Suppose stock AAA has an expected return of $20\%$ and volatility of $10\%$ and stock BBB has an expected return of $40\%$ and volatility of $20\%.$ The correlation coefficient is $0.$ Which are correct?

jjj$)$ It is possible to construct a portfolio with positive weight in stock AAA and stock BBB such that the

expected return of the portfolio is strictly higher than the expected return of stock BBB

kkk$)$It is possible to construct a portfolio with positive weight in stock AAA and stock BBB such that the

volatility of the portfolio is strictly lower than the volatility of stock BBB

lll$)$ A portfolio with equal weight in stock AAA and BBB has volatility of $15\%$

mmm$)$ It is possible to construct a portfolio with positive weight in stock AAA and stock BBB such that the

expected return of the portfolio is strictly higher than the expected return of stock AAA

nnn$)$ It is possible to construct a portfolio with positive weight in stock AAA and stock BBB such that the

volatility of the portfolio is strictly lower than the volatility of stock AAA