You are an investor with a quadratic utility function ( i . e . , mean - variance preferences ) , in a CAPM world

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You are an investor with a quadratic utility function $($i$.$e$.,$ mean$-$variance preferences$),$ in a CAPM

world comprised of the following three uncorrelated risky assets, and the risk free asset.

The risk free rate is $5\%.$

$($a$)$ What is the minimization problem one would solve to determine the efficient frontier?

What is the expected shape of the efficient frontier in this setup?

$($b$)$ What is the composition of the tangency portfolio?

$($c$)$ For each of the three assets above, X$,$ Y$,$ and Z$,$ what proportion of total risk $()$ is

systematic risk?

$($d$)$ What is the equation of the capital market line?

$($e$)$ What is the equation of the security market line?