Problem $2$

Assume there are two assets with the following parameters: ${}_1=20\%,{}_2=30\%$ the assets

are perfectly negatively correlated $({}_{1,2}=-1).$

$($a$)$ Compute the weights of the portfolio that has a standard deviation of zero.

$($b$)$ Now assume that the correlation is ${}_{1,2}=1.$ Can you still find a portfolio with zero

risk? If instead you are trading in a financial market that has banned short$-$selling,

will your answer change? Is so how and why?