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A note on portfolios of averages of lognormal variables

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  • Boyle, Phelim
  • Jiang, Ruihong

Abstract

This paper establishes conditions under which a portfolio consisting of the averages of K blocks of lognormal variables converges to a K-dimensional lognormal variable as the number of variables in each block increases. The associated block covariance matrix has to have a special structure where the correlations and variances within the block submatrices are equal. We show why the variance homogeneity assumption plays a key role in the derivation.

Suggested Citation

  • Boyle, Phelim & Jiang, Ruihong, 2023. "A note on portfolios of averages of lognormal variables," Insurance: Mathematics and Economics, Elsevier, vol. 112(C), pages 97-109.
    • Handle: RePEc:eee:insuma:v:112:y:2023:i:c:p:97-109
    DOI: 10.1016/j.insmatheco.2023.06.001
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    References listed on IDEAS

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    1. Victor DeMiguel & Lorenzo Garlappi & Raman Uppal, 2009. "Optimal Versus Naive Diversification: How Inefficient is the 1-N Portfolio Strategy?," The Review of Financial Studies, Society for Financial Studies, vol. 22(5), pages 1915-1953, May.
    2. repec:taf:jnlbes:v:30:y:2012:i:2:p:212-228 is not listed on IDEAS
    3. Asmussen, Søren, 2018. "Conditional Monte Carlo for sums, with applications to insurance and finance," Annals of Actuarial Science, Cambridge University Press, vol. 12(2), pages 455-478, September.
    4. Archil Gulisashvili & Peter Tankov, 2013. "Tail behavior of sums and differences of log-normal random variables," Papers 1309.3057, arXiv.org, revised Jan 2016.
    5. Zdravko I. Botev & Robert Salomone & Daniel Mackinlay, 2019. "Fast and accurate computation of the distribution of sums of dependent log-normals," Annals of Operations Research, Springer, vol. 280(1), pages 19-46, September.
    6. Jorge Cadima & Francisco Lage Calheiros & Isabel Preto, 2010. "The eigenstructure of block-structured correlation matrices and its implications for principal component analysis," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(4), pages 577-589.
    7. Furman, Edward & Hackmann, Daniel & Kuznetsov, Alexey, 2020. "On log-normal convolutions: An analytical–numerical method with applications to economic capital determination," Insurance: Mathematics and Economics, Elsevier, vol. 90(C), pages 120-134.
    8. Asmussen, Søren & Rojas-Nandayapa, Leonardo, 2008. "Asymptotics of sums of lognormal random variables with Gaussian copula," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2709-2714, November.
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    More about this item

    Keywords

    Lognormal distribution; Sum of lognormals; Block covariance matrix; Limiting distribution; Moment formulae;
    All these keywords.

    JEL classification:

    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions

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