Mean Variance Optimization

### Section: Mean-Variance Optimization Estimated study time: 45 minutes Content: Exam weight (2026 curriculum): Asset Allocation — 15–20% of the CFA Level III exam (common core); Portfolio Construction — 15–20% (common core). Source: CFA Institute Level III Exam page, fetched 2026-06-29. MVO is the quantitative engine underlying both of these topic areas, making it among the highest-priority technical topics at Level III. Asset allocation and portfolio construction together represent 30–40% of the common core, which is itself approximately 65–70% of the total exam. Mean-variance optimization (MVO) is the mathematical foundation of modern portfolio theory, originating with Harry Markowitz's 1952 paper. The core insight is that investors care about both expected return and variance (risk), and that diversification reduces portfolio variance without proportionally reducing expected return. The efficient frontier represents the set of portfolios that offer the maximum expected return for a given level of risk, or equivalently, the minimum risk for a given expected return. Inputs to MVO are expected returns, variances, and covariances (or correlations) for all assets in the opportunity set. These inputs are the primary source of MVO's practical weakness: small changes in expected return estimates cause large changes in portfolio weights, making the optimization highly sensitive to estimation error. This "error maximization" problem means MVO tends to produce concentrated portfolios that are optimal in-sample but perform poorly out-of-sample. Several techniques are used to improve MVO robustness. Resampling averages optimal portfolios across many simulated input sets to produce more stable, diversified results. The Black-Litterman model combines a market equilibrium prior (from CAPM) with the investor's own views…