Black Litterman Model

Black Litterman Overview

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. 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 problem.¹

Please review either the following paper or video for a detailed overview of the Black Litterman Theory.

Detailed review of Black Litterman theory

How does PrimeSolve apply Black Litterman?
PrimeSolve applies the Black Litterman theory across both direct equities and managed funds. To use the Black Litterman tool simply apply your house views in our portfolio optimization tool. We require:
1. Nominate any stocks, industries or countries you expect to outperform.
2. Nominate the stocks, industries, and countries you expect to underperform relatively to outperforming strategies identified in step 1.
3. Specify an outperformance metric.
4. Nominate a confidence interval for the specified outperformance.

PrimeSolve tracks the industry weightings and country allocations for managed funds via Thomson Reuters Lipper data feeds. This allows us to arrive at an implied equilibrium returns based on the weighting each fund has applied to relevant sectors and/or countries.

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