Survey_HL_2006

Abstract

We focus on a kernel estimator originally proposed by Zhou (1996) that incorporates the first-order autocovariance. A similar estimator was applied to daily return series by French, Schwert, and Stambaugh (1987). Our use of this estimator has three purposes. First, we compare this simple bias-corrected version of the realized variance to the standard measure of the realized variance, and find that these results are generally quite favorable to the bias-corrected estimator. Second, our analysis makes it possible to quantify the accuracy of results based on no-noise assumptions, such as the asymptotic results by Jacod (1994), Jacod and Protter (1998), BarndorffNielsen and Shephard (2002), and Mykland and Zhang (2006) and to evaluate whether the bias-corrected estimator is less sensitive to market microstructure noise. Finally, we use the biascorrected estimator to analyze the validity of the independent noise assumption. We analyze stock returns for the 30 equities of the DJIA. The sample period spans 5 years, from January 3, 2000 to December 31, 2004. We report results for each of the years individually, but give some of the more detailed results only for the years 2000 and 2004 to conserve space. The tick size was reduced from 1/16 of 1 dollar to 1 cent on January 29, 2001, and to avoid mixing mix days with different tick sizes, we drop most of the days during January 2001 from our sample. The data are transaction prices and quotations from NYSE and NASDAQ, and all data were extracted from the Trade and Quote (TAQ) database. We filtered the raw data for outliers, and discarded transactions outside the period 9:30 AM–4:00 PM and removed days with less than 5 hours of trading from the sample. This reduced the sample to the number of days reported in the last column of Table 1. The filtering procedure removed obvious data errors, such as zero prices. We also removed transaction prices that were more than one spread away from the bid and ask quotes. (Details of the filtering procedure are described in a technical appendix available at our website.) The average number of transactions/quotations per day are given for each year in our sample, these reveal a steady increase in the number of transactions and quotations over the 5-year period. The numbers in parentheses are the percentages of transaction prices that differ from the proceeding transaction price and similarly for the quoted prices. The same price is often observed in several consecutivetransactions / quotations, because a large trade may be divided into smaller transactions, and a “new” quote may simply reflect a revision of the “depth” while the bid and ask prices remain unchanged. We use all price observations in our analysis. Censoring all of the zero intraday returns does not affect the RV, but has an impact on the autocorrelation of intraday returns. Our analysis of quotation data is based on bid and ask prices and the average of these (mid-quotes). The RVs are calculated for the hours that the market is open, approximately 390 minutes per day (6.5 hours for most days). Our tables present results for all 30 equities, whereas our figures present results for two equities, Alcoa (AA) and Microsoft (MSFT), which represent DJIA equities with low and high trading activities. The corresponding figures for the other 28 DJIA equities are available on request.