Question $2$: $(10$ marks$)$

You have decided to invest in $100,000$ shares of stock A at a price of $$10$ per share, and $50,000$ shares of stock B at a price of $$20$ per share. You have also concluded that next year returns are the values in the table below. You estimate that the correlation between the two stocks in $+0\mathrm{.}7.$

Stock A:

Boom: Probability $=0\mathrm{.}4$; Return $=0\mathrm{.}15$

Stable: Probability $=0\mathrm{.}4$; Return $=0\mathrm{.}10$

Recession: Probability $=0\mathrm{.}2$; Return $=0\mathrm{.}05$

Stock B:

Boom: Probability $=0\mathrm{.}3$; Return $=0\mathrm{.}12$

Stable: Probability $=0\mathrm{.}3$; Return $=0\mathrm{.}10$

Recession: Probability $=0\mathrm{.}4$; Return $=0\mathrm{.}08$

b$)$ now assume that you want to create a portfolio combining only stock A and the risk$-$free asset. You want to create a portfolio such that the beta of the portfolio is $1\mathrm{.}5.$ You know that the beta of stock A is $2.$ What is the expected rate of return of this portfolio?