Deconstructing Black-Litterman Optimization: A Brief Overview


Having a strong research and development presence is an extremely important part of any serious investment management effort. The most important theoretical concept underlying portfolio management today – Modern Portfolio Theory (MPT) — is a work-in-progress.

Even though MPT won a Nobel Prize, it has demonstrated a strained relationship with practice. In 1992, the research department from Goldman Sachs produced a paper claiming some improvements to the original Markowitz Mean Variance optimization. The portfolio construction method was named after its authors, Fischer Black and Robert Litterman (B-L Optimization). Given its prestigious origin, ease of application, and use of subjective investor views, B-L has been a popular tool over the past decades and has been responsible for trillions of investment portfolio assets under management. However, when the research department at New Frontier took a closer look at B-L, it became apparent that B-L was flawed in its statistical, mathematical and financial approach.

In fact it inherits many of the flaws of Markowitz’s original algorithm because it can be characterized as a Markowitz optimization with particular inputs. It suppresses estimation error by nullifying it with reverse-engineered inputs. Research and development in a competitive environment is an important dynamic in furthering knowledge that can lift all boats. Thus, in 1998, Richard and Robert Michaud came out with a revolutionary improvement to the original MPT optimization methods. Not surprisingly, the new model is called Michaud Optimization.  Bottom-line, Michaud Optimization produces a better portfolio through its use of statistical computation to relax the error-free input assumptions and use the inputs more consistently with their inherent uncertainty. As an introduction to a new article “DECONSTRUCTION OF BLACK-LITTERMAN:  HOW TO GET THE PORTFOLIO YOU ALREADY KNEW YOU WANTED” published in the Journal Of Investment Management, the following are some of the main flaws in the Black-Litterman Optimization.

  • Estimation Error: First of all, using any statistical analysis based upon historical data has an inherent weakness: mean and variance can change over time, but only one observation is available at any given time, so historical data must be used to get reliable estimates. This means that inputs come with built-in error. Both the original Markowitz and Black-Litterman optimizations assume precise and accurate inputs. Misrepresented accuracy produces over- or under-weighting of assets. Given that estimation errors in both expected returns and covariances always exist in practice, resulting portfolios from either method could deliver extremely poor performance when true asset return probabilities do not match estimates. The Michaud Optimization, on the other hand, uses Monte Carlo re-sampling methods to address uncertainty in risk-return estimates by using averages of many outcomes of Markowitz MV Efficient Frontier portfolios covering a range of market assumptions, leaving investors covered for a variety of market conditions.
  • Inverse Returns: The Black-Litterman Optimization procedure calls for the use of inverse returns to neutralize estimation error. The method Black-Litterman uses is inconsistent with statistical inference and Bayesian analysis, because it also neutralizes any information entering through historical data through either the covariance matrix or the returns which were replaced by the inverse returns. The Michaud Optimization strictly adheres to modern statistical procedures and analysis, taking best advantage of all sources of available information.
  • Risk Aversion: The Black-Litterman Optimization produces a single optimal portfolio but does not take into account the investor sensitivity of risk aversion. Yes, the maximum Sharpe Ratio may represent the optimal ratio of reward to risk, but it does not accommodate the investor’s risk tolerance. Most professionals in the finance and investment industry believe (and practice) that the investor risk profile is a major consideration when establishing an investment portfolio. Extending the B-L optimization to a frontier of risk preferences does not give sensible portfolios for risks different from the maximum Sharpe ratio portfolio.

Research and development are integral to the continued health and development of the investment industry. Indeed, testing and critical evaluations are keys to improving and building upon previous insights and existing theories. For more information about New Frontier and the Michaud Optimization, go to www.newfrontieradvisors.com.

About the author

Dr. Richard Michaud is President and CEO of New Frontier Advisors, LLC.  He earned a PhD in Mathematics from Boston University and has taught investment management at Columbia University.  He is the author of Efficient Asset Management (1998, 2nd ed. 2008 with Robert Michaud), a CFA Research Monograph (1999) on Global Asset Management, and numerous academic and research articles available on www.ssrn.com and www.researchgate.com.  He is co-holder of four U.S. patents in portfolio optimization and asset management, a Graham and Dodd Scroll winner for his work on optimization, a former editorial board member of the Financial Analysts Journal, associate editor of the Journal Of Investment Management, and former director of the “Q” Group.

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