macrocephalopod

Its a one way problem isn't it? How often does a stock rise in price and then get dropped from the index for a stock that just fell in price?

Stocks that get removed tend to be those that have decreased in market cap. Stocks that get added tend to be those that have increased. I'm unclear why you think this is a form of performance bias in the index.

To bias the performance of the index you would need to believe that the stocks being added would have different future expected returns than the stocks being removed.

This isn't about the index its about the performance of the individual stock. If a stock falls below $5 and then comes back above it later, your data set does not include the gain the stock received. I the above example, your data says stock lost 8%. In real life it was flat.

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.

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.

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.