You are thinking about investing your money in the stock market. You have the following two stocks in mind: stock A and stock B$.$ You know that the economy can either go in recession or it will boom. Being an optimistic investor, you believe the likelihood of observing an economic boom is two times as high as observing an economic depression. You also know the following about your two stocks:

State of the Economy Probability RA RB

Boom $10\%2\%$

Recession $6\%40\%$

i$.$ Calculate the expected return for stock A and stock B$.$

ii$.$Calculate the total risk $($variance and standard deviation$)$ for stock A and for stock B$.$

b$.$ A portfolio consists of the following assets with associated betas:

Security Beta Value

X $0\mathrm{.}9$ P$1000000$

Y $1\mathrm{.}2$ P$2000000$

Z $0\mathrm{.}7$ P$2000000$

Calculate the beta of the portfolio