Trading in altcoins can be started even at 0.001btc but that kind of trading doesnt worth any think,the minimum amount i say should be 0.25btc reserved for that.Its not neccessary to use them all at once,must that much must be in reserve.
even with 0.001 bitcoin you can make a good profit out of it if you can manage to always get profit,it's indeed will be cut off by the fees but only small percents so it's not going to be a problem,it's worth trying to be honest
Certain exchanges indeed allow you to buy and sell with amounts as low as 0.001BTC, but this is an amount only used by people that are either new to trading, or people that put it into what seems to be a dead altcoin in the hope that it explodes in value.
You can have some decent luck a few times, but you can't constantly depend on luck when you try to multiply such a low amount. It's a waste of time and effort.