Final answer:
A risk-free portfolio can theoretically be created from two stocks with a correlation coefficient of -1, where the returns of one stock perfectly offset the returns of the other, thus eliminating volatility.
Step-by-step explanation:
To demonstrate that a combination of two stocks creates a risk-free portfolio when the correlation coefficient (r) between the returns of stock A and B is -1, we must understand how correlation affects risk. With a correlation of -1, stock A's and stock B's returns move in exactly opposite directions. Thus, an investment strategy can be formed where any gain in one is offset by a loss in the other, resulting in a net return that is stable, which translates into no risk.
When forming a risk-free portfolio, an investor can allocate funds between A and B so that the gains and losses perfectly cancel each other out. For example, if stock A goes up by a certain percentage, stock B will go down by the same percentage. By investing equal amounts in both stocks, the overall value of the portfolio remains unchanged whatever the market condition, hence it is risk-free.