If what you said was true, no bank or hedge fund would run a trading desk. HFT captures just a slice of overall trading profits.
Which backs GPs point.
But occasion matters! Life isn't a nice continuous stream, it's lumpy. Circumstantial performance makes a difference - and that's why Greece could win the Euros despite probably not being a good football team.
Day trading is probably quite a hard discipline to follow, but that doesn't mean that everyone who does it is destined to fail.
Anecdotally 50% of marriages end in divorce but that apparently doesn't stop most people getting married...
Now, brownian motion is just a model for a stock price so YMMV, but still an interesting idea. An investor can pick whatever time horizon interests them and that they're most suitable to take advantage of; e.g. HF traders take advantage of low latencies, technical analysis for day traders, and macro / micro economic analysis for value.
As the OP said, there are these three ways to look at this and at the end of the day, all are gambling with different time-horizons and this is possible because of this scale-invariance property.
Loose = Not firmly fixed into place.
Lose = Cease to retain.
Lose is the verb you want to use here.
Individual day trading is less clear. Sure, you can get better at it to increase your odds but it seems like that isn’t enough to make those skilled people in aggregate make money.
The analogy in a casino is that perfect play means you’ll do better but there’s still house advantage and so on average perfect players will still lose money.
The claim to prove is that having some level of knowledge or skill makes the expected gains of day trading positive.
Big institutional traders are limited by risk, the fact that they are market makers for stocks in many cases, and the returns required need to be high, since their salaries are pretty ridiculous. Because of this, the fact that you're generally worse than them isn't a dealbreaker, just find a mid volume niche and learn it really well, then trade around general market volatility.
It's true that you will not outperform HFTs consistently. But that's fine, you don't have to outperform them to make money. That's because the stock market is not just you and the HFTs, there are hundreds of thousands of other traders.
If there's enough liquidity, you and the HFT can make the exact same trade and have the exact same profit (percentage). The HFT is not necessarily against you. You might buy low and sell high to an HFT, and the HFT might sell even higher and make additional profit. Again, you both made money and weren't against each other.
Its payment for order flow which is earning off the spread while also keep it tight and liquidity in the market.
I’m not sure if my answer is good enough but the volatility is always there to exploit.
The only single stock investments I have came from employment, either through RSUs or employer sponsored stock buying programs. RSUs are just coming to you, and why would I not take stock at 50% discount?
The only exception would be money I don't need. So gambling, as I don't care if I loose it or not. But usually I do other stuff with that money.