Blacklitterman.Org an independent web site with a thorough coverage of the Black–Litterman model, maintained by J.Idzorek: A Step-By-Step Guide to the Black-Litterman Model - Incorporating user-specified confidence levels Jay Walters: The Black-Litterman Model in Detail.Meucci: The Black-Litterman Approach: Original Model and Extensions Guangliang He and Robert Litterman: The Intuition Behind Black-Litterman Model Portfolios.and Litterman R.: Global Portfolio Optimization, Financial Analysts Journal, September 1992, pp. 28–43 JSTOR 4479577 and Litterman R.: Asset Allocation Combining Investor Views with Market Equilibrium, Journal of Fixed Income, September 1991, Vol. Markowitz model for portfolio optimization.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 problem. From this, the Black–Litterman method computes the desired (mean-variance efficient) asset allocation.
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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. Asset allocation is the decision faced by an investor who must choose how to allocate their portfolio across a number of asset classes. 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.īlack–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. This holds true for the larger portion of occa-sions when modifying key input variables such as transaction costs, risk aversion, certainty level and time horizon. In principle Modern Portfolio Theory (the mean-variance approach of Markowitz) offers a solution to this problem once the expected returns and covariances of the assets are known. For example, a globally invested pension fund must choose how much to allocate to each major country or region. Asset allocation is the decision faced by an investor who must choose how to allocate their portfolio across a number of asset classes.
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