Portfolio diversification index as a measure to improve investment portfolio performance
Van Dyk, Francois
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Diversification is one of the three most prominent elements of portfolio management with risk and return being the other two. In addition, diversification is a core objective for combining assets and is a central tenet of portfolio construction. It is also widely known that diversification is concerned with the number of unrelated sources of return and in essence the aim of diversification is to eliminate unsystematic risk from an investment portfolio while systematic risk will remain as it can not be diversified away. This study focuses on the concept of diversification in an investment portfolio setting, while specifically investigating a relatively "new" diversification measure, the Portfolio Diversification Index (PDI). The objectives of this study are twofold. First, establishing whether or not the PDI is a good diversification measure compared to the conventional/traditional and widely used residual variance method. The traditional method of measuring diversification remains inexact as this method measures portfolio diversification relative to a market index. When the market index itself is, however, poorly or not appropriately diversified it becomes problematic as the diversification measurement of the residual variance method is influenced. The PDI is a diversification measurement concept which is essentially free from the influences of the overall market index. This relatively "new" measure of diversification, the PDI, is based on the number of independent factors observed in a portfolio. These independent factors are quantified using Principal Components Analysis (PCA). In ascertaining the first objective the PDI battles "head-to-head" against the residual variance method of diversification by comparing fund ranking results of five South African unit trusts. This method of testing is used as no suitable statistical method exists. The fund ranking results of the two diversification measures are compared to a number of risk performance measures, including the Sharpe- and Sortino ratios. Extensive use is also made of the Omega ratio in this study as the Omega emerges as the dominant risk performance measure. The second objective of this study is to determine whether the PDI can be used as a tool by fund managers to assist in constructing funds (or changing the composition of existing fund) to reduce (or minimise) portfolio risk without a concomitant reduction in portfolio return. The PDI is used to determine the most independent factors of a South African unit trust where after' this fund is optimised, using the information of the independent factors, in order to reduce the risk of this fund. The Omega ratio is used to evaluate the results of the PDI while the marginal portfolio diversification concept is also investigated. A thorough literature study also presents the most relevant and important concepts and topics of the theory, management and construction of portfolios. Throughout the literature study the concept of diversification along with the topics most relevant to diversification are extensively focused and elaborated on. The method of testing used not only confirms that the PDI is a good diversification measure compared to the residual variance method, but that the PDI can also be used as a tool when constructing (or changing the composition of an existing portfolio) in order to reduce the portfolio risk without a concomitant reduction in portfolio return.
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