The Markowitz efficient set, also known as the efficient frontier, is a fundamental part of modern portfolio theory (MPT), developed by future Nobel laureate Harry Markowitz in 1952. It presents a set of portfolios with the highest expected returns for a given level of risk or, alternatively, the lowest risk for a certain amount of expected returns. At its heart, it seeks to answer basic questions facing any investor: how much in returns can I expect if I don’t want too much risk? And if I increase my risk tolerance, how much more in returns might I get? The portfolios in the Markowitz set are efficient because they offer, mathematically, the best balance of risk and reward.

Understanding the Markowitz Efficient Set

Harry Markowitz (1927-2023), the Nobel Prize-winning economist, is considered a founder of MPT. His article, “Portfolio Selection,” in the Journal of Finance in 1952, took up the challenge of showing how the returns of a group of investments in a portfolio are linked to risk, along with concepts like variance and covariance used to measure potential risk and returns.

Markowitz noted that investors focus on two things: risk and return. He thought that investors choose among options that optimally balance the two. Some seek the highest returns and thus will take on more risk; others can’t afford such risk and thus are willing to stomach less in potential returns. The best combination of investments in a portfolio can be charted along the “efficient frontier,” essentially a line on a graph that shows the highest possible returns you can expect from a portfolio for a specific level of risk.

Implementing the Markowitz Efficient Set

Because different combinations of assets have different levels of potential returns, the Markowitz efficient set is meant to show the best combinations to maximize returns at a chosen risk level. In this way, the Markowitz efficient set reveals how returns vary given the amount of risk assumed.

The Markowitz efficient set is represented on a graph with returns on the Y-axis and risk (standard deviation) on the X-axis. The efficient set lies along the frontier line, representing that the higher the risk, the greater the potential returns. The task is to construct a set of portfolios to yield the highest returns at a given level of risk.

Individuals have different levels of risk tolerance: some might stomach quite a bit of risk if it means greater rewards, while others are unwilling to take such chances. Moreover, you can’t assume you will be automatically rewarded with extra returns if you take greater risk. The set becomes inefficient when returns decrease at greater levels of risk. Once the risk reaches a certain point, there’s no increase in potential rewards (at one extreme, using your portfolio for lottery tickets), just as at the other end, once the risk gets so low, there’s no potential return (at the other extreme, keeping your money under your mattress).

Diversification in the Markowitz Efficient Set

At the core of a Markowitz efficient set is diversification of assets, which lowers portfolio risk. Diversification is the strategy of spreading investments across various types of assets to reduce the overall risk in your portfolio.

MPT is premised on the idea that different assets react differently to the same market conditions. Diversification is at the heart of MPT because it means you can take advantage of the returns volatile sectors offer if you wish, but you should keep that balanced with other kinds of assets that won’t react the same way. Some assets tend to move in the same direction, increasing or decreasing in value together (e.g., stocks in the same sector), while others tend to go in opposite directions (e.g., the value of gold and the U.S. dollar).

The relationship between how two assets move in relation to each other is measured by covariance. When assets have a lower covariance, they are more likely to move in the opposite direction, which lowers the risk of the portfolio.

Variance, meanwhile, measures how much an investment’s returns differ from their average over time, indicating their risk. High variance means your asset’s returns can fluctuate significantly, bringing greater risk, while lower variance suggests you’ll have more stable, predictable returns.

Given these principles, the efficient frontier of the Markowitz efficient set is curved, not straight, since these assets don’t move all in the same direction in the same market conditions.

The Bottom Line

The Markowitz efficient set is a mathematical concept introduced by Nobel Laureate Harry Markowitz in 1952 to represent the returns of a portfolio for given levels of risk. It is represented on a graph that charts portfolios or investments on a scale of return (y-axis) versus risk (x-axis). Portfolios that are below the efficient frontier are judged unable to provide enough return for the level of risk and vice versa. While relatively simple in graphic form, this turned out to be an important invention in finance and investments. The Markowitz efficient set continues to show why diversification is crucial for balancing risk and reward while managing your portfolio.