This paper consolidates insights from the relatively few works on the model and provides step-by-step instructions that enable the reader to implement this complex model. A new method for controlling the tilts and the final portfolio weights caused by views is introduced. This is an intuitive technique for specifying one of most abstract mathematical parameters of the Black-Litterman model. The Black-Litterman asset allocation model, created by Fischer Black and Robert Litterman, is a sophisticated portfolio construction method that overcomes the problem of unintuitive, highly-concentrated portfolios, input-sensitivity, and estimation error maximization. These three related and well-documented problems with mean-variance optimization are the most likely reasons that more practitioners do not use the Markowitz paradigm, in which return is maximized for a given level of risk. The Black-Litterman model uses a Bayesian approach to combine the subjective views of an investor regarding the expected returns of one or more assets with the market equilibrium vector of expected returns the prior distribution to form a new, mixed estimate of expected returns.
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Input sensitivity is a well- documented problem with mean- variance optimization and is the most likely reason that more portfolio managers do not use the Markowitz paradigm, in which return is maximized for a given level of risk. The Black-Litterman Model uses a Bayesian approach to combine the subjective views of an investor regarding the expected returns of one or more assets with the market equilibrium vector the prior distribution of expected returns to form a new, mixed estimate of expected returns.
The majority of articles on the Black-Litterman Model have addressed the model from a global asset allocation perspective; therefore, this article presents a domestic example, based on the Dow Jones Industrial Average DJIA. I treated table 1 as known, and I calculate the result of table 2, and compare the difference. In order to calculate table 2, I use the note 7 in the paper to do it. The code is showed as below.
The original data of table 2 is The result and the difference I get are showed as below: This is the difference between the paper and the result I get. Even for the historical data, compare to the historical weight, the differences are also small.
The reason of causing the difference may be the optimal method or the initial start point or both are different. Part 2 calculate table 4 Prior to advancing, it is important to introduce the Black-Litterman formula and provide a brief description of each of its elements. Throughout this article, k is used to represent the number of views and n is used to express the number of assets in the formula.
The Black-Litterman Model allows such views to be expressed in either absolute or relative terms. Below are three sample views expressed using the format of Black and Litterman Each expressed view results in a 1 x n row vector. Thus, k views result in a k x n matrix.
We can see the differences are very small. We can also calculate the new weight by the same method I used to calculate table 2. The result is showed as below. Finally, I get the similar table like table 4. I just keep 2 decimal. This is the original one, we can see there are very close. The difference between the weight is just by using different optimal method or the initial start point.
This the code I use, you can see it in my archive.
Download: A Step-by-step Guide To The Black-litterman Model.pdf
Sharpe 33 Estimated H-index: A Demystification of the Black-Litterman Model: The black-litterman model in central guise practice: Xinfeng Zhou 1 Estimated H-index: Having attempted to decipher several articles about the Black-Litterman Model, I have found that none of the relatively few articles on the Black-Litterman Model ot enough step-by-step instructions for the average practitioner to derive the new vector of expected returns. Managing Quantitative and Traditional Portfolio Construction journal of asset management. Ref 11 Source Add To Collection. Weighted arithmetic mean Mathematical notation Posterior probability Black—Litterman model Financial economics Bayesian probability Data mining Engineering Asset allocation Prior probability Portfolio. Heinz Zimmermann 29 Estimated H-index: Fischer Black 35 Estimated H-index: The Black-Litterman Model uses a Bayesian approach to combine the subjective views of an investor regarding the expected x of one or more assets with the market equilibrium vector the prior distribution of expected returns to form a new, mixed estimate of stwp-by-step returns. Ref 5 Source Add To Collection.