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If I see a Bid at 181.77 and and Ask at 181.78 for SPY and then immediately see a trade filled at 181.77 on BATS, then what can we conclude about market making activity? i.e At what price did the market maker buy from the seller and at what price did he sell to the buyer?

I thought since MM takes the other side of each trade, he bought at 181.78 and sold at 181.77 but obviously this is false since he is at a loss here.

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"MM" isn't one individual. It could be HFT or buyside execution. If it is execution, losing trades are consistent since they have a mandate from a client they need to execute with the objective of minimising transaction costs (not necessarily maximising profits). –  user2763361 Feb 11 at 18:38
    
Are you asking what is the fair (theoretical) price this market maker trades off? On the other note I think there's an error in your question. The MM bought at 181.77 not sold. –  derenik Feb 12 at 2:39
    
Oh this is a matter of confusion to me since a long time. The Bid and Ask is posted by the MM and not by other retail traders. –  Kaushik Feb 12 at 14:39

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Market making refers to an activity in the markets that provides a market for a given securities. Each market has different rules on market making (see LSE rules). However, I do not see a need for a market maker to fill at a loss necessarily, because he may warehouse the securities. That is, he may still hold securities that were bought at an even lower price and he may choose to sell these before he sells more expensive ones.

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Ok so in this case, he will sell from his warehouse and the sell order posted on the book will still remain unfilled? –  Kaushik Feb 11 at 20:10
    
I can't see why it would. But perhaps I do not, after all, understand your question. –  RndmSymbl Feb 11 at 21:00
    
If the market maker sold to the buyer from his own inventory, what happens to the original seller's Ask? Is it still on the book? Sorry for not being clear, I am still learning –  Kaushik Feb 11 at 21:14
    
I cannot answer this question very well. I believe it depends on the market rules in specific and the market makers judgement. I am not in particular familiar with BATS rules, but p. 69 of the BATS rules ( cdn.batstrading.com/resources/regulation/rule_book/…) make reference to two-sided operations. Therefore, I assume the ask would need to be taken by the market maker. –  RndmSymbl Feb 11 at 21:27

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