*The Business Professor*, updated February 24, 2020, last accessed October 26, 2020, https://thebusinessprofessor.com/lesson/black-litterman-model-definition/.

### Black-Litterman Model Definition

The Black-Litterman model is a model used for an asset or portfolio allocation. This model was developed by two theorists at Goldman Sachs in 1990. The Black-Litterman model was named after Fischer Black and Robert Litterman, the theorists who developed it. The goal of the theory is to relieve the burden of institutional investors as it pertains to asset and portfolio allocation.

### A Little More on What is the Black-Litterman Model

The Black-Litterman model combines two core portfolio theories namely the capital asset pricing model (CAPM) and the modern portfolio theory. This model offers enormous benefits to institutional investors and portfolio managers by helping them adequately apply CAPM, optimization theory and modern portfolio theory in the practice of asset allocation.

A Black-Litterman model is a mathematical approach to asset allocation that helps portfolio managers handle errors that might occur during allocation. This model also enhances the achievement of the expected portfolio returns within the concept of mean-variance optimization framework.

The Black-Litterman model is in two versions which are the Black-Litterman (BL) model and the unconstrained Black-Litterman (UBL) model. While the former uses reverse optimization alongside investor’s views on expected return as major factors in achieving a diversified market portfolio, the latter considers the weight asset weights as they reflect on investor’s perspectives to determine the allocation of assets in a portfolio.

The BL model aims to reduce the problem of return sensitivity in asset allocation. It also ensures that stable and efficient portfolios with adequate returns are achieved.

Reference for āBlack-Litterman Modelā

https://www.investopedia.com āŗ Investing āŗ Financial Analysis

https://en.wikipedia.org/wiki/BlackāLitterman_model

https://www.portfoliovisualizer.com/black-litterman-model

https://www.stat.berkeley.edu/~nolan/vigre/reports/Black-Litterman.ppt

https://www.mathworks.com/discovery/black-litterman.html

Academics research on āBlack-Litterman Modelā

A demystification of theĀ **Black**ā**Litterman model**: Managing quantitative and traditional portfolio construction, **Satchell, S., & Scowcroft, A. (2000). A demystification of the BlackāLitterman model: Managing quantitative and traditional portfolio construction.Ā ***Journal of Asset Management***,Ā ***1***(2), 138-150. **The purpose of this paper is to present details of Bayesian portfolio construction procedures which have become known in the asset management industry as BlackāLitterman models. We explain their construction, present some extensions and argue that these models are valuable tools for financial management.

A step-by-step guide to theĀ **Black**–**Litterman model**: Incorporating user-specified confidence levels, **Idzorek, T. (2007). A step-by-step guide to the Black-Litterman model: Incorporating user-specified confidence levels. InĀ ***Forecasting expected returns in the financial markets***Ā (pp. 17-38). Academic Press. **This chapter focuses on the insights of the BlackāLitterman model and provides step-by-step instructions for implementation of the complex model. It details the process of developing the inputs for the BlackāLitterman model, which enables investors to combine their unique views regarding the performance of various assets with the market equilibrium for generation of a new vector of expected returns. The new combined return vector leads to intuitive, well-diversified portfolios. The two parameters of the BlackāLitterman model that control the relative importance placed on the equilibrium returns versus the view returns, the scalar and the uncertainty in the views, are very difficult to specify. The BlackāLitterman formula with hundred percent certainty in the views enables determination of the implied confidence in a view. Using this implied confidence framework, a new method for controlling the tilts and the final portfolio weights caused by the views is introduced. The method asserts that the magnitude of the tilts should be controlled by the user- specified confidence level based on an intuitive zero percent to hundred percent confidence level. Overall, the BlackāLitterman model overcomes the most-often cited weaknesses of mean-variance optimization helping users to realize the benefits of the Markowitz paradigm. Likewise, the proposed new method for incorporating user-specified confidence levels should increase the intuitiveness and the usability of the BlackāLitterman model.

The intuition behindĀ **Black**–**Litterman modelĀ **portfolios, **He, G., & Litterman, R. (1999). The intuition behind Black-Litterman model portfolios.Ā ***Available at SSRN 334304***. **In this article we demonstrate that the optimal portfolios generated by the Black-Litterman asset allocation model have a very simple, intuitive property. The unconstrained optimal portfolio in the Black-Litterman model is the scaled market equilibrium portfolio (reflecting the uncertainty in the equilibrium expected returns) plus a weighted sum of portfolios representing the investor’s views. The weight on a portfolio representing a view is positive when the view is more bullish than the one implied by the equilibrium and the other views. The weight increases as the investor becomes more bullish on the view, and the magnitude of the weight also increases as the investor becomes more confident about the view.

TheĀ **Black**–**Litterman modelĀ **for structured equity portfolios, **Jones, R., Lim, T., & Zangari, P. J. (2007). The Black-Litterman model for structured equity portfolios.Ā ***Journal of Portfolio Management***,Ā ***33***(2), 24.**

TheĀ **Black**–**Litterman Model**: mathematical and behavioralĀ **financeĀ **approaches towards its use in practice, **Mankert, C. (2006).Ā ***The Black-Litterman Model: mathematical and behavioral finance approaches towards its use in practice***(Doctoral dissertation, KTH). **The financial portfolio model often referred to as the Black-Litterman model is analyzed using two approaches; a mathematical and a behavioral finance approach. After a detailed description of its framework, the Black-Litterman model is derived mathematically using a sampling theoretical approach. This approach generates a new interpretation of the model and gives an interpretable formula for the mystical parameter**Ā Ļ**, the weight-on-views. Secondly, implications are drawn from research results within behavioral finance. One of the most interesting features of the Black-Litterman model is that the benchmark portfolio, against which the performance of the portfolio manager is evaluated, functions as the point of reference. According to behavioral finance, the actual utility function of the investor is reference-based and investors estimate losses and gains in relation to this benchmark. Implications drawn from research results within behavioral finance indicate and explain why the portfolio output given by the Black-Litterman model appears more intuitive to fund managers than portfolios generated by the Markowitz model. Another feature of the Black-Litterman model is that the user assigns levels of confidence to each asset view in the form of confidence intervals. Research results within behavioral finance have, however, shown that people tend to be badly calibrated when estimating their levels of confidence. Research has shown that people are overconfident in financial decision-making, particularly when stating confidence intervals. This is problematic. For a deeper understanding of the use of the Black-Litterman model it seems that we should turn to those financial fields in which social and organizational context and issues are taken into consideration, to generate better knowledge of the use of the Black-Litterman model.