Consider the following market: ‘I roll a d10 once per day. Will I roll a 0 within the first 10 days from when this market starts?’.
Now consider what happens if I don’t actually roll a 0:
Day 0, this market’s value is ~65% Day 1, this market’s value is ~61% Day 2, this market’s value is ~57% Day 3, this market’s value is ~52% Day 4, this market’s value is ~47% Day 5, this market’s value is ~41% Day 6, this market’s value is ~34% Day 7, this market’s value is ~27% Day 8, this market’s value is ~19% Day 9, this market’s value is ~10% Day 10, this market’s value is ~0%
The market is purely rational, and yet the market shows a monotonic decrease over time (effectively, due to survivorship bias). What am I missing here, that this sort of monotonic movement is unexpected?
As an aside, I am also surprised why people seem to consider this unexpected for financial markets and stocks.
If a company has an X% chance of ruin / day over a fixed time period, you end up with exactly the same sort of rational monotonic movement so long as said ruin doesn’t happen.
You see this sort of thing with acquisitions. Say company A is currently priced at $100, and company B announces that it’s acquiring A for $200 per share. A will jump up to something like $170 per share, and then slowly increase to $200 on the acquisition date. The $30 gap is there because there’s some probability that the acquisition will fall through, and that probability decreases over time (unless it actually does fall through, in which case the price drops back down to ~$100).
Consider the following market: ‘I roll a d10 once per day. Will I roll a 0 within the first 10 days from when this market starts?’.
Now consider what happens if I don’t actually roll a 0:
Day 0, this market’s value is ~65%
Day 1, this market’s value is ~61%
Day 2, this market’s value is ~57%
Day 3, this market’s value is ~52%
Day 4, this market’s value is ~47%
Day 5, this market’s value is ~41%
Day 6, this market’s value is ~34%
Day 7, this market’s value is ~27%
Day 8, this market’s value is ~19%
Day 9, this market’s value is ~10%
Day 10, this market’s value is ~0%
The market is purely rational, and yet the market shows a monotonic decrease over time (effectively, due to survivorship bias). What am I missing here, that this sort of monotonic movement is unexpected?
As an aside, I am also surprised why people seem to consider this unexpected for financial markets and stocks.
If a company has an X% chance of ruin / day over a fixed time period, you end up with exactly the same sort of rational monotonic movement so long as said ruin doesn’t happen.
You see this sort of thing with acquisitions. Say company A is currently priced at $100, and company B announces that it’s acquiring A for $200 per share. A will jump up to something like $170 per share, and then slowly increase to $200 on the acquisition date. The $30 gap is there because there’s some probability that the acquisition will fall through, and that probability decreases over time (unless it actually does fall through, in which case the price drops back down to ~$100).