Over the past $10$ years a mutual fund realized an average annual return of $16$

percent per year.

$$ The return on the mutual fund had a beta of $1\mathrm{.}2$ and the standard deviation of the

mutual fund$$s annual returns was $29$ percent $(0\mathrm{.}29).$

$$ The riskless rate was $5$ percent per year, and the realized average annual return on

the market portfolio of risky assets was $13$ percent per year. The standard

deviation of the annual returns on the market portfolio of risky assets was $17$

percent $(0\mathrm{.}17).$

a$)$ What was the alpha $(\backslash$alpha $)$ of the fund?

b$)$ Suppose that going forward, the expected return on the market portfolio of risky

assets is $10$ percent, that the riskless rate will be $5$ percent, and that the mutual fund$$s

beta will still be $1\mathrm{.}2.$ What is the expected return on the fund for the coming year

assuming the fund$$s alpha is the same going forward as it was in the past?

c$)$ How much non$-$systematic risk did the fund take on in the past, i$.$e$.$ what was $\backslash$sigma $2^\backslash$epsi for the fund$$s annual return?