Problem $13-23$ Portfolio Returns and Deviations $[$LO$2]$

Consider the following information about three stocks:

$\backslash$table$[[,,$Rate of Return if State Occurs$],[$State of Economy,Probability of State,,,$],[$of Economy,Stock A$,$Stock B$,$Stock C$,],[$Boom$,\mathrm{.}25,\mathrm{.}36,\mathrm{.}48,\mathrm{.}52],[$Normal$,\mathrm{.}44,\mathrm{.}20,\mathrm{.}15,\mathrm{.}12],[$Bust$,\mathrm{.}31,\mathrm{.}04,-\mathrm{.}26,-\mathrm{.}44]]$

a$-1.$ If your portfolio is invested $40$ percent each in A and $B$ and $20$ percent in $C,$ what is the portfolio expected return? $($Do not round intermediate calculations and enter your answer as a percent rounded to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

a$-2.$ What is the variance? $($Do not round intermediate calculations and round your answer to $5$ decimal places, e$.$g$.,\mathrm{.}16161.)$

a$-3.$ What is the standard deviation? $($Do not round intermediate calculations and enter your answer as a percent rounded to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

b$.$ If the expected T$-$bill rate is $4\mathrm{.}60$ percent, what is the expected risk premium on the portfolio? $($Do not round intermediate calculations and enter your answer as a percent rounded to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

c$-1.$ If the expected inflation rate is $4\mathrm{.}10$ percent, what are the approximate and exact expected real returns on the portfolio?

C$-2.$ What are the approximate and exact expected real risk premiums on the portfolio?