Bob Litterman

The Black-Litterman global asset allocation model provides a framework for combining market equilibrium with tactical views about investment opportunities. In order to understand the benefits of the model, it should be recognized that its development was motivated not at all by a belief that equilibrium provides useful short-term forecasts of returns. Rather, it was developed as a solution to a practical problem associated with portfolio optimization. As is well known, the standard mean-variance portfolio optimization discussed in Chapter 4 is not well behaved. Optimal portfolio weights are very sensitive to small changes in expected excess returns. Thus, the historical development of the Black-Litterman model began with a financial engineering question-"How can we make the standard portfolio optimizer better behaved?"-rather than, as developed in this book, as a natural extension of the global CAPM equilibrium.

The problem faced in 1989 in the fixed income research function at Goldman Sachs was a particularly badly behaved optimization exercise. We were advising investors with global bond portfolios, typically with some currency exposures. Many currencies, and most of the yield changes in bonds in the developed fixed income markets, have high correlations to each other. Changes in the forecasts of yields well below the precision with which any forecaster had confidence (for example, on the order of only a few basis points over a period of as much as six months into the future) would create major swings in optimal portfolio allocations. Moreover, it was virtually impossible, without significant constraints on both maximum and minimum holdings, to get portfolios that looked at all reasonable.

At the same time these portfolio optimization issues were being faced, Fischer Black had just finished his "Universal Hedging" paper on the global CAPM equilibrium. It was his suggestion that incorporation of the CAPM equilibrium into the mean-variance optimizer might make it better behaved. In retrospect, the suggestion perhaps seems obvious. It is well known that the properties of many statistical estimators can be improved by some shrinkage toward a neutral point that acts as a