Index Arbitrage and Refresh Time Bias in Covariance Estimation

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