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Diversification measures and the optimal number of Stocks in a portfolio: An information theoretic explanation

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  • Adeola Oyenubi

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.
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Suggested Citation

  • Adeola Oyenubi, 2017. "Diversification measures and the optimal number of Stocks in a portfolio: An information theoretic explanation," ERSA Working Paper Series 666, Economic Research Southern Africa.
    • Handle: RePEc:rza:ersawp:666
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    Cited by:

    1. is not listed on IDEAS
    2. Azra Zaimovic & Adna Omanovic & Almira Arnaut-Berilo, 2021. "How Many Stocks Are Sufficient for Equity Portfolio Diversification? A Review of the Literature," JRFM, MDPI, vol. 14(11), pages 1-30, November.
    3. Christos Alexakis & Michael Dowling & Konstantinos Eleftheriou & Michael Polemis, 2021. "Textual Machine Learning: An Application to Computational Economics Research," Computational Economics, Springer;Society for Computational Economics, vol. 57(1), pages 369-385, January.
    4. Jiawen Xu & Yixuan Li & Kai Liu & Tao Chen, 2023. "Portfolio selection: from under-diversification to concentration," Empirical Economics, Springer, vol. 64(4), pages 1539-1557, April.

    More about this item

    Keywords

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    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G51 - Financial Economics - - Household Finance - - - Household Savings, Borrowing, Debt, and Wealth

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