An investor must decide on its portfolio balance for the year. There are three assets available and their returns depend on whether the economy is weak or strong $($both states equally likely$)$ as follows:$$Asset

Government Bond Wall Street Firm Main Street Mart

Strong Weak

$2\%2\%10\%-2\%5\%1\%1.$ Determine the budget set for this investor if all that matters is the expected return $\backslash$mu and the standard deviation $\backslash$sigma of the chosen portfolio.

$2.$ Determine the budget set for this investor if we invert Main Street Mart$$s returns to $5\%$ in a weak economiy and $1\%$ in a strong economy. Explain which asset becomes irrelevant.