Gus is considering two portfolios:a$.$

$1)$ Portfolio A with a return of $12\%$ and a standard deviation of $20\%,$ and

$2)$ Portfolio B with a return of $6\%$ and a standard deviation of $10\%.$

Which of the following statements are correct about portfolio return and risk?

a$.$ If the correlation between A and B is $1\mathrm{.}0,$ then the standard deviation of a $50/50$ portfolio will be the same as an $80/20$ portfolio.

b$.$ At a correlation of $-1,100\%$ of the portfolio invested in B will generate the lowest portfolio standard deviation.

c$.$ Both a and b are correct.

d$.$ Neither a or b is correct.