In general, an increase in liquidity can lead to an improvement in price discovery for that market. In addition, it is not known whether improvements in price discovery lead to more liquidity in the market. Such regulation helps create a more integrated market and therefore may affect a market's contribution to price discovery.
Third ... we find that in the case of cross-listed stocks, algorithmic trading activity negatively affects price discovery. As a result, a market's contribution to price discovery tends to be inversely related to the bid-ask spread.
Liquidity Measures and Algorithmic Trading Proxy
We omit the first and last five minutes of the trading day to avoid capturing the effects of the market opening and closing. This results in a relative trading volume of 52% for the US market, indicating that US trading activity is slightly higher. In terms of effective spread, the US relative effective spread for the US market is 45%, which indicates that on average, trading costs in the US are lower than in Canada.
This is reflected in an increase in the bid-to-trade ratio in both sample periods of 34% in the US and 441% in Canada. Spreads on both markets widened in mid-2008 due to the...financial crisis.
Measuring Price Discovery
This can be attributed to the fact that the Canadian market has increased its algorithmic trading activity in recent years, especially after the emergence of alternative trading systems in mid-2007 to compete with the TSX (Clark, 2011). It measures the contribution of each market to the common factor, where the contribution is a function of the rate of adjustment coefficients. This ratio gives an indication of the degree of dominance of one market over the other market.
Therefore, a PTU S of zero implies that the NYSE does not contribute to the price discovery of the stocks, whereas a PTU S greater than zero implies feedback from the NYSE to the TSX. IS measures the proportion of variance that a market contributes with respect to the variance of the innovations in the common e¢ cient price.
Modelling Price Discovery Dynamics
The Cholesky decomposition of orthogonalizes the innovation terms and assigns all common variance to one market. To take multiple markets into account, Hasbrouck (1995) proposes using different orderings of the innovation terms so that the upper and lower bounds of the information share can be calculated. MatrixA captures the structural parameters and is normalized such that all diagonal elements are equal to 1, and the off-diagonal elements capture the simultaneous interactions between the variables, i.e.
For example, a12; a13; a14 represent the simultaneous influence of Ratio_V ol; Ratio_Espread and Ratio_AT in IS, while a21; a31; a41 represent the simultaneous influence of IS on the ratio_V ol; Ratio_Espreadand Ratio_AT. Since equation (13) can be estimated by OLS, it serves as the basis for the heteroskedasticity identification scheme to obtain the parameters in A. In this section, we begin by showing how price discovery measures for Canadian cross-listed stocks change over time.
We then present the Granger causality results from the reduced form VAR and the results from the structural VAR as formal approaches to assess the dynamics of price discovery.
Price Discovery Over Time
The Augmented Dickey Fuller (ADF) test statistics are insignificant, indicating that unit roots are present in the IS and PT series. The series have skewness values close to zero with excess kurtosis, indicating that observations occur mainly around the mean. We do not see that the first differences are serially correlated, as the AC quickly drops to zero after one delay.
Furthermore, the ADF test statistic is highly significant as it confirms that ... the first types of differences for IS and PT are stationary. IS and PT closely track each other, with PT consistently higher than IS. This is consistent with previous studies showing that the home market for the Canada-U.S
One possible explanation for the increased US contribution to price discovery is the implementation of Reg. The NMS which began in 2006 and was approved in October 2007, an explanation we consider in Section 5.5. Apart from the slight decrease in IS and PT at the end of 2008, the upward trend in price discovery measures does not appear to be substantially affected by the Global Financial Crisis.
Once a particular market gains price discovery, it tends to stay in that market.
Reduced-Form VAR Results
This shows that as trading costs decrease, price discovery increases, indicating intermarket competition among liquidity providers. High-frequency traders aggressively compete by creating market congestion to slow each other down and create exploitable arbitrage opportunities (Gai et al., 2014; Egginton et al., 2016). In doing so, they create a crowding-out effect that drives away speed-disadvantaged investors.
This may reduce investors' incentives to obtain information in the first place, leading to the discovery of lower prices. This ...again shows that greater AT activity has a negative impact and drives away other traders in the market who are at a speed disadvantage. Granger causality tests show statistically significant results, suggesting that trading costs decrease as the market's contribution to price discovery increases.
This ... finding suggests that algorithmic trading activities increase as the market's contribution to price discovery decreases, i.e. we attribute this ... finding to high-frequency traders who implement arbitrage strategies to exploit price differences between securities. The results in Table 5 suggest that a relative increase in liquidity (ie, a higher relative trading volume and a lower effective spread) results in a greater market contribution to price discovery, while an improvement in price discovery leads to greater liquidity.
We also see that an increase in the algorithmic trading activity of one market relative to another market leads to lower price discovery. Studies such as Hendershott et al. 2015) document that high-frequency trading has improved the informativeness of quotes and increased the price discovery of the faster traders. We find evidence that AT competition in one market for latency arbitrage opportunities shifts traders to another market.13 Thus, consistent with Stein (2009) and Egginton et al. 2016), we conclude that HFTs while tracking a certain trading strategy entail negative external effects, which reduces the contribution of a market to price formation.
Structural VAR Results
However, we do not observe a significant simultaneous causal effect of IS (PT) on Ratio_V ol. Furthermore, the simultaneous effect of Ratio_AT on Ratio_V ol is highly significant … not to indicate that the effect of AT on relative trading volume is more widespread simultaneously, ie. in the fourth column, we observe that P T negatively affects Ratio_Espread with a coe¢ cient of -0.018, suggesting that an increase in PT leads to a decrease in the relative spread.
We also observe that Ratio_AT has a significant effect on Ratio_Espread, which was not observed in Table 4. We interpret this to mean that AT crowds out other traders in the market who are relatively speed-disadvantaged, causing the spread to widen. Finally, in the last column we observe similar significant relationships as previously observed in Table 5.
Overall, our results in Table 6 show that not only lagged, but also concurrent relationships exist between relative liquidity, AT activity and price development. It is important to note that the Canadian market has become significantly fragmented after 2009 due to the opening of alternative trading platforms such as Alpha Trading, Chi-X and Pure Trading. V olCAN_ALL and EspreadCAN_ALL are calculated as the total traded volume and the volume-weighted effective spread across all exchanges, respectively.
ATCAN_ALL is calculated based on the total number of messages sent and the total trading volume in dollars across all Canadian exchanges. The reduced form VAR of equation (13) and the structural VAR of equation (12) are then reestimated using pooled data.
Price Discovery Dynamics Pre- and Post-Regulation NMS
Conversely, we observe that changes in IS lead to positive changes in relative trading volume as shown by the first row of the third column in each panel. Third, once the regimes are identified, we estimate the variance-covariance matrices, es, of the reduced-form residuals in the variance regime s (s. Given that s are the variance-covariance matrices of the SVAR for which we are interested , and assuming that the following moment conditions exist,.
Therefore, the basic idea of identification through the heteroscedastic approach is to increase the number of available moments or equations and obtain the matrix A which satisfies equation (A.3) in a different regime, s. If the variance of the shocks in the system varies across different regimes, but the parameters in the matrix A remain constant, the system can be identified. That is, provided the relationship is constant over time, the method yields stable estimates of concurrent effects.
This is an important identification requirement, especially to disentangle the dynamics of each of the variables in the VAR, which are normally highly correlated. What matters is that the coefficient estimates are consistent regardless of how the heteroskedasticity is modeled. This table reports the variances of the residuals of the reduced VAR in equation (A.2).
This table presents the coe¢ cients of the VAR variables after accounting for the fragmentation of the Canadian … financial market. A new approach to the decomposition of economic time series into permanent and transitory components with special attention to the measurement of the 'Business Cycle'. This table shows the sum of the lag coefficients for the VAR in equation (13).
The x-axis represents the sample period from January 2004 to January 2011, while the y-axis represents the value of the levels for each respective variable. This table shows the sum of the lag coefficients for IS VAR in equation (13) at two sub-periods around Reg.
