= Robert Litterman
{c}
<Robert Litterman> developed the <Black-Litterman model> with <Fischer Black>. Their 1992 paper makes equilibrium <expected returns> a neutral starting point for <portfolio> modeling, then incorporates views that can differ in their confidence. The contribution addresses how uncertain inputs enter <modern portfolio theory>, rather than treating every proposed expected return as equally reliable.<Global Portfolio Optimization by Fischer Black and Robert Litterman>[Publisher abstract: neutral equilibrium reference and views with differing confidence]{ref}
An elementary <Bayesian inference> analogy illustrates the role of uncertainty. For an unknown quantity $\mu$ with <normal distribution> prior $N(m_0,s_0^2)$ and an independent observation error giving $y\mid\mu\sim N(\mu,s_y^2)$, <Gaussian conditional expectation> gives the posterior mean
$$
m=\frac{m_0/s_0^2+y/s_y^2}{1/s_0^2+1/s_y^2}.
$$
The more uncertain input receives less weight. This scalar example explains a modeling principle; the full <Black-Litterman model> treats related <expected returns> jointly, with a <covariance matrix> describing their uncertainty.
\Image[https://www.goldmansachs.com/images/migrated/our-firm/history/moments/150th-multimedia/1990-black-litterman-model/800x450.jpg]
{title=<Robert Litterman> with <Fischer Black> in 1994}
{description=Historical photograph hosted and identified by Goldman Sachs, linked externally.}
{source=https://www.goldmansachs.com/our-firm/history/moments/1990-black-litterman-model}
{width=400}
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