Assume that risk$-$free rate is $5\%$ and your degree of risk$-$aversion is $6.$ Your utility function is Up $=$ E$($rp$)-1$A$*07$ Now in addition to investing these two risky assets, you can also invest in one risk$-$free asset. What is the weight of each asset $($Asset A$,$ Asset B$,$ and the risk$-$free asset$)$ in the optimal portfolio which gives you the highest utility? $($Hint: first, calculate the expected return and the variance of the risky portfolio with the highest sharp ratio $($the portfolio derived in $3.$c$).$ Second, use the risky portfolio constructed above and the risk$-$free asset to form a portfolio which will give you the highest utility$)$ Use the same portfolio information as above. Assume that your degree of risk aversion increases to $8.$ Then, in the risky portfolio which has the highest sharp ratio $($the tangency portfolio$),$ the weight of asset A will $($in other words, will the answer in Q$4$ change$)$ Use the same portfolio information as above. Assume that your degree of risk aversion increases to $8.$ Then, in the optimal portfolio which gives you the highest utility level, the weight of the risk$-$free asset will increase, decrease or unchanged? Explain.