Estimation of the effective bid-ask spread on high frequency Danish bond data

In this paper the effective bid-ask spread is estimated using 12 high frequency Danish bond samples. A clear-cut MA(1)-model for the mean of the return series, and a GARCH(1,1)-model for the variance, are found. Basically, Roll's model is used, but three different methods of calculating the first-order autocovariance are suggested. Each of these in turn produces three possible ways of estimating the effective bid-ask spread. First, Roll's original autocovariance estimate is used. Second, the autocovariance is calculating using the parameters of an estimated MA(1) model. Third, the autocovariance is obtained from the parameters of a joint MA(1)-GARCH(1,1) model. By means of bootstrapping the standard error of the bid-ask spread estimates are found. It is shown that the gain in efficiency, measured by the relative difference in the standard error of the estimates, is 29% when going from method one to method two, but only 1% when going from method two to method three. These results indicate that the extra gain in efficiency obtained by taking account of the MA(1) structure of the data is noteworthy, but the gain when incorporating the GARCH-effects is negligible.