Black–Litterman

Markowitz optimization with raw mean estimates produces unstable portfolios. The Black-Litterman model fixes this by starting from market-implied equilibrium returns (reverse-engineered from current market weights) and Bayesian-updating them with your own views.

The implied equilibrium return is $\Pi = \delta\, \Sigma\, w_{\text{mkt}}$ where $\delta$ is risk aversion. Treat this as a prior. Specify views — opinions like "asset A will outperform asset B by $2\%$" — with associated confidence. The posterior mean is a weighted average of $\Pi$ and your views, weighted by their relative precisions.

The result is portfolios that tilt toward your views without exploding away from market weights. When you have no views, you get the equilibrium portfolio. As you express more confident views, the optimization tilts more aggressively.

Black-Litterman is the standard for institutional active managers because it produces stable, intuitive portfolios that are easy to explain and that automatically degrade gracefully when views are weak.