But there’s a problem here: a high-probability win doesn’t have to be profitable. Consider tossing a coin and winning $1 each times heads comes up, whereas losing $1 otherwise. You exit the game once you either have won $1 in total or you have reached 1000 coin tosses, whatever comes first. Then your probability of winning is 97.5% but one can show mathematically that your expected profit is zero. That is because the losses incurred in the 2.5% of losing cases overwhelm all possible gains. What’s worse, due to the small loss probability, you will likely underestimate your losses whenever you backtest your strategy against a reasonably long series of coin tossing data. You would simply see your PnL increasing over time.
Great post! I am curious though if ChatGPT has confessed it's love to you and tried to get you to leave your fiancée yet
Thanks for sharing.
But there’s a problem here: a high-probability win doesn’t have to be profitable. Consider tossing a coin and winning $1 each times heads comes up, whereas losing $1 otherwise. You exit the game once you either have won $1 in total or you have reached 1000 coin tosses, whatever comes first. Then your probability of winning is 97.5% but one can show mathematically that your expected profit is zero. That is because the losses incurred in the 2.5% of losing cases overwhelm all possible gains. What’s worse, due to the small loss probability, you will likely underestimate your losses whenever you backtest your strategy against a reasonably long series of coin tossing data. You would simply see your PnL increasing over time.
I guess something similar is going on here.
Cool idea! It would be interesting to calculate the average MAE between the signal bar and the high/low.
Could you link the episode of the podcast you appear in?
I'd really like to listen to it but I can't seem to find it in the recent ones