Is there a precise definition of what getting picked off means. In particular I want to check whether I have been picked off. How can I measure this quantitatively?
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Is there a precise definition of what getting picked off means
no, there exists no uniform metric defining what it means to get "picked off".
You will hear this term often in the context of high frequency trading and market making, both of which are heavily latency-constrained trading strategies. All that really means is that their success is conditional on receiving and parsing market data very quickly, and determining what they want to do very quickly as well.
The firms and institutions that engage in this kind of trading typically can (and will!) arb across multiple exchanges.
What does this mean for, e.g., a retail investor?
- retail investor has brokerage account and wants to buy X. say whatever brokerage service you have is displaying "real-time" quotes, and you see X's market (as far as you're concerned) which is \$100.20 @ \$100.35.
- retail investor sends order for 50 shares of X.
- now comes a HFT, and there are way too many differences to enumerate so we'll focus on the most relevant one: the HFT has a much better idea of the broader market's "opinion" on X; they're aggregating quotes from every single venue where X exists, including ones you don't even know exist.
- now the HFT also sees your order; BUY 50 shares of X @ $100.33. say they see a sell order for 50 shares on a different exchange, for \$100.29.
The HFT will: buy 50 shares for \$100.29 $\rightarrow$ sell 50 shares of X to retail investor for \$100.33 $\rightarrow$ profit is the difference between how much was paid between the exchange hops; $2.
But you never even saw that quote!
Given that getting "picked off" is not defined in any kind of empirical way, there does not exist any kind of certain way to know whether you were "picked off". I have only explained one (fairly trivial) scenario, however there are a multitude of other microstructure phenomenon to learn about that also play into this.