21) Profitable trading implies a worldview that is more aligned with reality than that of the market’s dollar weighted average participant.
This isn’t true, and it’s easy see by thinking about what causes profitable trading. Profitable trading occurs when your novel information is valuable.
Suppose there is a relatively efficient market in some sports event. The market is calibrated. ie if the market price says something happens 10% of the time, it does happen 10% of the time and also high resolution, as in if the “true” probability of an event is 40% the market is pricing within a small margin of error of this value.
Suppose some trader comes along, who is wildly badly calibrated. They think that if it’s raining the home team will win 100% of the time. Imagine also that it’s true that rain favours the home team by a small amount and this isn’t accounted for in the market price. (So the market price is some probability-weighted rain/not-rain price). Clearly rain shouldn’t affect the prices much, since the market has high resolution, it just hasn’t discovered the rain effect yet.
Then our trader, who systematically bets on the home team if it’s raining, will:
Be profitable (assuming they’re small enough not to move the market and betting sensibly relative to their bankroll)
Have a much less aligned view of reality than the market.
You bring up a good point that profitable trading doesn’t imply a globally better calibrated worldview, just a locally better calibrated one.
In your example:
If someone thinks that if it’s raining, the home team will win 100% of the time, then they will bet too much size.
Betting “sensibly relative to their bankroll” is 100% of your bankroll if you truly think the chance of something occurring is 100%.
Revealed belief vs. Preferred belief.
100% + size accordingly ⇒ eventual ruin via ergodicity
100% + size small ⇒ they don’t actually believe 100%; their behavior encodes meta-uncertainty, and optimal sizing assuming long run profitability converges to the true conditional edge after costs.
This isn’t true, and it’s easy see by thinking about what causes profitable trading. Profitable trading occurs when your novel information is valuable.
Suppose there is a relatively efficient market in some sports event. The market is calibrated. ie if the market price says something happens 10% of the time, it does happen 10% of the time and also high resolution, as in if the “true” probability of an event is 40% the market is pricing within a small margin of error of this value.
Suppose some trader comes along, who is wildly badly calibrated. They think that if it’s raining the home team will win 100% of the time. Imagine also that it’s true that rain favours the home team by a small amount and this isn’t accounted for in the market price. (So the market price is some probability-weighted rain/not-rain price). Clearly rain shouldn’t affect the prices much, since the market has high resolution, it just hasn’t discovered the rain effect yet.
Then our trader, who systematically bets on the home team if it’s raining, will:
Be profitable (assuming they’re small enough not to move the market and betting sensibly relative to their bankroll)
Have a much less aligned view of reality than the market.
,
You bring up a good point that profitable trading doesn’t imply a globally better calibrated worldview, just a locally better calibrated one.
In your example:
If someone thinks that if it’s raining, the home team will win 100% of the time, then they will bet too much size.
Betting “sensibly relative to their bankroll” is 100% of your bankroll if you truly think the chance of something occurring is 100%.
Revealed belief vs. Preferred belief.
100% + size accordingly ⇒ eventual ruin via ergodicity
100% + size small ⇒ they don’t actually believe 100%; their behavior encodes meta-uncertainty, and optimal sizing assuming long run profitability converges to the true conditional edge after costs.