Preprint B88/2016
Avaliação do Modelo de Alocação de Carteira de Black-Litterman
FRANCESCA MUNIA MACHADO
Keywords: Asset Allocation | Black-Litterman | Markowitz | Times Series | GARCH | Risk and Uncertainty.

The problem of asset allocation was first theorized as a mathematical problem by Markowitz,
with his Mean-Variance model (MV). His approach assumed that only two factors mattered
to investors: risk and return of the assets. The main idea of the model is to create a portfolio
by maximizing the expected returns subject to a given risk level. Despite its prominence in
financial studies, the model presents some problems when translated into practice, such as poorly
diversified portfolios, counterintuitive results, disregarding the opinion of the decision maker
on the performance of the assets in the future and high sensitivity to the variables.
As an alternative to the Mean-Variance model, Black and Litterman [6] proposed a new
approach which uses Bayesian statistical methods to match the long-term market balance -
derived from the CAPM ( Capital Asset Pricing Model) - with investor’s views about future
returns. While similar to the Mean-Variance model, the Black-Litterman model (BL) optimizes
the returns subject to a risk matrix, but with two significant contributions. The first one is
the idea of the BL model to set a neutral starting point in portfolio optimization process. The
second is the possibility to incorporate investor’s opinions about asset returns to the model.
The main purpose of the Black-Litterman approach is to introduce a portfolio allocation
model that gives intuitive and stable results, overcoming the problems observed in the Markowitz
approach. Additionally, the BL model has the advantage of including expectations and
subjective expert opinions, creating a portfolio that does not purely depend on past information.
These innovations have made the model a support tool for decision-making by market
analysts, hoping for greater credibility and stability of the results. Consequently, there have
been a number of new studies about the Black-Litterman model.
Despite the important contribution of the BL model to portfolio theory, their effectiveness
in the world of finance is still not well known. Two of the most important outstanding questions
are if the use of Black-Litterman really solves the problems of the Markowitz model, as well
as if the results obtained from running the model are consistent with observations in the real
world.
Another major question is to determine how the investor’s view could be estimated considering
that such parameters are subjective and depend on the investor’s analysis of assets. A
possible method to determine such views is to calibrate time series models, such as ARMA and
GARCH. This approach may be more advantageous since it offers a robust methodology for
the view selection.
This study aims to test the Black-Litterman model with a case study using 15 highly
traded assets which are part of São Paulo Stock Exchange index (Ibovespa) as variables. It is
expected that the results of this study will provide information about the performance of the
Black-Litterman model verses the Mean-Variance model. Also, we will test the effectiveness of
time-series models ARMA and GARCH in obtaining investor’s views for the application of the
BL model.