This chapter shows the cases that AMAFMMs investigated active and passive funds. The first one investigated the effects of patient and impatient investors on market price formation and showed that the patient investors traded frequently only in the rare situation that a market became unstable and inefficient due to the market price getting away from the fundamental price. The last one investigated the effect of increasing horizontal shareholding with index funds on competition and market prices and showed that even when the holding ratio of index funds is not that high, the funds lessen competition.