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Article

Implementing Black-Litterman Using an Equivalent Formula and Equity Analyst Target Prices

Leon Chen, Zhi Da and Ernst Schaumburg
The Journal of Investing Spring 2015, 24 (1) 34-47; DOI: https://doi.org/10.3905/joi.2015.24.1.034
Leon Chen
is an assistant professor of finance at Minnesota State University in Mankato, MN.
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  • For correspondence: yilin.chen@mnsu.edu
Zhi Da
is an associate professor of finance at the University of Notre Dame’s Mendoza College of Business in Notre Dame, IN.
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  • For correspondence: zda@nd.edu
Ernst Schaumburg
is a research officer at the Federal Reserve Bank of New York in New York, NY.
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  • For correspondence: ernst.schaumburg@gmail.com
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Abstract

We examine an alternative and equivalent Black and Litterman [1992] formula using classical multivariate analysis, which is easier to interpret and allows more general view formulations than the original formula. Specifically, the equivalent formula provides a more intuitive explanation under the limiting case of deterministic views, and makes it easier to show the resulting optimal portfolio as a combination of the market portfolio and a long–short view portfolio. The equivalent formula also allows for more convenient empirical implementations when views and expected return priors are correlated. We then use a numerical example to illustrate the equivalent formula, and we also implement the formula in an optimal asset-allocation setting, using equity analysts’ 12-month-ahead target price forecasts for the period 1999–2010. We show that the optimal portfolio outperforms the market (S&P 500) and this result is robust across different time periods and model parameter choices.

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The Journal of Investing: 24 (1)
The Journal of Investing
Vol. 24, Issue 1
Spring 2015
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Implementing Black-Litterman Using an Equivalent Formula and Equity Analyst Target Prices
Leon Chen, Zhi Da, Ernst Schaumburg
The Journal of Investing Feb 2015, 24 (1) 34-47; DOI: 10.3905/joi.2015.24.1.034

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Implementing Black-Litterman Using an Equivalent Formula and Equity Analyst Target Prices
Leon Chen, Zhi Da, Ernst Schaumburg
The Journal of Investing Feb 2015, 24 (1) 34-47; DOI: 10.3905/joi.2015.24.1.034
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  • Article
    • Abstract
    • AN EQUIVALENT BLACK-LITTERMAN FORMULA
    • COMPARISON OF THE EQUIVALENT AND THE ORIGINAL FORMULA
    • AN EXAMPLE OF BL ASSET ALLOCATION THAT ALLOWS VIEW CORRELATION USING THE EQUIVALENT FORMULA
    • EMPIRICAL IMPLEMENTATION USING EQUITY ANALYST TARGET PRICES
    • CONCLUSION
    • APPENDIX A
    • APPENDIX B
    • APPENDIX C
    • APPENDIX D
    • APPENDIX E
    • ENDNOTES
    • REFERENCES
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