Beta-Adjusted Covariance Estimation

The increase in trading frequency of Exchanged Traded Funds (ETFs) presents a positive externality for financial risk management when the price of the ETF is available at a higher frequency than the price of the component stocks. The positive spillover consists in improving the accuracy of pre-estimators of the integrated covariance of the stocks included in the ETF. The proposed Beta Adjusted Covariance (BAC) equals the pre-estimator plus a minimal adjustment matrix such that the covariance-implied stock-ETF beta equals a target beta. We focus on the Hayashi and Yoshida (2005) pre-estimator and derive the asymptotic distribution of its implied stock-ETF beta. The simulation study confirms that the accuracy gains are substantial in all cases considered. In the empirical part of the paper, we show the gains in tracking error efficiency when using the BAC adjustment for constructing portfolios that replicate a broad index using a subset of stocks.