Business, Legal & Accounting Glossary
The efficient frontier is the curve along all market securities which delivers the highest returns for the lowest risk. Any investment below the dotted line in the image (right) will deliver lower returns for the same amount of risk and is therefore not ideal.
Investing on the right (upper) side of the frontier means using leverage, and of course, means higher risk.
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 one year is typically assumed. Today’s values for all available risky investments 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 available instruments.
The notion of “optimal portfolio” can be defined in one of two ways:
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 that is obtained from the other. That set of optimal portfolios is called the efficient frontier. This is illustrated in Exhibit 1:
Exhibit 1: For every point in the achievable region, there will be at least one portfolio that can be constructed from available risky assets that have the volatility and expected return corresponding to that point. The efficient frontier is the orange curve that runs along the top of the achievable region. Portfolios on the efficient frontier are optimal in both the sense that they offer a maximal expected return for some given level of risk and minimal risk for some given level of expected return. For example, the indicated portfolio is optimal in the sense of having the maximum expected return possible at 15% volatility. It is also optimal in the sense of having the minimum volatility possible for a 9% expected return.
In Exhibit 1, the green region on the right corresponds to the achievable region in the risk-return space. For every point in that region, there will be at least one portfolio constructible from available risky investments that have the volatility and expected return corresponding to that point. Outside the achievable region is the unachievable region. No portfolios can be constructed from available risky assets corresponding to points in that region.
The orange 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 that are most highly diversified. Less diversified portfolios tend to be closer to the middle of the achievable region.
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This glossary post was last updated: 3rd March, 2022 | 0 Views.