What is Mean-Variance Analysis?
Mean-variance analysis, introduced by Harry Markowitz in 1952, is the mathematical core of modern portfolio theory. It takes expected returns (means), risks (variances/standard deviations), and correlations between assets as inputs, then calculates the asset allocation that maximizes return for a given risk level. This work earned Markowitz the 1990 Nobel Prize in Economics.
The Efficient Frontier
The efficient frontier is the curve on a risk-return graph connecting all optimal portfolios. Portfolios on this curve offer the highest return for their risk level or the lowest risk for their return level. Any portfolio below the frontier is suboptimal because a better risk-return combination exists. The tangent point where a line from the risk-free rate touches the frontier identifies the theoretically optimal risky portfolio.
Limitations and Practical Value
The framework's main weakness is sensitivity to input estimates. Small changes in expected returns or correlations can dramatically shift the optimal allocation. Returns are assumed to follow normal distributions, but real markets exhibit fat tails with more extreme events than predicted. Despite these limitations, mean-variance analysis fundamentally changed investing by mathematically proving that diversification reduces risk and by providing a rigorous framework for thinking about the risk-return tradeoff.