$8.$ Assume the following inputs for parts a$,$ b$,$ and c below. The market portfolio has an expected return of $12\%$ and a standard deviation of returns of $20\%.$ The risk$-$free rate is $5\%.$

a$)$ The stock ABC has a standard deviation of $50\%.$ Its correlation with the market is $0\mathrm{.}5.$What is the expected rate of return for ABC as per CAPM? $(3$ points$)$

b$)$ You estimate ABC to go up from $$40$ to $$48$ over the next year. Calculate the alpha for

the stock and assess if ABC is over$-$ or under$-$ priced according to CAPM? $(3$ Points$)$

c$)$ Suppose CAPM holds. A stock XYZ has an expected return of $10\%$ and a standard deviation of returns of $50\%.$ What fraction of the XYZ stock$$s variance represents unsystematic risk?