the better the properties of the estimator. In the Black-Litterman model, the global CAPM equilibrium provides this center of gravity. At the time of Fischer Black's suggestion, though, despite the fact that mean-variance optimization and versions of the CAPM equilibrium had both been well understood for more than 20 years, it was not at all obvious that what the portfolio optimizer needed was the incorporation of such an equilibrium. In fact, our first naive attempt to use the global equilibrium failed rather miserably. Rather than focus on expected excess returns as unknown quantities to be estimated, we simply tried to take a weighted average of investor-specified expected excess returns with the equilibrium values. We found, as we will show by example, that simply moving away from the equilibrium risk premiums in a naive manner quickly leads to portfolio weights that don't make sense. Further reflection on the nature of the problem led us to think about the uncertainty in the equilibrium risk premiums as well as the nature of information that the investors are trying to incorporate through their views. We also realized that it is essential to take into account the likely correlations among the expected returns of different assets. The estimator that we developed to take these issues into account eliminates the bad behavior of the optimization exercise and provides a robust framework for managing global portfolios. What we discovered, however, was not simply a better optimizer, but rather a reformulation of the investor's problem. In the context of Black-Litterman, the investor is not asked to specify a vector of expected excess returns, one for each asset. Rather, the investor focuses on one or more views, each of which is an expectation of the return to a portfolio of his or her choosing. We refer to each of these portfolios for which an investor specifies an expected return as a "view portfolio." In the Black-Litterman model, the investor is asked to specify not only a return expectation for each of the view portfolios, but also a degree of confidence, which is a standard deviation around the expectation. This reformulation of the problem can be applied more generally, and among other benefits has greatly facilitated the use of quantitative return forecasting models in asset management. In an unconstrained optimization context, the Black-Litterman model produces a very simple and intuitive result. The optimal portfolio is a weighted combination of the market capitalization equilibrium portfolio and the view portfolios.2 The sizes of the tilts toward the view portfolios are a function of both the magnitude and the confidence expressed in the expected returns embedded in the investor-specified views. In fact, the solution is so straightforward one might question whether the model is actually adding value. The answer is that most portfolio optimizations are not so simple. When there are benchmarks, constraints, transactions costs to consider, or other complications, the optimal portfolios are not so obvious ]See, for example, the literature on Bayes-Stein estimation, including C. Stein, "Inadmissabil-ity of the Usual Estimator for the Mean of a Multivariate Normal Distribution," Proceedings of the Third Berkeley Symposium on Probability and Statistics (Berkeley, CA: University of California Press, 1955), and Jorion, Philippe, "Bayes-Stein Estimation for Portfolio Analysis," Journal of Financial and Quantitative Analysis, September 1986. 2The mathematical derivation of these results is included in "The Intuition behind Black-Lit-terman Model Portfolios," by Guangliang He and Robert Litterman, Goldman Sachs Investment Management Research paper, December 1999.