Index Arbitrage and Refresh Time Bias in Covariance Estimation

16 Pages Posted: 15 Jan 2012 Last revised: 23 Jan 2012

Dale W. R. Rosenthal

University of Illinois at Chicago - Department of Finance

Jin Zhang

Illinois Institute of Technology

Date Written: January 14, 2011

Abstract

Estimating covariance matrices using high-frequency data is crucial for market makers, investors in newly-issued securities, and risk managers. These estimations often handle the asynchrony of high-frequency trades by using returns for periods between when all instruments have traded (refresh times). We show that index arbitrage trading biases estimates of variances and covariances. The mean reversion of the index arbitrage spread adds a second data generating process which biases variance estimates. That second process creates refresh times simultaneous with trading-induced comovement of index members which bias covariance estimates. Initial results show there is a bias, that removing likely index arbitrage trades yields a lower estimate of covariances, and that estimators may converge sooner using such cleaned data. Our results suggest overestimates of variances and covariances of about 2%-3% -- equivalent to expected returns of 3%-6% higher and implying overly diversified portfolios.

Keywords: high-frequency volatility estimation, refresh times, bias, data cleaning

JEL Classification: C32, C31, C83

Suggested Citation

Rosenthal, Dale W. R. and Zhang, Jin, Index Arbitrage and Refresh Time Bias in Covariance Estimation (January 14, 2011). Available at SSRN: https://ssrn.com/abstract=1985254 or http://dx.doi.org/10.2139/ssrn.1985254

Dale W. R. Rosenthal (Contact Author)

University of Illinois at Chicago - Department of Finance ( email )

2431 University Hall (UH)
601 S. Morgan Street
Chicago, IL 60607-7124
United States

HOME PAGE: http://tigger.uic.edu/~daler

Jin Zhang

Illinois Institute of Technology ( email )

565 West Adams Street
Chicago, IL 60661
United States

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