### What Is the Markowitz Efficient Set?

The Markowitz efficient set is a portfolio with returns that are maximized for a given level of risk based on mean-variance portfolio construction. The efficient solution to a given set of mean-variance parameters (a given riskless asset and a given risky basket of assets) can be plotted on what is called the Markowitz efficient frontier.

### Understanding Markowitz Efficient Set

Harry Markowitz (1927 - ), a Nobel Prize-winning economist who now teaches at the Rady School of Management of the University of California at San Diego, is considered a father of modern portfolio theory. His article, "Portfolio Selection," which appeared in the *Journal of Finance* in 1952, interwove the concepts of portfolio returns, risk, variance, and covariance. Markowitz explained that "since there were two criteria, risk and return, it was natural to assume that investors selected from the set of Pareto optimal risk-return combinations." Known as the Markowitz efficient set, the optimal risk-return combination of a portfolio lies on an efficient frontier of maximum returns for a given level of risk based on mean-variance portfolio construction.

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 line (frontier line) where increased risk is positively correlated with increasing returns, or another way of saying this is "higher risk, higher returns," but the key is to construct a set of portfolios to yield the highest returns at a *given level of risk*. Individuals have different risk tolerance levels, and therefore these portfolio sets are subject to various returns. Moreover, investors cannot assume that if they assume greater amounts of risk, they will be automatically rewarded with extra returns. In fact, the set becomes inefficient when returns decrease at greater levels of risk. At the core of a Markowitz efficient set is diversification of assets, which lowers portfolio risk.