$1.$ Consider the following information $($show your calculations$)(10$ points$)$

Probability of State of Economy Stock A Stock B Stock C

Boom $0\mathrm{.}20\mathrm{.}240\mathrm{.}360\mathrm{.}55$

Normal $0\mathrm{.}550\mathrm{.}170\mathrm{.}130\mathrm{.}09$

Bust $0\mathrm{.}250\mathrm{.}00-0\mathrm{.}28-0\mathrm{.}45$

a$.$ If your portfolio is invested $40\%$ each in A and B and $20\%$ in C$,$ what is the portfolio expected return? The variance? The standard deviation?

b$.$ If the expected T$-$bill rate is $3\mathrm{.}8\%,$ what is the expected risk premium on the portfolio?