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

Consider the following information about three stocks:

State of Economy Probability of State of Economy Rate of Return if State Occurs

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? $($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$.,32\mathrm{.}16.)$