Estimating Unbiased and Precise Realized Covariances

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Abstract
Existing empirical work on realized covariances partitions the trading day in 5- or 30-minute intervals and then computes the sample covariance based on the resulting 5- or 30-minute returns. Such frequencies are heuristically or subjectively chosen to minimize the bias and avoid market microstructure effects. However, it is also important to consider the preciseness of the covariance estimator. This study compares different methods. Both when only non-trading matters (using midpoints of quotes) and when also bid-ask bounce matters (using transaction prices) the bias-adjusted sample covariance of returns (averaging over all possible subsamples) computed from interpolated prices around equidistant time marks performs well based on the root mean squared error. The optimal choice substantially lowers the RMSE compared to existing heuristic choices.