Spring
The Black-Litterman Model
Capstone Project Presentation
Samuel Wood
April, 27th 2015
Agenda
I.
Background
03
II.
Problem Statement & Objectives
05
III.
Methods
06
IV.
Results
09
V.
Analysis & Conclusions
11
VI.
Summary
12
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:
1. Simpler staring point for predicting asset returns
2. Clear method for specifying investors views on returns
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
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
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.
Methods: Mean-Variance Optimization
Methods: Black-Litterman
Methods: Measures of Performance
Sharpe Ratio:
Treynor Measure:
Alpha:
Methods: Measures of Risk
Beta:
Volatility:
VaR:
Methods: The Experiment
1. 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.
2. 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.
Results
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
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.
References
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
R. C. Merton, “An Intertemporal Capital Asset Pricing Model,” Econometrica, vol. 41, no. 5, pp. 8
67–887, Sep. 1973.
F. Black and R. Litterman, “Global Portfolio Optimization,” Financial Analysts Journal, vol. 48, n
o. 5, pp. 28–43, Sep. 1992.
W. F. Sharpe, “Mutual Fund Performance,” The Journal of Business, vol. 39, no. 1, pp. 119–138, J
an. 1966.
H. Markowitz, “Portfolio Selection*,” The Journal of Finance, vol. 7, no. 1, pp. 77–91, Mar. 1952.
A. J. McNeil, R. Frey, and P. Embrechts, Quantitative Risk Management: Concepts, Techniques, a
nd Tools: Concepts, Techniques, and Tools. Princeton University Press, 2010.
C. F. A. Walters, “The Black-Litterman Model in Detail,” Social Science Research Network, Roche
ster, NY, SSRN Scholarly Paper ID 1314585, Jun. 2014.
C. Mankert, “The Black-Litterman Model : mathematical and behavioral finance approaches towards it
use in practice,” 2006.
C. Mankert, “The Black-Litterman Model : mathematical and behavioral finance approaches towards it
use in practice,” 2006.
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 908569, Jun. 200
6.
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. 2014.
C. F. A. Walters, “The Factor Tau in the Black-Litterman Model,” Social Science Research Networ
k, Rochester, NY, SSRN Scholarly Paper ID 1701467, Oct. 2013.
M. C. Jensen, “The Performance of Mutual Funds in the Period 1945-1964,” Social Science Rese
arch Network, Rochester, NY, SSRN Scholarly Paper ID 244153, May 1967.
P. Jorion, Value at Risk: The New Benchmark for Managing Financial Risk, 3rd Edition, 3rd edition
nn. New York: McGraw-Hill, 2006.