No
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That's a bias because there is no way for the opposite to occur. And this isn't about momentum or mean reversion, its just about randomness.
There’s no bias. The data doesn’t include moves from $4.80 to $5.20 but it also doesn’t include equally likely moves from $4.80 to $4.40. Adding or dropping stocks based on their past price moves can’t introduce a bias unless future price moves are correlated with past moves.
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This could all be simulated with a portfolio of random "coins" to find out.https://twitter.com/goldstein_aa/status/1372308799911047177 …
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You definitely could, although you don’t need to do that because you can reason mathematically about the behaviour of coin flips.
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If this bias existed then it would be trivially easy to make money by shorting stocks that were just above the price level and closing when the dropped below it, and only reopening the short when they came back above the price level.
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momentum factor is fake news?
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If you drop stock because it fell, and add a stock because it rose, then there is a bias in the data you collected. There will be more losses than gains in the data because you added it into your set after that happened.
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No, absolutely not. If you drop *future* observations after a fall or add *future* observations after a rise, there is no bias. It would induce a bias if you didn’t include the -ve return that took a stock below $5, or you *did* include the +ve return that took it above $5.
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