If you trade shares and also hold shares for investing, then you can claim the 50% discount on the latter if held for more than one year, but not on the former. The former are treated as income not capital gains.
However, you cannot change the purpose of a particular purchase at a subsequent date. For instance, if you buy a batch of shares with the intention of trading them on the revenue account and for whatever reason don't sell them so that you end up owning them for more than a year, then you cannot simply decide that these are held in the capital account and claim the 50% CG discount on whatever gain you make when you eventually sell them.
How would the ATO know that you changed your mind on that batch you might well ask? They don't, but if audited you will have to convince them that you bought the shares with the intention of holding them in the capital account and if they don't believe you, you will be denied the 50% discount (and perhaps pay a penalty if they think you deliberately tried to mislead them)
So if you intend to both trade shares and hold some in the capital account (invest), then it is advisable that you clearly separate your trading from investing so that you don't run into problems with the ATO. One way to do this would be to have two separate accounts, either with the same broker or two different brokers and use one for trading and one for investing. If you do a lot of trading it might be worth setting up a company (which is a seperate legal entity to you) for trading which means your profits are only taxed at 30% max (27.5% if < $2M revenue) while held in the company, giving you more funds to play with. You can also pay yourself dividends from the company's profits in an amount that suits your own personal tax situation.