An Optimal and Unbiased Measure of Realized Variance Based on Intermittent High-Frequency Data Peter Reinhard Hansen ∗ Brown University Department of Economics, Box B Providence, RI 02912 Phone: (401) 863-9864 Email: Peter Hansen@brown.edu Asger Lunde The Aarhus School of Business Department of Information Science Fuglesangs All´ e 4 DK-8210 Aarhus V Phone (+45) 89486688 Email: alunde@cls.dk Preliminary version: November 3, 2003 Abstract We consider the problem of estimating a measure of daily volatility from intermittent high-frequency data that are subject to market microstructure effects. We show that a simple Newey-West type modification of the realized variance (RV ) yields an unbiased measure of volatility for the ‘open’ part of the day. The modified RV is unbiased even if 1-minute intra-day returns are used. Further, within a class of conditionally unbiased RV s we characterize the optimal RV in terms of the mean squared error criterion, and we determine the optimal combination of the RV and squared over-night return to form a measure of volatility for the whole day. We apply our results to the 30 stocks of the Dow Jones Industrial Average and an exchange-traded fund that tracks the S&P 500 index, and we construct five years of daily volatilities for these 31 equities. JEL Classification: C10; C22; C80. Keywords: Realized Variance; High-Frequency Data; Quadratic Variation; Conditional Variance; Integrated Variance. ∗ Financial support from the Danish Research Agency, grant no. 24-00-0363 is gratefully acknowledged. All errors remain our responsibility. 1