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Bayesian Alternatives to Black-Litterman 

Published July 2020 in the International Journal of Statistics and Probability:

The Black-Litterman model combines investor's personal views with historical data in order to give optimal portfolio weights. Albeit the original approach uses only one prior on the mean of the returns, in this project we introduce alternative approaches which also add two different priors on the covariance of the returns.

Example of personal views

The investor chooses the stocks they want to invest in (let us say AAPL,AMZN,GOOG,MSFT) and the investment horizon (1 month for example). Let us say that the investor believes that: 

  • AMZN beats AAPL by 2% in the next month with a certain level of confidence.

  • GOOG beats MSFT by 5% in the next month with a certain level of confidence.

The personal views will be (the columns of the matrix are coefficients for AAPL,AMZN,GOOG,MSFT, respectively): 

BL original formulas.png

Original version

personal views.png
BL v1 formulas.png

First version

BL v2 formulas.png

Second version

First version-profits (100,000$ initial capital for January 2018) and posterior distance to opinions for different confidence levels

distance first version.png
profit first version AMZN.png

Change AMZN to FB.

distance first version 2.png
profit first version FB.png

Second version-profits (100,000$ initial capital for January 2018) and posterior distance to opinions for different confidence levels

distance second version.png
profits second version AMZN.png
profit second version FB.png
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University of California, Santa Barbara

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