Question $3[8$ marks$]$

Consider the following information about three stocks:

$\backslash$table$[[$State of economy,$\backslash$table$[[$Probability of State$],[$of Economy$]],$State of Return if State Occurs$],[$Stock A$,$Stock B$,$Stock C$],[$Boom$,0\mathrm{.}25,0\mathrm{.}20,0\mathrm{.}25,0\mathrm{.}60],[$Normal$,0\mathrm{.}55,0\mathrm{.}15,0\mathrm{.}11,0\mathrm{.}05],[$Bust$,0\mathrm{.}20,0\mathrm{.}01,-0\mathrm{.}15,-0\mathrm{.}50]]$

a$.$ If your portfolio is invested $40$ percent each in A and $B$ and $20$ percent in $C,$ what is the portfolio expected return? The variance? The standard deviation?

b$.$ If the expected T$-$bill rate is $3\mathrm{.}80$ percent, what is the expected risk premium on the portfolio?

c$.$ If the expected inflation rate is $3\mathrm{.}50$ percent, what are the approximate and exact expected real returns on the portfolio? What are the approximate and exact expected real risk premiums on the portfolio?