple & Microsoft$)$

iii$)$ Find the expected return and standard deviation for a portfolio that weighs Apple $2/3$

and Microsoft $1/3.$

iv$)$ Measure systematic risk $($Beta$)$ for apple and Microsoft.

$($b$)-$ Write the Capital Asset Pricing Model $($CAPM$)$

$-$ What is the Security Market Line?

$-$ What is the role of Risk Free rate $($Rf$)$ is Security Market Line

$-$ What is the slope of the security market line

$-$ What should be the expected return of stock X if T bill rate is $4\%,$ market return is $12\%$ and the

Beta for Stock X is $1\mathrm{.}4$