April, 27th 2015

The Black-Litterman Model

Spring

Capstone Project PresentationSamuel Wood

AgendaI. Background 03II. Problem Statement & Objectives 05III. Methods 06IV. 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 MATLAB2. 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

Alpha:

Treynor Mea-sure:

Sharpe Ratio:

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.

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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,”

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