No. Stock prices represent the markets approximation of the value of a share in the company, and its potential for future growth. Stocks can (sort of) be thought of as currency which represents companies rather than a government's reserve systems. A US dollar is worth $1 because you and the person you are giving it to expect it to be worth $1 (roughly) tomorrow. When you move stocks, it's a similar agreement on the value of what is being moved.

Of course, with stocks you have a much larger ability to measure your trust.