Your colleague, Donald Davis, is also studying for the CFA exam. He makes the following three statements listed below. State whether each statement is correct or incorrect and support your answer.

$1.$Active management is appropriate for large$-$cap stocks. Where managers can take big enough positions to capital on pockets of inefficiency$.$

$2.$Because the S&P $500$ index is price$-$weighted, outperforming stocks tend to have more and more influence on its value$.$

$3.$Institutional investors who want exposure to smaller capitalization stocks should employ a passive index vehicle, such as the Russell $2000$ index fund. The market for small$-$cap stock tends to be more efficient than the market for large$-$cap stocks and would provide more opportunities for investors to benefit from active management$.$