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I'm reading about latency arbitrage in regards to direct exchange feeds vs. SIP feeds. SIP feeds are on average 1 millisecond slower than direct feeds, which allows HFTs to see an NBBO update before the SIP reflects that update.

All I'm seeing is that HFTs rely on ISOs to react to NBBO changes, and there's no arbitrage mechanism to actually lock in a risk-free profit. For example, suppose TSLA is currently trading \$200.00 bid at \$200.05 offer. A large buyer comes in and knocks out the \$200.05 offer, so the new best offer is now \$200.06. Knowing the next marketable buy order that comes in will be trading against the new \$200.06 offer, an HFT can send ISOs to sell/short TSLA at \$200.06, guaranteeing to be first in line to execute at the new price level. But what's the arbitrage mechanism to close out the trade? The HFT will have sold/shorted shares of TSLA at \$200.06, but it's really only an arbitrage if they have bought it at a lower price before sending the ISO or can guarantee to buy at a lower price in the future.

It seems like everyone is defining 'latency arbitrage' to be the informational advantage that those with lower latencies have, but really the definition of arbitrage is that you're making a risk-free profit.

Edit: Here's another (different) latency arbitrage example I found:

NBBO is determined by the SIP (consolidated) feed, which is about 1 ms slower than the direct feed from an exchange E. A HFT with a direct feed to E will detect, for e.g. the raising of the bid above the NBBO, before everyone else, and send a sell/short Intermarket Sweep Order to E to take out that bid. By the time the order arrives at E, E will have the official NBB (since SIP has finally been updated), and so the order is allowed to execute there, and will likely be filled because it is first-in-line.

In this second example, seems like the 'arbitrage' is that you're able sell using an ISO at the new higher bid. But arbitrage is really only arbitrage if you are guaranteed to have bought at a lower price earlier. If you're already an HFT market maker, how is selling with an ISO at the higher bid any better than selling at the offer with a limit order?

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Even though HFT traders can make good money on average thanks to their lower latency while trading on a single exchange, it seems like the term "Latency arbitrage" refers to in practice simultaneous purchases and sells on different exchanges. The arbitrage would come from short lived price differences that other traders are relatively too slow to exploit and eliminate. This academic paper investigates its size and here is an article discussing the paper.

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