Portfolio Possibilities Curve is a term from portfolio theory referring to all of the lowest-risk portfolios. At each level of return, this curve includes the one portfolio with the lowest risk. This represents the edge, or border, of the parabola containing all combinations of portfolios drawn from every risky asset. Graphically, it is depicted on a risk-return plot with risk on the x-axis and return on the y-axis.
The portfolio possibilities curve represents the whole curve where the efficient frontier is only the top half. The efficient frontier is more well known because it is the only solution a theoretical investor would choose because it shows the highest returning portfolio at every level of risk.