Problem $11-9$ Returns and Standard Deviations

Consider the following information:

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

Stock A Stock B Stock C

Boom $\mathrm{.}15\mathrm{.}33\mathrm{.}43\mathrm{.}34$

Good $\mathrm{.}50\mathrm{.}20\mathrm{.}14\mathrm{.}08$

Poor $\mathrm{.}30\mathrm{.}01\mathrm{.}09\mathrm{.}03$

Bust $\mathrm{.}05\mathrm{.}17\mathrm{.}29\mathrm{.}10$

a$.$

Your portfolio is invested $32$ percent each in A and C$,$ and $36$ percent in B$.$ What is the expected return of the portfolio? $($Do not round intermediate calculations and enter your answer as a percent rounded to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)10\mathrm{.}16$

b$-1.$ What is the variance of this portfolio? $($Do not round intermediate calculations and round your answer to $5$ decimal places, e$.$g$.,\mathrm{.}16161.)$

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