Financial crises, price discovery, and information transmission: a high-frequency perspective

Ederington and Lee (1993) document that most of the price adjustments to major announcements occur within the first minute. See also Christensen et al. (2011) for a literature overview on sampling intervals over the last four decades.

We refrained from using quotes mainly for two reasons. First, in our sample, we usually see only low liquidity at the top levels of the bid and ask side. This concern was further exacerbated by the upcoming discussion on order spoofing and other manipulation attempts. We therefore decided to use transaction data. Secondly, we find substantial differences in the market interactions for our three different subsamples, but all three subsamples should be affected similarly by bounces in transaction prices between trades at the bid and ask quote (negative autocorrelation).

To convert the irregularly spaced tick-by-tick prices into time series with fixed time intervals, we take the last transaction price within the interval [t, t+1] as the price, \(P_t\).

We remove the opening and closing prices resulting from the respective auctions at 8:00 and 22:00 when the German futures markets open and close. When the underlying markets open at 9:00, we find a spike in the futures markets, showing that there is a daily volatility pattern associated with stock market opening and closing.

We also find significant negative first-order autocorrelations in asset returns with higher-order autocorrelations around or within the 95% confidence band. The volatilities of all five markets follow a long-memory process.

We also analyzed announcement data from the European Monetary Union (EMU). However, we find that aggregate EMU news is generally insignificant, with the exception of a minor impact on the USD/EUR exchange rate. One explanation for the insignificant effect of macroeconomic data from the EMU lies in the non-revision of forecasts. Only some survey participants revise their reported forecasts for the EMU after announcements from single countries, but most do not, which leads to a biased measurement of surprises.

In total we use 18 different macroeconomic indicators from the US and Germany. For all US announcements we have 72 observations except for initial unemployment rate with 313 observations. For Germany the number varies between 61 and 71. For German GDP we only have 23 observations.

It is important to note that only those events that coincide with announcements are listed. For example, the Lehman Brothers collapse took place when no macroeconomic news was released.

We do not apply a minimum threshold as a deviation from the expectation (as, e.g., in Hanousek and Kocenda 2011), as this would only eliminate very few observations.

Chaboud et al. (2010) use a USD/EUR dataset from ICAP and demonstrate that 15- to 20-s intervals can be used without contaminating the realized variance with market microstructure noise. For a simple realized kernel estimator, they find no noticeable bias, even for 2- to 5-s intervals. They show that sampling intervals may be even shorter for days when US macroeconomic data are released.

We compare the realized variance with the realized kernel for DAX and Bund futures and for the USD/EUR exchange rate for different sampling frequencies. The realized kernels converge to a stable level at a frequency of roughly 1 min, while realized volatility approaches true volatility at a 20-min frequency. The volatilities of E-mini S&P500 and 10-year Treasury note futures tend to be underestimated using realized kernels at lower frequencies. Realized kernels based on 5-s to 1-min intervals are closer to the true volatilities. We also use Bandi and Russel’s (2005) MSE approach to calculate the optimal time interval for realized volatility, which confirms the results from the signature plot (i.e., an optimal interval of about 20 min).

We also extend the time window to one and a half hours after the announcements. However, the results do not change materially. Furthermore, a 1-h time window is sufficient to capture the volatility response.

Note that \({\hat{\sigma }}_{d(t)}\) is the daily unconditional volatility based on a realized kernel, whereas \(|\varepsilon _t |\) is the conditional (mean) volatility on a 1-min sampling frequency. Related to the unbiased estimate based on realized kernels, the conditional volatility \(|\varepsilon _t |\) converges toward the 1-min adjusted unconditional volatility \({\hat{\sigma }}_{d(t)}\) in the long term. Under this assumption, the 1-min adjusted expected value of \({\hat{\sigma }}_{d(t)}\) equals the expected value of \(|\varepsilon _t |\).

Because of its periodic patterns (see Fig. 1), we further filter the USD/EUR exchange rate volatility by using a flexible Fourier form (FFF), \(\sum \nolimits _{q=1}^{Q}\left( \varphi _{q}\ \cos (\frac{q2\pi t}{720})+\eta _{q}\ \sin \left( \frac{q2\pi t}{720}\right) \right) \) as in Andersen et al. (2003b). We also tested other ARFIMA(p,d,q) model specifications. However, we found that the selected filter is most suitable for whitening the volatility process.

In order to keep the number of lags consistent for all five OLS regressions, we choose the lag length based on a VAR model. We also test specific lag lengths for each single OLS regression model. However, the lag lengths vary only slightly and the results are qualitatively the same.

Note that we use \(\xi _t\) from the ARFIMA process as the filtered volatility, and not the absolute values, because the absolute returns, \(|R_t|\), already represent the volatility process. Thus, taking the absolute values of the residuals derived from the ARFIMA process would reflect the filtered volatility of the return volatility process. From the filtering process, we necessarily obtain positive and negative values; however, the negative deviations are not significantly different from zero.

We also tried to include first and second leads in the model, but we found no pre-announcement impact on returns. The choice of minutes around the news releases shown in Figure  was done on the basis of significant price changes in the data, with effects mainly observed in the − 3 to \(+\) 8 min window around announcements.

Table C1 in the Internet Appendix shows the results for the whole sample and for all macroeconomic news.

We also added a variable for standardized trading volume in our return equation in order to capture liquidity effects on the volatility. However, the coefficients are economically small.

We define the cumulative impact on return as the sum of continuous significant coefficients (as long as they do not involve a sign change). The accumulation of return responses begins from the first significant coefficient, and ceases when an insignificant coefficient or changing sign is observed. We impose this relatively conservative measure to avoid overestimation or amplification of the cumulative responses.

We also examine the volatility response for 10 min before the news release. We find slight increases in volatility for some important economic indicators. However, the magnitude is very small, and there is no distinctive pattern.

The polynomial response functions of Eqs. (5a) and (5b) replace the coefficients of news dummies in Eq. (4). The average intraday volatility accounts for most of the variation. Other factors (news dummies and average intraday volatility, as well as calendar, event, crisis, and day-of-the-week dummies) that influence volatilities are also incorporated into the volatility equation as discussed in the previous section. Thus, the polynomial responses capture only the macroeconomic news effects.

By definition, positive US news has a negative impact on the USD/EUR exchange rate, while positive German news affects FX positively. Therefore, we observe opposite signs of conditional correlation coefficients between USD/EUR exchange rate and any other market in response to US and German news, e.g., \(\rho _{USD/EUR,Bund\,\,Futures}^{US;\,\,Pre-crisis}=0.479\) and \(\rho _{USD/EUR,Bund\,\,Futures}^{German;\,\,Pre-crisis}=-\,0.303\).

We also calculated the Bravais-Pearson correlation coefficient and a realized volatility-based coefficient. Both qualitatively confirm our realized kernel-based results.

To conserve space we do not report the full tables with the estimated coefficients here; however, they are shown in Table E1 in the Internet Appendix.

We also run a placebo test by choosing days without announcements. Unsurprisingly, the robustness checks for selected days reported in Table D1 in the Internet Appendix show substantially lower estimates. This finding supports the assumption that information transmissions predominantly occur at the time of a news release.

We used the same days without announcements that were used for the placebo test for the return spillovers (see footnote 26). The indicative robustness checks reported in Table D2 show again much smaller interaction coefficients.