Spectral Analysis of Time-Dependent Market-Adjusted Return Correlation Matrix

7 Pages Posted: 6 Sep 2010  

Michael James Bommarito II

LexPredict, LLC; Bommarito Consulting, LLC; Chicago-Kent College of Law - Illinois Institute of Technology; Michigan State College of Law

Ahmet Duran

University of Michigan at Ann Arbor

Date Written: May 26, 2010

Abstract

We present an adjusted method for calculating the eigenvalues of a time-dependent return correlation matrix that produces a more stationary distribution of eigenvalues. First, we compare the normalized maximum eigenvalue time series of the market-adjusted return correlation matrix to that of logarithmic return correlation matrix on an 18-year dataset of 310 S&P 500-listed stocks for two (small and large) window or memory sizes. We observe that the resulting new eigenvalue time series is more stationary than time series obtained through the use of existing method for each memory. Later, we perform this analysis while sweeping the window size τ ε {5, ..., 100} in order to examine the dependence on the choice of window size. We find that the three dimensional distribution of the eigenvalue time series for our market-adjusted return is significantly more stationary than that produced by classic method. Moreover, our model offers an approximate polarization domain of smooth L-shaped strip. The polarization with large amplitude is revealed, while there is persistence in agreement with small amplitude most of the time.

Keywords: market-adjusted return, return correlation matrix, maximum eigenvalue, random matrix theory

JEL Classification: C14, C32, C44, C61

Suggested Citation

Bommarito, Michael James and Duran, Ahmet, Spectral Analysis of Time-Dependent Market-Adjusted Return Correlation Matrix (May 26, 2010). Available at SSRN: https://ssrn.com/abstract=1672897 or http://dx.doi.org/10.2139/ssrn.1672897

Michael James Bommarito II (Contact Author)

LexPredict, LLC ( email )

MI
United States

HOME PAGE: http://lexpredict.com

Bommarito Consulting, LLC ( email )

MI 48098
United States

HOME PAGE: http://bommaritollc.com

Chicago-Kent College of Law - Illinois Institute of Technology ( email )

565 W. Adams St.
Chicago, IL 60661-3691
United States

Michigan State College of Law ( email )

318 Law College Building
East Lansing, MI 48824-1300
United States

Ahmet Duran

University of Michigan at Ann Arbor ( email )

500 S. State Street
Ann Arbor, MI 48109
United States

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