finance Finance is the study and discipline of money, currency and capital assets. It is related to, but not synonymous with economics, the study of production, distribution, and consumption of money, assets, goods and services (the discipline of fina ...

, the Black–Litterman model is a

mathematical model A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in the natural sciences (such as physics, ...

for

portfolio allocation Portfolio optimization is the process of selecting the best portfolio (asset distribution), out of the set of all portfolios being considered, according to some objective. The objective typically maximizes factors such as expected return, and minimi ...

developed in 1990 at

Goldman Sachs Goldman Sachs () is an American multinational investment bank and financial services company. Founded in 1869, Goldman Sachs is headquartered at 200 West Street in Lower Manhattan, with regional headquarters in London, Warsaw, Bangalore, H ...

Fischer Black Fischer Sheffey Black (January 11, 1938 – August 30, 1995) was an American economist, best known as one of the authors of the Black–Scholes equation. Background Fischer Sheffey Black was born on January 11, 1938. He graduated from Harvard ...

and

Robert Litterman Robert Bruce Litterman (born 1951) is chairman of the Risk Committee and a founding partner of Kepos Capital in New York. Prior to Kepos Capital, Litterman spent 23 years at Goldman Sachs, where he was head of the Quantitative Resources Group i ...

, and published in 1992. It seeks to overcome problems that institutional investors have encountered in applying

modern portfolio theory Modern portfolio theory (MPT), or mean-variance analysis, is a mathematical framework for assembling a portfolio of assets such that the expected return is maximized for a given level of risk. It is a formalization and extension of diversificatio ...

in practice. The model starts with an asset allocation based on the equilibrium assumption (assets will perform in the future as they have in the past) and then modifies that allocation by taking into account the opinion of the investor regarding future asset performance.

Background

Asset allocation is the decision faced by an investor who must choose how to allocate their portfolio across a number of asset classes. For example, a globally invested pension fund must choose how much to allocate to each major country or region. In principle

(the mean-variance approach of Markowitz) offers a solution to this problem once the

expected return The expected return (or expected gain) on a financial investment is the expected value of its return (of the profit on the investment). It is a measure of the center of the distribution of the random variable that is the return. It is calculated ...

s and covariances of the assets are known. While modern portfolio theory is an important theoretical advance, its application has universally encountered a problem: although the covariances of a few assets can be adequately estimated, it is difficult to come up with reasonable estimates of expected returns. Black–Litterman overcame this problem by not requiring the user to input estimates of expected return; instead it assumes that the initial expected returns are whatever is required so that the equilibrium asset allocation is equal to what we observe in the markets. The user is only required to state how his assumptions about expected returns differ from the markets and to state his degree of confidence in the alternative assumptions. From this, the Black–Litterman method computes the desired (mean-variance efficient) asset allocation. In general, when there are portfolio constraints – for example, when

short sales In finance, being short in an asset means investing in such a way that the investor will profit if the Market value, value of the asset falls. This is the opposite of a more conventional "Long (finance), long" Position (finance), position, wh ...

are not allowed – the easiest way to find the optimal portfolio is to use the Black–Litterman model to generate the expected returns for the assets, and then use a mean-variance optimizer to solve the

constrained optimization In mathematical optimization, constrained optimization (in some contexts called constraint optimization) is the process of optimizing an objective function with respect to some variables in the presence of constraints on those variables. The obj ...

proble

References

Black F. and Litterman R.: Asset Allocation Combining Investor Views with Market Equilibrium, Journal of Fixed Income, September 1991, Vol. 1, No. 2: pp. 7-18

Black F. and Litterman R.: Global Portfolio Optimization, Financial Analysts Journal, September 1992, pp. 28–43

External links

Discussion
Guangliang He and Robert Litterman: The Intuition Behind Black-Litterman Model Portfolios

A. Meucci: The Black-Litterman Approach: Original Model and Extensions

Jay Walters: The Black-Litterman Model in Detail

Thomas M. Idzorek: A Step-By-Step Guide to the Black-Litterman Model - Incorporating user-specified confidence levels
Resources *Spreadsheet implementations:

*

*Applets:

{{DEFAULTSORT:Black-Litterman Model Financial models Investment Portfolio theories

Background

See also

References

External links