$3$ Covariance and correlation

Suppose there are three states of the world, which are all equally likely, and two different

financial assets. In the first state of the world, the first asset returns $8\%$ and the second

asset returns $-6\%.$ In the second state, the first asset returns $-4\%$ and the second asset

returns $14\%.$ In the third state, the first asset returns $11\%$ and the second asset returns

$7\%.$

$($a$)$ What is the expected return on each asset? What are the variance and standard

deviation of the return on each asset? Use natural units, not percentages $($i$.$e$.,$ for

$9\%,$ use $0\mathrm{.}09$ instead of $9).$

$($b$)$ What is the covariance of the returns of the two assets? What is the correlation

between the two returns?

$($c$)$ Consider an equal weighted portfolio of the two assets. Compute the mean return,

variance and standard deviation.

$($d$)$ How would a mean$-$variance optimizing investor rank the three assets $($asset $1,$

asset $2,$ equal weighted portfolio$)?$ Does your answer depend on the coefficient of

risk aversion A$?$ Explain.