Correlation As Probability: Applications of Sheppard’s Formula to Financial Assets

19 Pages Posted: 27 Dec 2018

See all articles by Javier Giner

Javier Giner

University of La Laguna - Faculty of Economics, Business and Tourism

Judit Mendoza

University of La Laguna

Sandra Morini

University of La Laguna

Date Written: July 27, 2017

Abstract

In this paper, a result for bivariate normal distributions (Sheppard, 1899) from statistics is transformed into a financial asset context in order to build a tool which could 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 of two stocks with the same sign of returns and how to split the average return of weighted stocks into four orthants.

Keywords: Correlation; Stock Returns; Joint Probability; Bivariate Normal Distribution

JEL Classification: G10; G110; G170

Suggested Citation

Giner, Javier and Mendoza, Judit and Morini, Sandra, Correlation As Probability: Applications of Sheppard’s Formula to Financial Assets (July 27, 2017). Available at SSRN: https://ssrn.com/abstract=3297529 or http://dx.doi.org/10.2139/ssrn.3297529

Javier Giner (Contact Author)

University of La Laguna - Faculty of Economics, Business and Tourism ( email )

Camino La Hornera s/n
La Laguna, Tenerife, 38071
Spain
+34 922317102 (Phone)

Judit Mendoza

University of La Laguna ( email )

La Laguna, Tenerife, 38071
Spain

Sandra Morini

University of La Laguna ( email )

La Laguna, Tenerife, 38071
Spain

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