Just provide evidence my dude. It's not hard. Where are you getting the idea from that "most people end up investing most of their money at the peak"...
I can give you an example of my APT experience. I bought most of my APT between $9 and $20... I topped up a small parcel at $70, so my average went from low $20s to mid $20s. Yes, I did top up as you suggested people do but since I'm paying $70 for APT (lets assume that was the peak), it still doesn't even remotely mean that most of my money was invested at the peak, quite the opposite.
This is just one example of course but it is far more likely that people invest this way rather than "invest most of their money at the peak". You're not providing evidence of your statement because there is none.. simple..
APT Price at posting:
$69.03 Sentiment: None Disclosure: Held
