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If a market maker is making profit in a considerably enough period, then does it mean that the clients that bought/sold from/to the market maker lost money?

If so, is it possible that market makers can make more profit by leveraging their clients' trades by reversing? Is there such a concept in the literature?

Thanks

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If you are market making equities or futures you tend to make your profits over the short term by flipping your inventory. So if I'm showing 3.00 bid at 3.01 ask on a stock I'm going to tend to flip it pretty quickly for 0.01 profit. The guys that bought and sold from me may make/lose money depending on the length of their holding period and market direction. Our profits are generally not related.

If I'm making markets in options I will be delta hedged and thinking in volatility terms. I may show a market of 3.00 bid at 3.05 ask in an option but what this really corresponds to is probably something like 20% implied vol bid at 22% implied vol ask. Since I'm going to delta hedge and try to eliminate directional exposure to the underlying, I'm really trying to collect that implied volatility bid-ask spread edge. The guys that buy and sell from me probably don't delta hedge. So if they buy the call from me at 3.05, the underlying may in fact go up (he profits on it) but the realized volatility is only 20% and (since I'm delta hedged) I profit as well. So again, our profits are not necessarily related in the way you described.

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Not usually done. There may be a few marketmakers who also make money by reversing the customers trades (for example some retail FX marketmakers), but this is risky because it requires taking a position in the underlying. A pure market maker avoids this exposure by keeping inventory low, getting rid of stock he buys by selling it to someone else as soon as possible. So these are two very different ways of making money which should not be mixed up in our minds (1) marketmaking (2) position taking based on customer trades. (Different risks, different success factors, different business model).

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Actually I think it is more case for the opposite. As a market-maker I regularly priced and executed trades for large hedge funds: Brevan-Howard, Pimco, Bluecrest etc. Being in a position to see their executed flow allows you to take a view on whether you think they are correct or not, either in establishing new positions or taking-profit or stopping out of existing positions. Large hedge funds have dedicated research and resources to analyse markets so the outcome of that analysis can be quite valuable, particularly if the fund is consistently profitable.

Of course, you have to prioritise the execution of the customers order, but after that there are no restrictions on how to position your own book in anticipation of new orders or potentially new market movements within the scope of your risk limit.

Of course the other answers relating to pure market-maker activity nicely document the difference between market-making and proprietary trading

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