Consider the following information on a portfolio of three stocks:

State of Economy Probability of State of Economy Stock A Rate of Return Stock B Rate of Return Stock C Rate of Return

Boom $\mathrm{.}15\mathrm{.}02\mathrm{.}32\mathrm{.}60$

Normal $\mathrm{.}55\mathrm{.}10\mathrm{.}12\mathrm{.}20$

Bust $\mathrm{.}30\mathrm{.}16\mathrm{.}11\mathrm{.}35$

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