Ch 3 Implied Alphas And Black-Litterman

Question 1

Black Litterman model incorporates 3 main components

Black Litterman is a form of (what) technique

Answer 1

1. Analysts forecasts, market’s view and analysts uncertainty
2. B-L is a form of shrinkage technique

Question 2

Black Litterman inputs
3 broad levels

Output:

Answer 2

B-L inputs

1. The market’s implied returns
2. Analysts views (matrix P) expressing what is being compared and vector Q expressing the quantum (eg equities will outperform bonds by 3%)
3. Analyst uncertainty

OUtput: Output is return forecasts that combine all views and the uncertainty about them.

Question 3

BL- Inputs

Market’s Implied Returns (4)

Answer 3

BL- Inputs

Market’s Implied Returns (4)

1. market portfolio (w)
2. variance-covariance matrix, denoted by Σ, preferably a forecast
3. risk aversion parameter, denoted by 𝜆
4. 𝑟_𝑚=𝑐𝑎𝑠ℎ 𝑟𝑒𝑡𝑢𝑟𝑛+ 𝜆Σ𝑤 (this last term is implied alphas based on weights)

Question 4

BL- Inputs

Analyst uncertainty (2)

Answer 4

BL- Inputs

Analyst uncertainty (2)

1. a scalar 𝜏, denotes the level of confidence analysts have in the market view
2. the matrix Ω, denotes the level of confidence analysts have about their own views

Question 5

BL: Outputs

Answer 5

BL - Outputs
Output is return forecasts that combine all views and the uncertainty about them. In the case of two assets and one view:

𝑟_𝐵𝐿=((𝑀𝑎𝑟𝑘𝑒𝑡 𝑉𝑖𝑒𝑤)⁄(𝑀𝑎𝑟𝑘𝑒𝑡 𝑈𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦)+(𝐴𝑛𝑎𝑙𝑦𝑠𝑡 𝑉𝑖𝑒𝑤)⁄(𝐴𝑛𝑎𝑙𝑦𝑠𝑡 𝑈𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦))/(1⁄(𝑀𝑎𝑟𝑘𝑒𝑡 𝑈𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦)+1⁄(𝐴𝑛𝑎𝑙𝑦𝑠𝑡 𝑈𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦))

Can also be done by matrix algebra for multiple assets and multiple views

Question 6

1. BL is an example of a _______ technique
2. STein and James-Stein shrink…. based on ….
3. Useful in ___ portfolio construction

Answer 6

1. BL is an example of a Shrinkage Estimators. These estimation methods the shrink a forecast towards a ‘prior’
2. Stein and James-Stein estimators are discussed which shrink asset class averages towards a grand mean based on the volatility of the asset classes
3. Such estimators can be shown to be better estimates of the ‘vector’ of asset class returns, and often very useful in MV portfolio construction through the reduction of forecast errors

Question 7

Stein and James-Stein estimators do what>….

Answer 7

shrink asset class averages towards a grand mean.
- These are better estimates of the ‘vector’ of asset class returns, often very useful in MV construction through reduction of forecast errors.