$7.$ A stock has a beta of $1\mathrm{.}05$ and an expected return of $11\mathrm{.}3\%.$ A risk$-$less asset is currently earning $3\mathrm{.}5\%.$

a$.$ What is the expected return on a portfolio that is equally invested in the two assets?

b$.$ If a portfolio of the two assets has a beta of $0\mathrm{.}5,$ what are the portfolio weights?

c$.$ If a portfolio of the two assets has an expected return of $10\mathrm{.}2\%,$ what is its beta?

d$.$ If a portfolio of the two assets has a beta of $2\mathrm{.}14,$ what are the portfolio weights? How do you interpret the weights for the two assets in this case?