Suppose stock A has an expected return of $10\%$ and a volatility of $50\%$ while stock B

has an expected return of $5\%$ and volatility of $20\%.$ These two stocks were perfectly

negatively correlated $($i$.$e$.,$ their correlation is $-1)$

a$)$ How to mix these two assets to create a portfolio with zero standard deviation?

b$)$ if there are no arbitrage opportunities, what is the risk$-$free rate of interest in this

economy?