Consider the following variance$-$covariance matrix in $\%^2$ for three stocks, as well as the percentage of a portfolio that each security comprises, and the expected returns. The risk$-$free rate of return is $3$ per cent.

Covariances $|$ Stock A $|$ Stock B $|$ Stock C

Stock A $|256|64|-134$

Stock B $|64|400|504$

Stock C $|-134|504|1764$

Weights $|40\%|25\%|35\%$

Expected returns $|8\%|10\%|12\%$

a$)$ Calculate Sharpe ratio for the individual stocks as well as for the portfolio.

b$)$ Compute the expected return and volatility of the portfolio with the lowest possible risk, given that you choose to include only two of the stocks in your portfolio.