Consider the following two assets A and B$,$ with normally distributed rates of return

$([tilde(r{)}_A],[tilde(r{)}_B])N[([0\mathrm{.}06],[0\mathrm{.}11]),([0\mathrm{.}002,0\mathrm{.}001],[0\mathrm{.}001,0\mathrm{.}004])]$

You seek to maximize the utility function: $u(widetilde(w))=-e^{-12\text{w}\text{i}\text{d}\text{e}\text{t}\text{i}\text{l}\text{d}\text{e}(w)}$

$($Hint: normalize initial wealth to one.$)$

$($a$)$ What is your optimal portfolio if A and B are the only assets available?

$($d$)$ There is no risk free asset in the economy anymore $-$ just assets A and B$.$ What is the

global minimum variance? Which portfolio achieves this?

$($e$)$ As in part $($d$),$ there is no risk free asset. The market capitalization of asset A is $1,$ and that

of asset B is $2.$ Is this compatible with the zero beta CAPM?