## Background

The idea of mean-variance analysis to choose an optimal portfolio was first introduced by Harry M. Markowitz in 1952, in a *Journal of Finance* article titled "Portfolio Selection."^{1} Markowitz later expanded his theory to include different portfolio scenarios and various mathematical models. His most recent book, published in 1989, is titled Mean-variance Analysis in Portfolio Choice and Capital Markets.

## Assumptions

The basic assumption of **Mean Variance Analysis** is that investors want greater returns (higher means) and less risk (lower variances).

Another assumption that dominates the theory of mean variance analysis, and leads to the development of the Capital Asset Pricing Model (CAPM), is that all transactions occur without friction.

This is to say: there are no transaction costs, there are no broker fees, there are no tax consequences, there are no commissions, there are plenty of buyers and sellers, the buying and selling occurs instantaneously, and the markets are not affected by the buying and selling. In reality, the assumption of "frictionless" financial markets are not realistic, but allow the theory to be employed.

## Plotting

Plotting return versus risk, or mean return versus Standard Deviation of Return, an efficiency frontier can be developed based on percentages invested in the securities that compose a portfolio. This is much like any plotted frontier from economics. The greatest tradeoff between risk/return (the most efficient portfolio investment) is found on the frontier. In this case, the efficiency frontier shows the greatest return for a given level of risk.

The benefit of Mean Variance Analysis comes from identifying the perfect mix of portfolio investments, risk-free and risky, that will result in returns on the boundary of the frontier, thus optimizing an investors desire for higher returns while limiting the risk.