Efficient Frontier

Explained:

The efficient frontier was first defined by Harry Markowitz in his groundbreaking (1952) paper that launched portfolio theory. That theory considers a universe of risky investments and explores what might be an optimal portfolio based upon those possible investments.

Consider an interval of time. It starts today. It can be any length, but a one-year interval is typically assumed. Today's values for all the risky investments in the universe are known. Their accumulated values (reflecting price changes, coupon payments, dividends, stock splits, etc.) at the end of the horizon are random. As random quantities, we may assign them expected returns and volatilities. We may also assign a correlation to each pair of returns. We can use these inputs to calculate the expected return and volatility of any portfolio that can be constructed using the instruments that comprise the universe.

The notion of "optimal" portfolio can be defined in one of two ways:

For any level of volatility, consider all the portfolios which have that volatility. From among them all, select the one which has the highest expected return.
For any expected return, consider all the portfolios which have that expected return. From among them all, select the one which has the lowest volatility.

Each definition produces a set of optimal portfolios. Definition (1) produces an optimal portfolio for each possible level of risk. Definition (2) produces an optimal portfolio for each expected return. Actually, the two definitions are equivalent. The set of optimal portfolios obtained using one definition is exactly the same set which is obtained from the other. That set of optimal portfolios is called the efficient frontier. This is illustrated in Exhibit 1:

Efficient Frontier
Exhibit 1

The green region corresponds to the achievable risk-return space. For every point in that region, there will be at least one portfolio that can be constructed and has the risk and return corresponding to that point. The efficient frontier is the gold curve that runs along the top of the achievable region. Portfolios on the efficient frontier are optimal in both the sense that they offer maximal expected return for some given level of risk and minimal risk for some given level of expected return.

In Exhibit 1, the green region corresponds to the achievable risk-return space. For every point in that region, there will be at least one portfolio constructible from the investments in the universe that has the risk and return corresponding to that point. The yellow region is the unachievable risk-return space. No portfolios can be constructed corresponding to the points in this region.

The gold curve running along the top of the achievable region is the efficient frontier. The portfolios that correspond to points on that curve are optimal according to both definitions (1) and (2) above.

Typically, the portfolios which comprise the efficient frontier are the ones which are most highly diversified. Less diversified portfolios tend to be closer to the middle of the achievable region.