Modern Portfolio Theory and Mean-Variance Optimization › Modern Portfolio Theory and Mean-Variance Optimization
Quantitative FinanceAll chapters Modern Portfolio Theory and Mean-Variance Optimization › Modern Portfolio Theory and Mean-Variance OptimizationOne section · Sections in this chapter1 / 12 ↓
Reading tools Definitions & inline links
Choose your expertise level to adjust how many terms are explained. Beginners see more tooltips, experts see fewer to maintain reading flow. Hover over underlined terms for instant definitions.
Article links
Make inline references clickable
In 1952, Harry Markowitz published "Portfolio Selection," developing a foundational mathematical framework for mean-variance portfolio selection. Investors already recognized risk and diversification; Markowitz made the relationship between portfolio risk, individual asset risks, and covariances operational.
In the mean-variance framework, investors prefer higher expected return and lower variance, all else equal. Portfolio risk is measured by return variance or standard deviation. Efficient portfolios offer undominated risk-return combinations; minimizing variance at an arbitrary exact target can also produce portfolios on the inefficient lower branch.
This chapter develops the mathematical machinery of mean-variance optimization from first principles. We'll see how diversification arises naturally from the mathematics of combining assets with less-than-perfect correlation, and we'll implement practical algorithms for finding optimal portfolios. The framework we develop here supplies the covariance and mean-variance tools used in CAPM and factor models. The next two chapters in Part IX cover CAPM and multi-factor models, respectively.