Question $1$: $8$ marks

The following data are available about the returns of two stocks and market portfolio:

$\backslash$table$[[$Economic State,Probability,Stock A $(\%),$Stock B $(\%),$Market portfolio $(\%)],[$Deep Recession,$0\mathrm{.}05,-3,-2,-13],[$Mild Recession,$0\mathrm{.}20,6,9,1],[$Average$,0\mathrm{.}50,11,12,15],[$Mild Boom,$0\mathrm{.}20,14,15,29],[$Strong Boom,$0\mathrm{.}05,19,26,43],[$Table $1,,,,]]$

You are required to:

a$)$ Compute the expected return for stocks A and $B(2$ marks$)$

b$)$ Compute the standard deviation for stocks A and B$.$ Which stock is riskier? $(3$ marks$)$

c$)$ Compute the expected return of a portfolio that comprises of $70\%$ stock A and $30\%$ stock B $(1$ mark$)$

d$)$ Compute the standard deviation of returns for the market portfolio $(1$ mark$)$

e$)$ Which, among stocks A$,$ B and the market is riskier? Respond in light of your computations $(1$ mark$)$