finance Finance refers to monetary resources and to the study and Academic discipline, discipline of money, currency, assets and Liability (financial accounting), liabilities. As a subject of study, is a field of Business administration, Business Admin ...

, the Black–Litterman model is a

mathematical model A mathematical model is an abstract and concrete, abstract description of a concrete system using mathematics, mathematical concepts and language of mathematics, language. The process of developing a mathematical model is termed ''mathematical m ...

for portfolio allocation developed in 1990 at

Goldman Sachs The Goldman Sachs Group, Inc. ( ) is an American multinational investment bank and financial services company. Founded in 1869, Goldman Sachs is headquartered in Lower Manhattan in New York City, with regional headquarters in many internationa ...

by Fischer Black and Robert Litterman. 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. Attilio Meucci (2010). https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1117574 he Black-Litterman Approach: Original Model and Extensions/ref>

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 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 ...

problem.

Literature

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References

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
Implementation

(Excel)
Implementing Black-Litterman asset allocation model
(Excel)

(Python)

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

Background

See also

Literature

References

External links