If I buy a stock for say $1 and that stock goes up to $2, can I sell my initial investment being $1 and then buy back into the same stock when it goes back down to $1 over and over only using my initial investment to accumulate shares without paying any tax? I hope this makes sense.
Elaborating on kelsham's answer:
You buy 100 shares XYZ at $1, for a total cost of $100 plus commissions.
You sell 100 shares XYZ at $2, for a total income of $200 minus commissions.
Exclusive of commissions, your capital gain is $100 for this trade, and you will pay taxes on that. Even if you proceed to buy 200 shares XYZ at $1, reinvesting all your income from the sale, you still owe taxes on that $100 gain. The IRS has met this trick before.
Unfortunately, we don't know your country, but I'd guess "Not US" with the hint being your use of the word bugger in a comment.
Realized profits are taxed by all tax authorities I'm aware of, i.e. the Tax Man in every country. Annually, so that you can let the profits run during the year, and offset by the losses during that year.
The exception is within a qualified retirement account. Many countries offer accounts that will let you do just what you're suggesting, start with XXX number of Quatloos in your account, trade for decades, and only take the tax hit on withdrawal. In some cases there's an opportunity to fund the account post tax, and never pay tax again. But to repeat, this is with a retirement account, not the usual trading accounts.
If you buy for $1 and sell $1 when the price goes to $2, you would have sold only half of your initial investment. So your investment would now be worth $2 and you sell $1 leaving $1 still in the market.
This means you would have sold half your initial investment, making a profit of $0.50 on this half of your initial investment, and having to pay CGT on this amount.
I think what you're asking is,
Can I buy 1000 shares of the stock at $1. For $1000.
it goes up to $2, then sell 500 shares of the stock with proceeds of $1000, now having my original $1000 out of it, and still owning 500 shares.
And that not create a taxable event. Since all I did was take my cost basis back out, and didn't collect any gains.
And then I want to repeat that over and over.
Nope, not in the USA anyway. Each sale is a separate taxable event. The first sale will have proceeds of $1000 and a cost basis of $500, with $500 of capital gains, and taxes owed at the time of that sale.
The remaining stock will have a cost basis of $500 and proceeds of whatever you sell it for in the future.
The next batch of stock will have a cost basis of whatever you pay for it.
The only thing that works anything like the way you're thinking, is a Roth IRA... You can put your cost basis in, pull it back out, and put it back in again, all tax free. But every time your cost basis cycles in, that counts towed your contribution limits unless you do it fast enough to call it a rollover.