A single mispriced asset has an alpha $a=3\mathrm{.}0\%,$ a beta $=1,$ and unsystematic risk ${}_{}^2=9\%.$ The market risk premium is $5\mathrm{.}0\%$ and the market's standard deviation is $0\mathrm{.}1.$

What is the information ratio of the mispriced asset?

In constructing an optimal allocation between this mispriced asset and the market portfolio, what proportion of your investment would you place in the mispriced asset?

a$.0\mathrm{.}33$;$6\mathrm{.}67\%$

b$.0\mathrm{.}1$;$66\mathrm{.}67\%$

c$.0\mathrm{.}33$;$6\mathrm{.}90\%$

d$.0\mathrm{.}1$;$6\mathrm{.}90\%$

e$.0\mathrm{.}1$;$6\mathrm{.}67\%$