Modern Portfolio Theory and the Efficient Frontier

Harry Markowitz's Modern Portfolio Theory (MPT), developed in 1952, transformed investing from art to science by formalizing the relationship between risk, return, and diversification. The key insight: the risk of a portfolio is not the average of its components' risks — it depends critically on how those components move relative to each other, measured by correlation. Correlation coefficient (ρ) ranges from −1 (perfectly negatively correlated — assets move in exactly opposite directions) through 0 (uncorrelated — no systematic relationship) to +1 (perfectly positively correlated — assets move identically). The portfolio benefit of diversification comes from combining assets whose returns are not perfectly correlated. When assets are not perfectly correlated (ρ < 1), some of one asset's bad days are offset by the other asset's good days — portfolio volatility is lower than the weighted average of the individual volatilities. Portfolio expected return = weighted average of component expected returns: E(Rp) = w₁×E(R₁) + w₂×E(R₂) + ... Portfolio variance = w₁²σ₁² + w₂²σ₂² + 2w₁w₂ρ₁₂σ₁σ₂ (for a two-asset portfolio). The last term is the covariance contribution — when ρ is low or negative, this term reduces portfolio variance below the weighted average of individual variances. This is the mathematical underpinning of diversification: you can reduce portfolio risk (variance) without reducing expected return, simply by combining assets with low correlations.