In 1952, Harry Markowitz published a 14-page paper that would win a Nobel Prize: the insight that what matters for portfolio risk is not individual volatility, but how assets move together. By combining assets with low or negative correlations, investors can achieve a given expected return with LESS risk than any single asset. This is the mathematical proof that diversification is the only free lunch in investing.

Portfolio return = weighted average of individual returns. But portfolio risk is NOT a weighted average — it's lower when correlation ρ < 1. Portfolio variance: σ²_p = w₁²σ₁² + w₂²σ₂² + 2w₁w₂σ₁σ₂ρ. The efficient frontier is the set of portfolios with minimum variance for each level of expected return. The tangency portfolio has the highest Sharpe ratio = (Rp − Rf) / σ_p — the best risk-adjusted return.