It is hard for actively managed funds to generate higher rates of return than passively managed index funds having similar levels of risk because

multiple choice $1$

actively managed funds have lower expenses, and arbitrage causes rates of return to equalize across similar assets.

actively managed funds have greater revenues, and arbitrage causes rates of return to diverge across similar assets.

actively managed funds have greater expenses, and arbitrage causes rates of return to equalize across similar assets.

actively managed funds have lower revenues, and arbitrage causes rates of return to diverge across similar assets.

A simple way for an actively managed fund to increase its average expected rate of return is to

multiple choice $2$

increase research expenditures.

become a passively managed fund, which is more attractive to investors trying to $$beat the market.$$

increase trading activities.

cut down trading activities that generate costs.