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Bayesian portfolio selection: an empirical analysis of JSE-ALSI 2003-2010

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par Frankie MBUYAMBA
Université de Johannesburg - Quantitative applications 2010
  

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BAYESIAN PORTFOLIO SELECTION: An empirical Analysis of the JSE-ALSI 2003-2010

M. Frankie MBUYAMBA

MCom Financial Economics (2010), University of Johannesburg, (frankiem@uj.ac.za)

1. Abstract

Finance theory can be used to form informative prior beliefs in financial decision making. This paper approaches portfolio selection in a Mean-Variance, Mean-Conditional Variance and Black Litterman covariance and Bayesian framework that incorporates a prior degree of belief in an asset pricing model. Sample evidence on a period of 8 years and value and size effects is evaluated from an asset-allocation perspective. Investor's belief in the domestic CAPM must be very strong to justify the home bias observed in their equity holdings. The same strong prior belief results in large and stable optimal positions in this selection.

Keywords: Bayesian CAPM, Bayesian portfolio selection, Black-Litterman(BL)

2. INTRODUCTION

Modem portfolio theory has providing a really framework for portfolio optimization when investors who are risk-averse prefer investment portfolios that are mean-variance efficient. Optimal portfolio selection requires knowledge of each asset's expected return, variance, and covariance with other asset returns. In practice, each asset's expected return, variance, and covariance with other asset returns are unknown and must be estimated from available historical or subjective information. We assume that the portfolio manager has a goal of maximizing the expected return for a given level of risk. We use monthly data comprise the performance of the benchmark; JSE-ALSI, to capture the behaviour of weekly data in 400 observations of prices. We construct our analysis by applying the mean conditional Value at Risk in order to determine the weights of the portfolio and after that the paper is implementing the work of Black and Litterman by using the variance-covariance matrix so that we can provide an analysis of asset allocation and the weights of choice of the optimal portfolio. Finally we look at the theory related to the Black Litterman Bayesian CAPM where we use the benchmark, the risk free rate and each of every stock so that we can have the weight value of the portfolio to be mean-variance efficient to the market stock.

In our analysis we are looking to the Bayesian portfolio selection because it's encountered the uncertainties problems of investors while the Mean-Variance model ignores them. The fundamental of Bayesian approach in portfolio selection is based on the notion of probability which is defined by a degree of belief and makes possible to incorporate a belief about the hypothesis which is valid to the probability that its alternative is valid. One of the major matters with mean-variance models is the function between variance-covariance/expected return inputs and the optimal portfolio weights is highly nonlinear and can be very sensitive to the small changes in the views of the manager1(*). The above reasoning tells us that errors in covariance estimation are less damaging than errors in covariance estimation which have less damage compare to the estimation error in the expected return.

The paper is based in the first section on presenting the paradigm of the portfolio optimization under uncertainty. The second section will describe the models and methods of capturing the distributions of the returns in three stages. The third section will be the presentation of the empirical results on the ALSI and the height stocks since 1995 till now. The last section is showing the implications of our results by stating the relevance, implications and significance of the findings.

* 1 Further reading of Polson and Tew

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