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Optimal portfolio selection based on first and second order Markov chains


  • Juan Manuel Gómez R

    (Universidad Nacional de Colombia)

  • José Alfredo Jiménez M

    (Universidad Nacional de Colombia)


Searching for create investment strategies in pursuit of maximizing the expected return on investment and minimizing the risk two models of selection of optimal portfolios are studied. The first portfolio composition model is adjusted using logarithmic returns, and the other uses principal component analysis (PCA) at these returns. Then, for each of them its weighted performance is established and measures are created to establish the states of the first and second order Markov chains, this allows to predict whether the shaped portfolios will have bullish or bearish behaviors given the probabilities of the states of the Markov chains. An application is made using the daily closing price returns of 21 COLCAP shares for the period from January 2014 to October 2017. Concluding that in the Colombian Market a portfolio formed by PCA of the returns has a higher expected profitability and less risk in the long term, having an accuracy of model’s forecast according with the stationary vectors of the Markov chains

Suggested Citation

  • Juan Manuel Gómez R & José Alfredo Jiménez M, 2020. "Optimal portfolio selection based on first and second order Markov chains," Lecturas de Economía, Universidad de Antioquia, Departamento de Economía, issue 92, pages 33-66, Enero-Jun.
  • Handle: RePEc:lde:journl:y:2020:i:92:p:33-66
    DOI: 10.17533/udea.le.n92a02

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    References listed on IDEAS

    1. repec:ebl:ecbull:v:7:y:2004:i:3:p:1-10 is not listed on IDEAS
    2. M. Hossein Partovi & Michael Caputo, 2004. "Principal Portfolios: Recasting the Efficient Frontier," Economics Bulletin, AccessEcon, vol. 7(3), pages 1-10.
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    More about this item


    portfolio selection; Markov chain; principal component analysis; risk aversion; stock index.;
    All these keywords.

    JEL classification:

    • G1 - Financial Economics - - General Financial Markets
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • O16 - Economic Development, Innovation, Technological Change, and Growth - - Economic Development - - - Financial Markets; Saving and Capital Investment; Corporate Finance and Governance


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