Combining Dimension Reduction, Distance Measures and Covariance (Presentation Slides)

40 Pages Posted: 18 May 2017  

Ravi Kashyap

Gain Knowledge Group; City University of Hong Kong (CityUHK) - Department of Economics & Finance

Multiple version iconThere are 2 versions of this paper

Date Written: June 04, 2017

Abstract

We consider a measure of similarity, the Bhattacharyya distance, across distributions of random variables. We develop a novel methodology based on the marriage between the Bhattacharyya distance and the Johnson Lindenstrauss Lemma, a technique for dimension reduction, providing us with a simple yet powerful tool that allows comparisons between data-sets representing any two distributions. We demonstrate a relationship between covariance and distance measures based on a generic extension of Stein’s Lemma. The degree to which different markets or sub groups of securities have different measures of their corresponding distributions tells us the extent to which they are different. This can aid investors looking for diversification or looking for more of the same thing. We consider an asset pricing application and then briefly discuss how this methodology lends itself to numerous Marketstructure studies and even applications outside the realm of finance / social sciences by illustrating a biological application.

Keywords: Uncertainty, Microstructure, Microscope, Price, Volume, Volatility, Distribution, Dimension, Covariance, Distance, Measure, Reduction

Suggested Citation

Kashyap, Ravi, Combining Dimension Reduction, Distance Measures and Covariance (Presentation Slides) (June 04, 2017). Available at SSRN: https://ssrn.com/abstract=2970367 or http://dx.doi.org/10.2139/ssrn.2970367

Ravi Kashyap (Contact Author)

Gain Knowledge Group ( email )

1 Austin Road West
Kowloon
Hong Kong

HOME PAGE: http://www.gainknowledge.com

City University of Hong Kong (CityUHK) - Department of Economics & Finance ( email )

83 Tat Chee Avenue
Kowloon
Hong Kong

HOME PAGE: http://www.cb.cityu.edu.hk/research/student/rkashyap3/

Paper statistics

Downloads
33
Abstract Views
213