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From what I understood, this contribution is not about making stuff nanoseconds faster, but about how this pushes spreads down. Anyone doing any trading will be happier to see the spreads smaller, wouldn't he?

Note: by spreads I mean the difference between buy and sell prices. I don't know if there is a special word for it in this context.

Exactly. HFT reduces counterparty risk for market makers (because with HFT, it's much more likely that there will be a counterparty for any given trade). This enables the market makers to reduce their bid-ask spreads; the profit from the bid-ask spread is what covers the risk a market maker faces from their market clearing obligations.

Do you know of any data on the size of the spreads over time?

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