More detailed response:
> By "easily" do you mean it happens for some measurable number of small-money participants (of which there are many, of course)?
I mean a relatively sophisticated trader, one who actually understands markets and understands where he can take advantage of markets, can achieve very high returns if he takes advantage of his, you could call it 'agile' position.
For instance, it's quite common for a stock to gain 1-2 percent per day, and to go on a 10% rally within a week or two. Let's say I'm bullish on a stock. I'll wait for a 5% or so pullback, then watch it on a down day. I see a dip, I'll buy in. I could be up half a percent by day's end. Then, if I'm right, it'll rally up to 10% within 2 weeks.
If I'm investing an 'optimized' amount (ie. one that's small enough to unload quickly, but big enough to make commissions a no-factor), then I can make money on a half-percent move. I can be happy with 2%, and very happy with 5-10%. If you repeat this enough, and have a batting average of 60% or higher (ie. consistently just over half with a very disciplined strategy), the interest compounds when you sell one stock to buy another.
Let's add up numbers in 2 percent moves, times 10 trades. You wind up at ~122 dollars, or 22% percent up from your original amount. 50 trades, you're at 269 dollars. Over double. 50 trades isn't very much for a dedicated trader, and that's not even what you'd call 'day trading'. Compounding interest and math is fun, eh?
> Or do you possibly mean that you invest in 10 different stocks and one doubles?
That would be stupid. Investing isn't about shooting in the dark and hoping you hit something. It's about optimizing your return through solid principles, and not giving a shit about any single stock.
> There is no basis for returns to "go down as numbers go up", except if you are forgetting to average in the losses when the numbers were small. (Maybe because they are small they don't feel like they "count"?)
Volume is everything when trading. If your position in a single stock is too big, you'll have a hard time loading or unloading a position. When you get into managing large amounts of money, it gets more difficult to get in and out of positions, which affects how much of a return you can make.