An efficient portfolio is one that provides the greatest expected return for a given level of risk, or equivalently, the lowest risk for a given expected return.

The science of risk-efficient portfolios is associated with a couple of Nobel laureates named Harry Markowitz and Bill Sharpe.

Suppose you have data for a collection of securities (like the S&P 500 stocks, for example), and you graph the return rates and standard deviations (a statistical measure of the historical volatility of a portfolio). Markowitz showed that you get a region bounded by an upward-sloping curve, which he called the efficient frontier.

It's clear that for any given value of standard deviation, you would like to choose a portfolio that gives you the greatest possible rate of return; so you always want a portfolio that lies up along the efficient frontier, rather than lower down, in the interior of the region. This is the first important property of the efficient frontier: it's where the best portfolios are.