Back End Floating Feeling

Hey, I've got a question.

I've just got my white sedan and am in the break-in period. Since I'm trying to keep the rpm below 4k, I've been satisfying myself with some spirited driving in the twisties just to get used to the handling characteristics of the car.

I've noticed a tendency for the rear end to feel like is is floating to the outside of the corner when carrying speed in the turn. The tires aren't letting go... the rear of the car just feels light.

Here's the question. Is that normal to this car and is that why so many people suggest a rear sway bar? Hey, now that I mention it, the car does feel like it is swaying...hmmm.

Or could it be caused by the stock tires, which I have heard many people complain about?

I know that if I get better tires/rims and the sway bar, it would probably take care of the issue, but I would like to pinpoint the most exact way to fix this. Besides, I would like to wear out my stock tires a little more before replacing them.

Thanks in advance for any input.