Diversification Measures and the Optimal Number of Stocks in a Portfolio: An Information Theoretic Explanation

Adeola Oyenubi

Computational Economics, 2019, vol. 54, issue 4, No 10, 1443-1471

Abstract: Abstract This paper provides a plausible explanation for why the optimum number of stocks in a portfolio is elusive, and suggests a way to determine this optimal number. Diversification has a lot to do with the number of stocks in a portfolio. Adding stocks to a portfolio increases the level of diversification, and consequently leads to risk reduction up to a certain number of stocks, beyond which additional stocks are of no benefit, in terms of risk reduction. To explain this phenomenon, this paper investigates the relationship between portfolio diversification and concentration using a genetic algorithm. To quantify diversification, we use the portfolio Diversification Index (PDI). In the case of concentration, we introduce a new quantification method. Concentration is quantified as complexity of the correlation matrix. The proposed method quantifies the level of dependency (or redundancy) between stocks in a portfolio. By contrasting the two methods it is shown that the optimal number of stocks that optimizes diversification depends on both number of stocks and average correlation. Our result shows that, for a given universe, there is a set of Pareto optimal portfolios containing a different number of stocks that simultaneously maximizes diversification and minimizes concentration. The choice portfolio among the Pareto set will depend on the preference of the investor. Our result also suggests that an ideal condition for the optimal number of stocks is when variance reduction benefit of diversification is off-set by the variance contribution of complexity.

Keywords: Information theory; Diversification; Genetic algorithm; Portfolio optimization; Principal component analysis; Simulation methods (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10614-016-9600-5

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