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 $1\mathrm{.}5$ and standard deviation of returns of $36\%.$ Stock B has

a beta of $0\mathrm{.}7$ and standard deviation of returns of $66\%.$ The risk$-$free rate is $4\%$ and the expected

return for the market is $9\%.$

Part a$.$

If the correlation between the returns of A and B is $0\mathrm{.}8$ and you allocate $60\%$ of your portfolio to

A and $40\%$ 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 $60\%$ of your portfolio to

A and $40\%$ to B$,$ what is the portfolio expected return and standard deviation?

Part c$.$

Suppose instead you allocate $70\%$ of your portfolio to A and $30\%$ to the risk$-$free asset, what is

the portfolio expected return and standard deviation?