Consider a capital market with only two risky assets A and $B.$ Their standard devia$-$

tions are $1$ and $2,$ respectively. There is no risk$-$free asset.

$($a$)$ When the correlation coefficient ${}_{AB}=0,$ construct a portfolio, whose variance

is strictly less than $1.[$Hint: you may want to try the portfolio that puts more

weights on the security with the lower standard deviation.$]$