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Correlation as probability: applications of Sheppard’s formula to financial assets

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  • Javier Giner
  • Judit Mendoza Aguilar
  • Sandra Morini-Marrero

Abstract

In this paper, a result for bivariate normal distributions from statistics is transformed into a financial asset context in order to build a tool which can translate a correlation matrix into an equivalent probability matrix and vice versa. This way, the correlation coefficient parameter is more understandable in terms of joint probability of two stocks’ returns, and much more useful in terms of the information it provides. We validate, empirically, our result for a sample covering the three market capitalization categories in the S&P 500 index over a ten-year period. Finally, the accuracy of this new tool is measured theoretically and some applications from the practitioners’ point of view are offered. Such applications include, for instance, the calculation of the number of trading days in a year in which two stocks have same sign returns and how to split the average return of weighted stocks into four orthants.

Suggested Citation

  • Javier Giner & Judit Mendoza Aguilar & Sandra Morini-Marrero, 2018. "Correlation as probability: applications of Sheppard’s formula to financial assets," Quantitative Finance, Taylor & Francis Journals, vol. 18(5), pages 777-787, May.
    • Handle: RePEc:taf:quantf:v:18:y:2018:i:5:p:777-787
    DOI: 10.1080/14697688.2017.1414510
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    Cited by:

    1. Laleh Tafakori & Armin Pourkhanali & Riccardo Rastelli, 2022. "Measuring systemic risk and contagion in the European financial network," Empirical Economics, Springer, vol. 63(1), pages 345-389, July.
    2. Giner, Javier, 2021. "Orthant-based variance decomposition in investment portfolios," European Journal of Operational Research, Elsevier, vol. 291(2), pages 497-511.

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