The Intuition Behind Black-Litterman Model Portfolios
Investment Management Division
The Intuition Behind Black-Litterman Model Portfolios s In this article and as our title suggests, we demonstrate a method for understanding the intuition behind the Black-Litterman asset allocation model. s To do this, we use examples to show the difference between the traditional meanvariance optimization process and the Black-Litterman process. We show that the mean-variance optimization process, while academically sound, can produce results that are extreme and not particularly intuitive. In contrast, we show that the optimal portfolios generated by the Black-Litterman process have a simple, intuitive property: − The unconstrained optimal portfolio is the market equilibrium portfolio plus a weighted sum of portfolios representing an investor’s views. − The weight on a portfolio representing a view is positive when the view is more bullish than the one implied by the equilibrium and other views.
− The weight increases as the investor becomes more bullish on the
view as well as when the investor becomes more confident about the view.
December 1999
Goldman Sachs Investment Management
Investment Management Research
Goldman Sachs Quantitative Resources Group
Guangliang He Robert Litterman (212) 357-3210 (212) 902-1677
Copyright 1999 Goldman, Sachs & Co. All rights reserved. The information in this publication is for your private information and is not intended as an offer or solicitation to buy or sell any securities. The information in this publication is for your private information and should not be construed as financial advice and it is not intended as an offer or solicitation to buy or sell any securities. The sole purpose of this publication is to inform the reader about the intuition behind the Black-Litterman model portfolios and is not intended as a solicitation for any Goldman Sachs product or service.
______________________________________________
Investment Management Research
1
The Intuition Behind Black-Litterman Model Portfolios s In this article and as our title suggests, we demonstrate a method for understanding the intuition behind the Black-Litterman asset allocation model. s To do this, we use examples to show the difference between the traditional meanvariance optimization process and the Black-Litterman process. We show that the mean-variance optimization process, while academically sound, can produce results that are extreme and not particularly intuitive. In contrast, we show that the optimal portfolios generated by the Black-Litterman process have a simple, intuitive property: − The unconstrained optimal portfolio is the market equilibrium portfolio plus a weighted sum of portfolios representing an investor’s views. − The weight on a portfolio representing a view is positive when the view is more bullish than the one implied by the equilibrium and other views.
− The weight increases as the investor becomes more bullish on the
view as well as when the investor becomes more confident about the view.
December 1999
Goldman Sachs Investment Management
Investment Management Research
Goldman Sachs Quantitative Resources Group
Guangliang He Robert Litterman (212) 357-3210 (212) 902-1677
Copyright 1999 Goldman, Sachs & Co. All rights reserved. The information in this publication is for your private information and is not intended as an offer or solicitation to buy or sell any securities. The information in this publication is for your private information and should not be construed as financial advice and it is not intended as an offer or solicitation to buy or sell any securities. The sole purpose of this publication is to inform the reader about the intuition behind the Black-Litterman model portfolios and is not intended as a solicitation for any Goldman Sachs product or service.
______________________________________________
Investment Management Research
1
References: [1] Black, Fischer and Robert Litterman, Asset Allocation: Combining Investor Views With Market Equilibrium, Goldman, Sachs & Co., Fixed Income Research, September 1990. [2] Black, Fischer and Robert Litterman, Global Portfolio Optimization, Financial Analysts Journal, pages 2843, September-October 1992. [3] Black, Fischer, Universal Hedging: Optimizing Currency Risk and Reward in International Equity Portfolios, Financial Analysts Journal, pages 16-22, July-August 1989. [4] Litterman, Robert, Hot Spots and Hedges, The Journal of Portfolio Management, pages 52-75, December 1996. [5] Markowitz, Harry, Portfolio Selection, Journal of Finance, pages 77-91, March 1952. ______________________________________________ Investment Management Research 18 ____________________________________________ The Intuition Behind Black-Litterman Model Portfolios