Black-Litterman model
Encyclopedia
In Finance
the Black–Litterman model is a mathematical model
for portfolio allocation developed in 1990 at Goldman Sachs
by Fischer Black
and Robert Litterman, and published in 1992. It seeks to overcome problems that institutional investors have encountered in applying modern portfolio theory
in practice. The model starts with the equilibrium assumption that the asset allocation of a representative agent should be proportional to the market values of the available assets, and then modifies that to take into account the 'views' (i.e. the specific opinions about asset returns) of the investor in question to arrive at a bespoke asset allocation.
In principle Modern Portfolio Theory
(the mean-variance approach of Markowitz
) offers a solution to this problem once the expected return
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. In other words, composing a portfolio based only upon statistical measures of risk and returns yields simplistic results; these are known as unconstrained optimizations.
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 market's 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.
Finance
"Finance" is often defined simply as the management of money or “funds” management Modern finance, however, is a family of business activity that includes the origination, marketing, and management of cash and money surrogates through a variety of capital accounts, instruments, and markets created...
the Black–Litterman model is a mathematical model
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 not only in the natural sciences and engineering disciplines A mathematical model is a...
for portfolio allocation developed in 1990 at Goldman Sachs
Goldman Sachs
The Goldman Sachs Group, Inc. is an American multinational bulge bracket investment banking and securities firm that engages in global investment banking, securities, investment management, and other financial services primarily with institutional clients...
by Fischer Black
Fischer Black
Fischer Sheffey Black was an American economist, best known as one of the authors of the famous Black–Scholes equation.-Background:...
and Robert Litterman, and published in 1992. It seeks to overcome problems that institutional investors have encountered in applying modern portfolio theory
Modern portfolio theory
Modern portfolio theory is a theory of investment which attempts to maximize portfolio expected return for a given amount of portfolio risk, or equivalently minimize risk for a given level of expected return, by carefully choosing the proportions of various assets...
in practice. The model starts with the equilibrium assumption that the asset allocation of a representative agent should be proportional to the market values of the available assets, and then modifies that to take into account the 'views' (i.e. the specific opinions about asset returns) of the investor in question to arrive at a bespoke asset allocation.
Background
Asset allocation is the decision faced by an investor who must choose how to allocate their portfolio across a few (say six to twenty) asset classes. For example a globally invested pension fund must choose how much to allocate to each major country or region.In principle Modern Portfolio Theory
Modern portfolio theory
Modern portfolio theory is a theory of investment which attempts to maximize portfolio expected return for a given amount of portfolio risk, or equivalently minimize risk for a given level of expected return, by carefully choosing the proportions of various assets...
(the mean-variance approach of Markowitz
Markowitz
Markowitz is a surname and may refer to:* Deborah Markowitz, Vermont secretary of state* Harry Markowitz, a financial economist and Nobel Laureate* John Markowitz, professor of psychiatry at Weill Cornell Medical College...
) offers a solution to this problem once the expected return
Expected return
The expected return is the weighted-average outcome in gambling, probability theory, economics or finance.It isthe average of a probability distribution of possible returns, calculated by using the following formula:...
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. In other words, composing a portfolio based only upon statistical measures of risk and returns yields simplistic results; these are known as unconstrained optimizations.
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 market's 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.