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

Consider the following information about three stocks:

$\backslash$table$[[$State of Economy,$\backslash$table$[[$Probability of State$],[$of Economy$]],$Rate of Return if State Occurs$],[$Stock $A,$Stock B$,$Stock C$],[$Boom$,\mathrm{.}20,\mathrm{.}24,\mathrm{.}36,\mathrm{.}58],[$Normal$,\mathrm{.}50,\mathrm{.}20,18,16],[$Bust$,\mathrm{.}30,\mathrm{.}04,-\mathrm{.}36,-\mathrm{.}45]]$

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$.,16161.)$

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$.,32\mathrm{.}16\mathrm{.}1.$

b$.$ If the expected T$-$bill rate is $4\mathrm{.}00$ 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 $3\mathrm{.}60$ percent, what are the approximate and exact expected real returns on the portfolio? $($Do not round intermediate calculations and enter your answers as a percent rounded to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

c$-2.$ What are the approximate and exact expected real risk premiums on the portfolio? $($Do not round intermediate calculations and enter your answers as a percent rounded to $2$ decimal places, e$.$g$.,32\mathrm{.}16.$