An investor is considering investing in a new equity fund managed by a financial institution. The fund manager expects the portfolio to earn a rate of return of $12\%$ this year. The beta of the portfolio is $1.$ The rate of return available on risk$-$free assets is $3\%,$ and the expected market risk premium is $8\%.$

What expected rate of return would the investor demand before being willing to invest in this equity fund? Is the fund attractive?

Show clearly each step of your calculations.