1. The Black-Litterman Model
Spring
The Black-Litterman Model
Capstone Project Presentation
Samuel Wood
April, 27th 2015

2. Agenda I. Background 03 II. Problem Statement & Objectives 05 III.
Methods 06
IV.
Results 09 V.
Analysis & Conclusions 11
VI.
Summary 12

3. Background: Black-Litterman Model
Risky asset allocation model for portfolios
Invented by the Fisher Black and Robert Litterman
Designed to improve upon traditional allocation method in two different was:
Simpler staring point for predicting asset returns
Clear method for specifying investors views on returns

4. Background: Timeline
In 1952 Harry Markowitz Introduces Modern Portfolio Theory (MPT)
In the early 1960s The Capital Asset Pricing Model (CAPM) was introduced independently by Treynor, Sharpe, Litner and Mossin
In 1990 the Black-Litterman Asset Allocation Model was created by Fisher Black and Robert Litterman while working at Goldman Sachs.
In 1992 the first public information about the Black-Litterman Model was published in the paper “Global Portfolio Optimization” in 1992

5. Problem Statement & Objectives
I would like to implement the Black-Litterman model for asset allocation close to its canonical form and test its performance in comparison with the original mean-variance optimization method. I will use various methods of portfolio comparison to test methods against each other using historical data.
Objectives:
1. Implement portfolio models using MATLAB
2. Evaluate whether BL is an easier or more effective model than traditional MPT

6. Methods: Modern Portfolio Theory
Attempts to maximize return and minimize risk for a given set of financial assets.
Based on assumptions that investors are risk adverse.

7. Methods: Mean-Variance Optimization

8. Methods: Black-Litterman

9. Methods: Measures of Performance
Sharpe Ratio:
Treynor Measure:
Alpha:

10. Methods: Measures of Risk
Beta:
Volatility:
VaR:

11. Methods: The Experiment
Blind Test: For a set time horizon of 3 years with five stock opinions using Black-Litterman. 20 large stocks.
Expected Results: No discernable difference between market cap weighted or mean-variance optimized portfolio.
Unblind Test: For a set time horizon of the same 3 years with five stock opinions using Black-Litterman. 20 large stocks.
Expected Results: BL followed by mean-variance optimized and then market cap weighted.

12. Results

13. Analysis
Pro:
If you are good at estimating mean returns Black-Litterman can obtain higher reward for your level of risk.
Cons:
Large amounts of decisions relative to the number of total stocks increase risk substantially

14. Conclusion
Black-Litterman is superior to traditional mean-variance optimization in that your lesser number of decisions with decisions made weighted against the market.
Black-Litterman can be a problem if you have too few assets or too many opinions as it can leave you open to substantial risk.

16. References
[1] R. C. Merton, “An Intertemporal Capital Asset Pricing Model,” Econometrica, vol. 41, no. 5, pp. 8 67–887, Sep
[2] F. Black and R. Litterman, “Global Portfolio Optimization,” Financial Analysts Journal, vol. 48, n o. 5, pp. 28–43, Sep
[3] W. F. Sharpe, “Mutual Fund Performance,” The Journal of Business, vol. 39, no. 1, pp. 119–138, J an
[4] H. Markowitz, “Portfolio Selection*,” The Journal of Finance, vol. 7, no. 1, pp. 77–91, Mar
[5] A. J. McNeil, R. Frey, and P. Embrechts, Quantitative Risk Management: Concepts, Techniques, a nd Tools: Concepts, Techniques, and Tools. Princeton University Press, 2010.
[6] C. F. A. Walters, “The Black-Litterman Model in Detail,” Social Science Research Network, Roche ster, NY, SSRN Scholarly Paper ID , Jun
[7] C. Mankert, “The Black-Litterman Model : mathematical and behavioral finance approaches towards it use in practice,” 2006.
[8] C. Mankert, “The Black-Litterman Model : mathematical and behavioral finance approaches towards it use in practice,” 2006.
[9] M. C. Jensen, F. Black, and M. S. Scholes, “The Capital Asset Pricing Model: Some Empirical Tets,” Social Science Research Network, Rochester, NY, SSRN Scholarly Paper ID , Jun
[10] J. T. Chong, Y. Jin, and G. M. Phillips, “The Entrepreneur’s Cost of Capital: Incorporating Downsi de Risk,” Business Valuation Review, vol. 33, no. 3, pp. 81–91, Sep
[11] C. F. A. Walters, “The Factor Tau in the Black-Litterman Model,” Social Science Research Networ k, Rochester, NY, SSRN Scholarly Paper ID , Oct
[12] M. C. Jensen, “The Performance of Mutual Funds in the Period ,” Social Science Rese arch Network, Rochester, NY, SSRN Scholarly Paper ID , May 1967.
[13] P. Jorion, Value at Risk: The New Benchmark for Managing Financial Risk, 3rd Edition, 3rd edition nn. New York: McGraw-Hill, 2006.