Essay regarding The Pure intuition Behind Black-Litterman Model Portfolios

Expense Management Division

The Intuition Behind Black-Litterman Model Portfolios

s In the following paragraphs and as each of our title implies, we display a method intended for understanding the instinct behind the Black-Litterman property allocation style. s To accomplish this, we employ examples to demonstrate the difference between the traditional meanvariance optimization method and the Black-Litterman process. We show that the mean-variance optimization process, although academically appear, can produce benefits that are extreme and not particularly intuitive. In contrast, we present that the optimum portfolios produced by the Black-Litterman process possess a simple, user-friendly property: в€’ The unconstrained optimal collection is the marketplace equilibrium profile plus a weighted sum of portfolios addressing an investor's views. в€’ The excess weight on a collection representing a view is great when the view is more bullish than the 1 implied by the equilibrium and other views. в€’ The fat increases as the trader becomes more bullish within the

view as well as when the entrepreneur becomes well informed about the view.

December 99

Goldman Sachs Investment Administration

Investment Management Research

Goldman Sachs Quantitative Resources Group

Guangliang This individual Robert Litterman (212) 357-3210 (212) 902-1677

Copyright 1999 Goldman, Sachs & Company. All privileges reserved. The info in this newsletter is for the private information which is not intended as an offer or solicitation to buy or perhaps sell any kind of securities. The knowledge in this newsletter is for the private information and really should not always be construed while financial suggestions and it is not really intended while an offer or perhaps solicitation to obtain or promote any investments. The sole purpose of this publication is to notify the reader about the pure intuition behind the Black-Litterman model portfolios and is also not intended as a solicitation for any Goldman Sachs products or services.


Purchase Management Analysis



The Instinct Behind Black-Litterman Model Portfolios

Goldman Sachs Investment Managing

Executive Synopsis

Since syndication in 1990, the Black-Litterman asset allowance model offers gained wide application in numerous financial institutions. While developed inside the original newspaper, the Black-Litterman model offers the flexibility to combine the market equilibrium with additional market opinions of the investor. In the Black-Litterman model, the user inputs numerous views or perhaps statements regarding the expected returns of arbitrary portfolios, and the model combines the views with equilibrium, producing both the set of expected comes back of resources as well as the ideal portfolio weights. In contrast to the Black-Litterman unit, in the classic mean-variance procedure the user inputs a complete pair of expected returns1, and the collection optimizer builds the optimal portfolio weights. However , users with the standard portfolio optimizers often find that all their specification of expected earnings produces output portfolio weight loads which may not really make sense (due to the intricate mapping among expected returns and stock portfolio weights and the absence of an organic starting point for the predicted return assumptions). In this article, we use illustrations to illustrate the difference between the traditional mean-variance optimization procedure and the Black-Litterman process. In so doing, we demonstrate how the Black-Litterman approach2 gives both a reference point pertaining to expected returning assumptions as well as a systematic approach to deviating from this point to express one's market opinions.

The Traditional MeanVariance Approach

The Markowitz formulation of the stock portfolio optimization problem is a brilliant quantification of the two basic objectives of investment: maximizing predicted return and minimizing risk. Having shaped the foundation of portfolio theory for the nearly half a century since its publication, this kind of framework provides stood the test of...

References: [1] Dark-colored, Fischer and Robert Litterman, Asset Portion: Combining Investor Views With Market Balance, Goldman, Sachs & Co., Fixed Cash flow Research, Sept 1990. [2] Black, Fischer and Robert Litterman, Global Portfolio Optimization, Financial Analysts Journal, internet pages 2843, September-October 1992. [3] Black, Fischer, Universal Hedging: Optimizing Currency Risk and Reward in International Fairness Portfolios, Economical Analysts Record, pages 16-22, July-August 1989. [4] Litterman, Robert, Hot-spots and Shrubs, The Diary of Profile Management, webpages 52-75, 12 , 1996. [5] Markowitz, Harry, Portfolio Assortment, Journal of Finance, pages 77-91, Drive 1952.


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The Intuition Behind Black-Litterman Unit Portfolios