Problem $4$

You are considering how to allocate your wealth. You can invest in a risk$-$free asset, or two stocks, A and B$.$ Stock A has a beta of $0\mathrm{.}8$ and standard deviation of returns of $36\%.$ Stock B has a beta of $1\mathrm{.}7$ and standard deviation of returns of $46\%.$ The risk$-$free rate is $5\%$ and the expected return for the market is $9\%.$

Part a$.$

If the correlation between the returns of A and $B$ is $0\mathrm{.}7$ and you allocate $40\%$ of your portfolio to A and $60\%$ to B $,$ what is the portfolio expected return and standard deviation?

Part b$.$

If the correlation between the returns of A and B is $0\mathrm{.}3$ and you allocate $40\%$ of your portfolio to A and $60\%$ to B $,$ what is the portfolio expected return and standard deviation?

Part c$.$

Suppose instead you allocate $80\%$ of your portfolio to A and $20\%$ to the risk$-$free asset, what is the portfolio expected return and standard deviation?