$1.$ Microgen had the following returns over the last four years.

Year Annual return

$2000-10\%$

$200115\%$

$2002-4\%$

$200323\%$

a$)$ What are the arithmetic and geometric average annual returns on this stock over this four$-$year period?

b$)$ What is the annual variance and standard deviation of returns of this stock over this four$-$year period?

c$)$ Suppose that there was a risk$-$free asset over these four years that returned $2\%$ annually. If you formed a portfolio with weights of $0\mathrm{.}5$ on Microgen and $0\mathrm{.}5$ on the risk$-$free asset, what would be the annual return and standard deviation of returns of this new portfolio over the four years?