QFIP-142-19: Modern Investment Management: An Equilibrium Approach, Ch. 7

Question 1

Traditional Mean-Variance Optimization Shortcomings

Answer 1

• Academic, but has practical shortcomings
• Very volatile results that are heavily dependent on inputs
• Unconstrained portfolios often have very large long and short positions that might not make intuitive sense
• Heavy reliance on very uncertain parameters. Ater all, if parameters are estimated historically, will the past predict the future?
• One solution is to impose strict caps/floors, but if that is the case, what is the true value of the optimizer?

Question 2

Black-Litterman model Overview

Answer 2

• The Black-Litterman model is a practical solution to optimization problems
• Typical mean-variance analysis often yields solutions that are very sensitive to model inputs
  
  • For example, a change in expected return of only a few basis points could drastically change the optimal portfolio
  • This can be very undesireable

Question 3

Describe the Black-Litterman Model.

Answer 3

• The Black-Litterman Model uses the global CAPM equilibrium as the center of gravity
• Additional view portfolios are considered, which specify:
  
  1. Expected Return
  2. Level of Confidence / Standard Deviation
  3. Correlation
• Under certain constraints (e.g. no transaction costs), the Black-Litterman optimized portfolio is a weighted average of the global CAPM equilibrium and the view portfolios

Question 4

What is the center of gravity for the Black-Litterman Model?

Answer 4

The global CAPM equilibrium

Question 5

What parameters are needed for the view portfolios in the Black-Litterman Model?

Answer 5

1. Expected Return
2. Level of Confidence / Standard Deviation
   
   • This parameter sets the level of strength each view portfolio can tilt the optimized portfolio from the center of gravity
3. Correlation

Question 6

State the two reasons why the Black-Litterman model is necessary.

Answer 6

1. The Black-Litterman model brings insights concerning the impact of different parameters on optimal weights
2. In the real world, one hardly ever optimizes in an unconstrained environment. The Black-Litterman model is great at handling more complex contexts.

Question 7

Describe the Mathematical Framework of the Black-Litterman Model with K view portfolios

Answer 7

Question 8

What determines the sizes of the tilts toward the view portfolios in a Black-Litterman model

Answer 8

The sizes of the tilts toward the view portfolios are a function of both the magnitude and the confidence expressed in the expected returns embedded in the investor-specified views.

Question 9

When is A view portfolio is given zero weight in a Black-Litterman model

Answer 9

1. If the portfolio is given no credibiity - so that the level of confidence parameter is set to 0%
2. When a view portfolio has a return equal to that implied by a combination of
   equilibrium and all other views.

Question 10

Sources of information in Black-Litterman model

Answer 10

• The Black-Litterman approach assumes there are two distinct sources of information about future excess returns: investor views and market equilibrium
• Both sources of information are assumed to be uncertain and are expressed in terms of probability distributions

Question 11

Best case use for Black-Litterman model

Answer 11

The real power of the Black-Litterman model arises when there is a benchmark, a risk or beta target, or other constraints, or when transaction costs are taken into account.

Question 12

Parameter Calibration of the Black-Litterman Model

Answer 12

• Parameter Calibration can vary quite a bit, and is generally up to the modeler
• The expected return and correlation parameters are often handled through historical/empirical estimation
• The level of confidence / standard deviation can be proxied through the amount of data available, although this is just one possible way to calibrate

Question 13

Describe the Mathematical Framework of the Black-Litterman Model with 1 view portfolio

Answer 13

Question 14

Black-Litterman formula for expected excess return vector U^*

Answer 14

Question 15

Compare and contrast standard MVO with the Black-Litterman approach

Answer 15

• Both methods provide optimized portfolio weights given a set of constraints
• Optimal weights under traditional MVO are sensitive to small changes in expected excess returns, while Black-Litterman is better behaved
• Traditional MVO portfolios may appear unreasonable without imposing significant constraints such as no shorting, while Black-Litterman does not require these constraints
• In traditional MVO the investor specifies a vector of excess returns, while in Black-Litterman the investor focuses on one or more “view portfolio” weights given a set of constraints

Question 16

Describe the three main steps to implement the Black-Litterman asset allocation model.

Answer 16

1. Start with an optimal portfolio with market capitalization weights and equilibrium expected excess returns
2. Investors formulate their views in terms of return expectation and degree of confidence
3. Produce the optimal portfolio asset allocation