Consider the following probability distribution for stocks A and $B$ :

$\backslash$table$[[$State of Economy,Probability of State of$,$Return on Security A$,$Return on Security B$],[,($ Economy $)/()],[$Boom$,0\mathrm{.}10,0\mathrm{.}10,0\mathrm{.}07],[$Strong Growth,$0\mathrm{.}20,0\mathrm{.}13,0\mathrm{.}06],[$Normal Growth,$0\mathrm{.}20,0\mathrm{.}12,0\mathrm{.}09],[$Weak Growth,$0\mathrm{.}30,0\mathrm{.}14,0\mathrm{.}08],[$Bust$,0\mathrm{.}20,0\mathrm{.}15,]]$

i$.$ What is the expected return of an equally weighted portfolio? What is the standard deviation of an equally weighted portfolio?

ii$.$ What is the standard deviation of Security A$?$ What is the standard deviation of Security B$?$

iii. Based on the information above, what is the correlation coefficient of the Security A to Security B$?$

iv$.$ Assuming both securities are on the same security market line. The equal weight portfolio has a Beta $=1\mathrm{.}0,$ Security A Beta is twice Security B Beta, what is the market risk premium?

v$.$ Assuming both securities are on the same security market line. The equal weight portfolio has a Beta $=1\mathrm{.}0,$ Security A Beta is twice Security B Beta, what is the risk$-$free rate?

vi$.$ Calculate the Sharpe Ratio for Security A$,$ Security B and the equally weighted portfolio.