Consider the following information about two stocks where the probability of an economic boom is $40\%$:

Economic State Return A $($RA$)$ Return B $($RB$)$

Boom $20\%-6\%$

Recession $4\%12\%$

a$.$ Calculate the expected return for stock A and stock B $($marginal returns for each stock$).$

b$.$ Calculate the standard deviation of stock A and stock B$.$

c$.$ Which stock is riskier?

d$.$ Calculate the Covariance and correlation between stock A and stock B$.$

e$.$ Calculate the expected return and the total risk $($standard deviation$)$ of a portfolio, where $1/3$of your money is invested in stock A$,$ and $2/3$ of your money is invested in stock B$.($Hint: use both the method with the formula for the risk of a portfolio $($i$.$e$.,$ using the covariance$)$ and the method of calculating the variance $($and standard deviation$)$ from the portfolio returns.

a$.$ Write out the portfolio as an equation

b$.$ Calculate the expected return portfolio

c$.$ Calculate the variance and the standard deviation of the portfolio.