Q$23.$ Consider the following information about three stocks:

$\backslash$table$[[\backslash$table$[[$State$],[$economy$]],$of$,\backslash$table$[[$Probability of$],[$stock of economy$]],$Rate of return if state occurs$],[,$Stock A$,$Stock B$,$Stock C$,],[$Boom$,0\mathrm{.}25,0\mathrm{.}21,0\mathrm{.}33,0\mathrm{.}55,],[$Normal$,0\mathrm{.}60,0\mathrm{.}17,0\mathrm{.}11,0\mathrm{.}09,],[$Bust$,0\mathrm{.}15,0\mathrm{.}00,-0\mathrm{.}21,-0\mathrm{.}45,]]$

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 $3\mathrm{.}30$ 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?