3.4 The impact of arbitrage on market liquidity
3.4.6 Exchange level: Impulse response functions of arbitrage activity and
In this section I estimate vector autoregressions on the exchange level, i.e. by first averaging stock specific estimates across all stocks from the same exchange. Previous research pro-vides empirical evidence that both the liquidity and the efficiency of single stocks improve and deteriorate at the same time (Chordia et al., 2000; Karolyi et al., 2012; R¨osch et al., 2015). Aggregating stock specific price deviations at the exchange level should reduce noise and other stock specific variations. Especially, periods during which stock-specific arbitrage opportunities mainly arise as a result of differences in information so that arbitrageurs would lower liquidity, could be diversified at the exchange level (compare, e.g. Lai et al. (2014)). In this case predictability between arbitrage activity and liquidity should be even stronger at the market level than at the stock level.
In addition to former impulse response functions on Opportunity-Profit and quoted spread, at the market level, I include a proxy for market demand, namely order imbalance, the absolute difference between the number of buyer and seller initiated trades.
If arbitrageurs trade against net market demand, as would be the case if price deviations arise as a result of demand shocks, a decrease in arbitrage activity should increase net order imbalances. The increase in order imbalances could then lead to a decline in contemporaneous and future liquidity (O’Hara and Oldfield, 1986; Chordia et al., 2002; Comerton-Forde et al., 2010).
Instead of tabulating the contemporaneous and cumulative five-day responses to a shock to arbitrage activity (as before), I now report graphs to highlight the day-to-day effect.
Figure 3.2 – Responses from shocks toOpportunity-Profit on home and cross-listed quoted spreads and order imbalance, 2003- 2013
This figure shows impulse response functions (IRF) from vector autoregression (VAR) estimated on exchange level (i.e. equally-weighted averages across all stocks in the sample from a given exchange) daily Opportunity-Profit, absolute net order imbalance in the home market (OIB Home), absolute net order imbalance in the cross-listed market (OIB Host), and average proportional quoted spread in the home- and host-market (PQSPR Home and PQSPR Host). For a description of these variables I refer to Table 2.1. All timeseries are detrended and expunged from other calendar regularities (i.e. residuals of regression Eq. 3.4) The lag length of each VAR is chosen individually (for each exchange) based on the Akaike information criterion. IRF are estimated for each different exchange (in columns) separately. All IRF show responses in standard deviations measured to Cholesky one standard-deviation shocks to Opportunity-Profit. All variables are measured during the overlapping trading time, i.e. when both the home market and the cross-listed market are in their continuous trading session. Each figure shows bootstrapped 95% confidence bands based on 1000 runs (lower, upper). All data underlying the computations are from TRTH.
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Figure 3.2 shows impulse response functions (IRFs) estimated from vector autoregres-sions on Opportunity-Profit, home and ADR order imbalance and proportional quoted spreads.
These impulse response functions have been estimated by exchange (column). For parsimony Figure 3.2 only reports IRFs from shocks to Opportunity-Profit. The x-axis tracks the response through time starting from 1 (the contemporaneous effect) till the n-th day, the lag-length of the VAR, which was chosen by Akaike information criteria individually for each exchange and varies from 8 for Germany to 12 for Mexico.
As before, for each individual stock all five series are first detrended (i.e. residuals from Eg. 3.4 are used), and winsorized at the 1% level. I then take the equal weighted average across all stocks from a given exchange and standardize each series. These adjusted series on market Opportunity-Profit, order imbalance, and quoted spread are the input series for the VAR, and of this order. The order is motivated by: First, Table 3.2 indicates that most price deviations arise because of a demand shock, and hence arbitrage activity should contemporaneously affect market order imbalance. This motivates using Opportunity-Profit as the first variable. Second, previous literature indicates that order imbalance has a contemporaneous effect on market liquidity (Chordia et al., 2002). This motivates the order between measures of order imbalance and measures of market liquidity.
The first (second) row of Figure 3.2 shows the effect (y-axis) of an orthogonalized, one-standard deviation shock to Opportunity-Profit on home-market (ADR) order imbalance by day (x-axis). Similar, the third (last) row of Figure 3.2 show the effect on home-market (ADR) quoted spread.
In all but one case the IRF is positive and significant in the first few days after the shock, then decreases and becomes statistically insignificant. The negative slope in the IRFs indicates previous Dickey-Fuller tests (untabulated) that reject the existence of a unit-root in the adjusted series at the 1% level in all cases.
A one standard deviation shock to Opportunity-Profit leads to a contemporaneous increase in order imbalance of the home-market share (from 0.10 standard deviations in the U.K. to 0.03 in France), order imbalance of the ADR (from 0.10 in Brazil to 0.03 in France), quoted spread of the home-market (from 0.20 in Germany and the U.K. to 0.01 in Mexico), and quoted spread of the ADR (from 0.13 in Germany to 0.03 in France). One day after the shock the effect on order imbalance and quoted spread remains positive in all but one cases, and statistically significant except for order imbalance of the home-market in France and Mexico, and for quoted spread of the home-market (ADR) in Mexico (France).
This indicates that a positive shock to Opportunity-Profit (a decrease in arbitrage
activ-ity) predicts an increase in order imbalance and quoted spread contemporaneously and over the next few days, and provides evidence that arbitrageurs trade against market demand and thereby improve liquidity.
The effect of arbitrage activity at the exchange-level is much stronger than at the individual stock-level. For the average stock a positive shock of one standard deviation to Opportunity-Profit predicts an increase in home- and host-market quoted spreads of 0.25 and 0.13 standard deviations after five days (from Table 3.4). For the average exchange the impact almost dou-bles and increases to around 0.35 and 0.20 standard deviations for the home- and host-market quoted spread and can be as high as 0.5 standard deviations for the home-market quoted spread in Brazil, the U.K., and Germany. By aggregating estimations at the exchange-level noise and other stock-specific variation is reduced, which potentially can explain the difference in mag-nitudes.
I unreported robustness tests I use effective spread, quoted depth, and the standard devia-tion of the pricing error (Hasbrouck, 1993) as alternative measures of market quality and both Traded-Profit and the velocity as alternative measures of arbitrage activity. In all cases the results are similar.
The results are also robust for using a slightly different time period and a different order of the endogeneous variables (as reported in a previous version of this paper). Using data from 2001 till 2011 with the default order the shock to Opportunity-Profit results in a cumulative significant response (at the 5% level) after 5-days for quoted spread, effective spread, and quoted depth in 22 out of the 30 cases (three variables times five exchanges, for both the home market and the ADR). Estimating IRFs with the reverse order in which Opportunity-Profit is last, indicates that a positive shock to Opportunity-Profit predicts an cumulative increase in illiquidity (quoted spread, effective spread, and quoted depth) in 26 out of 30 cases and 15 of these are significant at the 5% level.