John: I don’t think Eliezer’s saying that a stock that has recently risen is now more likely to fall. Quite the opposite in fact. Any given stock should be about as likely to fall as to rise, at least if we weight by the amount of the rise. That is, if I hold a share of XYZ, which costs $100, and I anticipate a 99% chance that the stock will rise to $101 tomorrow, then I should also expect a 1% chance that the stock will drop to $1 tomorrow. Were that not true, the share would be worth nearly $101 right now, not tomorrow.
John: I don’t think Eliezer’s saying that a stock that has recently risen is now more likely to fall. Quite the opposite in fact. Any given stock should be about as likely to fall as to rise, at least if we weight by the amount of the rise. That is, if I hold a share of XYZ, which costs $100, and I anticipate a 99% chance that the stock will rise to $101 tomorrow, then I should also expect a 1% chance that the stock will drop to $1 tomorrow. Were that not true, the share would be worth nearly $101 right now, not tomorrow.
See also: Conservation of Expected Evidence