Improving the Markowitz Model using the Notion of Entropy

The Mean-variance framework proposed by Markowitz is the most common model for portfolio selection problem. The most important concept in his theory is diversification. Diversification means designing an investment portfolio that reduces exposure risk by combining a variety of investments. But actually, the portfolios’ weights are often extremely concentrated on few assets when using mean-variance framework; this is a contradiction to the notion of diversification. Entropy is a well accepted measure of diversity. In this thesis, we discuss an improved mean-variance model based on maximum entropy theory (MVME). Entropy can be viewed as a measure of disparity from the uniform probability distribution. This approach can be viewed as a direct shrinkage of portfolio weights. The estimation errors, stability of portfolio weights, portfolio performance and degree of diversification for both mean-variance and the MVME framework are tested. Compared with the mean-variance framework, the improved model leads to a well diversified portfolio.