The Properties of Co-Quantiles and Their Applications to Momentum Spillovers

17 Pages Posted: 27 Dec 2019

See all articles by Oh Kang Kwon

Oh Kang Kwon

The University of Sydney - Discipline of Finance

Stephen E. Satchell

University of Cambridge - Faculty of Economics and Politics

Date Written: December 6, 2019

Abstract

This paper introduces a generalization of quantiles, order statistics, and concomitants that we term co-quantiles, and investigates their statistical properties. The probability density functions for the co-quantiles are obtained along with their moments under the assumption that the distribution of the underlying data are multivariate normal. In contrast to the conventional order statistics that rank and record the same attribute of a population, or concomitants that consider different attributes observed over the same time period, co-quantiles allow the ranking and recording of different attributes across different time periods. The co-quantile results naturally reduce to those for order statistics and concomitants, and generalize those on the distributions of linear combinations and the maxima of vector valued random variables obtained in Arellano-Valle and Genton (2007, 2008) and those on cross sectional momentum returns obtained in Kwon and Satchell (2018). By applying the results to momentum spillover returns, we establish theoretically that these returns are susceptible to sudden changes in the skewness and the kurtosis during periods of market uncertainty. Since momentum spillover and cross sectional momentum are structurally very similar, this provides a theoretical explanation for the momentum crashes reported in the empirical literature over such periods.

Keywords: co-quantiles, cross sectional momentum, momentum spillover

JEL Classification: C40, G10

Suggested Citation

Kwon, Oh Kang and Satchell, Stephen E., The Properties of Co-Quantiles and Their Applications to Momentum Spillovers (December 6, 2019). Available at SSRN: https://ssrn.com/abstract=3499507 or http://dx.doi.org/10.2139/ssrn.3499507

Oh Kang Kwon (Contact Author)

The University of Sydney - Discipline of Finance ( email )

Discipline of Finance
Codrington Building H69
The University of Sydney, NSW 2006
Australia

Stephen E. Satchell

University of Cambridge - Faculty of Economics and Politics ( email )

Austin Robinson Building
Sidgwick Avenue
Cambridge, CB3 9DD
United Kingdom
44 (0)1223 335213 (Phone)
44 (0)1223 335475 (Fax)

HOME PAGE: http://www.econ.cam.ac.uk/faculty/satchell/index.h

Here is the Coronavirus
related research on SSRN

Paper statistics

Downloads
13
Abstract Views
162
PlumX Metrics