key: cord-0960184-qwtmoae7
authors: Foley, Sean; Kwan, Amy; Philip, Richard; Ødegaard, Bernt Arne
title: Contagious margin calls: How COVID-19 threatened global stock market liquidity
date: 2021-10-30
journal: Journal of Financial Markets
DOI: 10.1016/j.finmar.2021.100689
sha: afff740f88a74cd5a4f5edbce283202264471344
doc_id: 960184
cord_uid: qwtmoae7

The outbreak of the COVID-19 pandemic caused some of the largest — and fastest — market dislocations in modern history. During the outbreak, liquidity quickly evaporated in a coordinated fashion across global markets. We show that a sudden increase in margin requirements during the pandemic is correlated with the withdrawal of global liquidity providers. These effects are concentrated in securities most exposed to high-frequency market makers, consistent with the binding nature of increased capital constraints.

"We can't bid on anything that adds to the balance sheet right now." 1 This quote from Vikram Rao -head bond trader of Capital Group -with respect to the purchase of U.S. Treasury bonds during the height of the COVID-19 pandemic exposes one of the major issues faced by global equity market makers -a downward liquidity spiral exacerbated by the significant increase in margin requirements the world over. A press release from the only listed global equity market makers, Virtu Financial, echoed a similar sentiment: 2 "Given the sustained levels of extraordinary volatility in the current macro environment . . . we consider it prudent to opportunistically supplement our borrowing capacity." Indeed, Virtu required a temporary addition of US $450 million in "additional broker dealer capital" to continue their global market making operations.

Their announcement came nine days after the World Health Organization (WHO) declared COVID-19 to be a global pandemic: A procyclical period of increasing margin requirements across global equities and futures markets.

According to recent theory models, there is potential for a negative liquidity spiral when there is a sharp drop in traders' funding liquidity. Brunnermeier and Pedersen (2009) document that the increased trading margins required by exchanges to minimize counterparty default risk between participants increases funding liquidity. These rising margin requirements cause reductions in market liquidity, resulting in a procyclical negative liquidity spiral. However, there are few empirical tests of these predictions, as large changes to margin requirements occur infrequently.

The WHO's declaration of the COVID-19 pandemic in March 2020 is associated with some of the largest dislocations in market history. Equity market values fell by 30%-40% globally, and the withdrawal of liquidity supply was correlated with a sharp increase in margin requirements for exchange-traded equity products, in some instances by more than requirements is correlated with a sharp reduction in equity market liquidity. This margininduced shock to funding liquidity impacted the available market liquidity exactly at the time equity market price levels were falling, due to the unprecedented global risk COVID-19 posed to company cash flows. Our findings suggest that traders must de-leverage their positions precisely at the point in time when prices are declining, thereby potentially further depressing prices and increasing margin, consistent with the theoretical findings of Morris and Shin (2004) . This process can create a margin loss-spiral, consistent with the rapid reduction in both market liquidity and prices observed in March 2020.

We contribute to the extant literature in two key ways. First, we empirically test theories documenting the procyclical nature of margin requirements and the negative spirals they could generate for market participants (Brunnermeier and Pedersen, 2009; Repullo and Suarez, 2013; Hugonnier and Morellec, 2017) . While Behn et al. (2016) and Berger et al. (2016) study the impacts of margin requirements during the 2008 Global Financial Crisis in a banking context, we are the first to test these theories in equity markets.

Second, we contribute to a growing literature seeking to understand and explain why the effects of the COVID-19 pandemic are so significant and swift for asset valuations and the overall trading environment. Market participants have come to expect the underlying market architecture, or "plumbing," to facilitate smooth and orderly trading of vast proportions within our financial institutions. Any failure of such systems, no matter how brief, must be examined and understood. For example, there are studies seeking to understand dislocations in U.S. Treasury assets (Cheng et al., 2020; Duffie, 2020) , dislocations from the NYSE trading floor (Brogaard et al., 2020) , and the magnitude of asset price responses and dislocations (Baker et al., 2020; Ramelli and Wagner, 2020) .

Our work provides a channel by which such dislocations can occur -namely changes in the margin required for liquidity suppliers.

The significance of the capital constraints faced by high-frequency market makers has become particularly important in a world where the majority of liquidity is provided 5 J o u r n a l P r e -p r o o f by only a handful of firms, such as Citadel and Virtu. When these firms represent the majority of liquidity provision not only within a market, but also across markets, the procyclicality of their available committed capital represents a systemic risk that should no longer be ignored.

The remainder of the paper is organized as follows. In Section 2, we discuss the relevant literature on margin requirements and market liquidity. In Section 3, we describe the data used in the study. Sections 4 and 5 report on the evolution of margin requirements and liquidity over the pandemic period, respectively. In Section 6, we present the results of our study and Section 7 concludes.

Theoretical models identify shocks to market liquidity following price declines in a variety of ways. Collateral-based models rely on market makers to absorb these temporary buy-sell imbalances. However, market makers with finite funding levels obtain financing by posting margins, utilizing the underlying securities they hold as collateral. When stock prices fall rapidly, intermediaries hit their funding limits and are forced to liquidate. This "liquidity spiral" is documented by Brunnermeier and Pedersen (2009) , and supported by the work of Weill (2007) . Procyclical increases in margins in response to volatility limit the ability of participants to provide liquidity, particularly when such constraints become binding. Similar models are proposed with funding constrained arbitrageurs as liquidity providers (Gromb and Vayanos, 2002) or with short-term traders unable to take on inventory due to funding constraints (Morris and Shin, 2004) . In a model proposed by Gârleanu and Pedersen (2011) , the impact of binding margin requirements becomes "priced," resulting in discounts on high-margin assets. This procyclicality has been studied extensively in previous banking studies in response to the 2007-2009 Global Financial Crisis (GFC), both theoretically (Repullo and Suarez, 2013; Hugonnier and Morellec, 2017) and empirically (Behn et al., 2016; Berger et al., 2016) . Empirically, studies of the margin requirements for equity market makers 6 J o u r n a l P r e -p r o o f Journal Pre-proof have been hindered by the availability of such data. In some markets, the link between liquidity provision and margin constraints have been explicitly documented. For example, in bond markets, Adrian et al. (2017) document larger reductions in liquidity after the GFC in bonds traded by firms with more leverage, indicating the binding nature of their margin requirements. Aramonte and Szerszeń (2020) use a supervisory dataset to examine U.S. corporate bonds and credit default swaps and show that dealer profitability plays a significant role in secondary market liquidity. Daskalaki and Skiadopoulos (2016) examine the commodity futures markets and show that an increase in margins following the Dodd-Frank Act increases transactions costs and reduces depth. Finally, Dudley and Nimalendran (2011) show that increases in the funding margins for futures markets increase the illiquidity and contagion risk of mutual hedge funds.

Empirical studies of equity trading have alluded to the the role binding margin constraints play in harming overall market liquidity, but have not been able to directly demonstrate this relation. For example, Hameed et al. (2010) document reductions in liquidity around market declines, particularly when the funding markets are tight, which are likely to arise from capital constraints on market makers. Similarly, Comerton-Forde et al. (2010) show that the inventory levels and trading revenues of NYSE market makers are correlated with their propensity to supply liquidity. In a global study, Karolyi et al. (2012) find that commonality in liquidity is greater in countries with higher market volatility, and is also higher at points in time when volatility is greatest, consistent with the impact of binding funding liquidity constraints. Despite this consistent evidence from equity markets of the potential role margin plays in equity market liquidity provision, to date, no study has been able to clearly identify this mechanism.

Our global findings for the equity markets align well with evidence from Duffie (2020), who investigates U.S. Treasury markets and shows that the inventory risk faced by dealers results in bid-ask spreads that increase to over 10 times their (relatively stable) prepandemic levels. The larger magnitudes observed in these markets likely reflects the greater leverage (and lower historic volatility) utilized in these settings. Similarly, other 7 J o u r n a l P r e -p r o o f recent papers, including Bent et al. (2019 ), Cheng et al. (2020 and Fleming and Ruela (2020) , show that increased margin requirements during the COVID-19 pandemic caused significant deterioration in overall measures of market liquidity in Treasury bond markets.

Our paper further complements studies examining the effects of COVID-19 on equity markets. While the majority of these papers aim to understand the asset pricing implications of the pandemic, 3 studies focusing on the working of financial equity markets during the COVID-19 crisis is more limited. For example, Brogaard et al. (2020) show that the suspension of trading by physical market makers on the trading floor at the NYSE deteriorates overall market quality.

In this section, we provide details on the markets investigated and describe the data sources. We also provide descriptive statistics on the main variables analyzed in the study.

Our analysis considers equity markets across a broad range of developed countries. Table 1 outlines the markets and index stocks in our sample. This set of markets yields not only a broad cross-section of the developed world, but also provides variation in the societal response to the COVID-19 crisis, as well as variation in the absolute scale of the outbreak. Figure 1 illustrates the disruption to global stock markets, showing how our sample markets fell from their price levels on February 1, 2020 (normalized to 100).

In Subsection 6.2, we investigate liquidity metrics for stocks that are index constituents of the market's main index, relative to stocks outside of the main index. For Hong Kong, we use stocks in the Hang Seng LargeCap and MidCap indices that are outside of the main Hang Seng Index as the sample of non-index stocks. For the U.K., we use data for the firms in the FTSE 250, but not within the FTSE 100, to represent our non-index stocks. For the remaining markets, we use data for all reasonably liquid non-index stocks listed on these exchanges, which we define as stocks above the median market capitalization among the non-index stocks, conditional on having more than 100 trades per day.

We source the data for this study from the Refinitiv database. 4 The data contain millisecond timestamped records of quotes and trades. For each stock, we calculate intraday quoted spread, effective spread, realized spread, and price impact. For the latter two, we use a 10-second delay in the calculations to capture the returns to HFMMs, consistent with the work of Conrad and Wahal (2020). 5 We consider only the trading activity during the continuous trading session at the main (listing) exchange. 6

In Subsection 6.1, we investigate the liquidity of an U.S.-traded ETF tracking the S&P 500 relative to a U.K.-traded ETF that also tracks the S&P 500. 7 We also collect data on the trades and quotes for these ETFs from Refinitiv. Similarly, we calculate the same liquidity measures outlined above, but we compute them as averages every trading hour, rather than as daily averages. Table 2 provides descriptive statistics for the stocks in our sample. To illustrate a representative non-pandemic period, these tables provide averages for the liquidity measures over the period January 1 to February 15, 2020. Panel A presents statistics for the stocks that are constituents of the market's main index, as listed in Table 1, while Panel B provides descriptive statistics for the sample of relatively liquid stocks outside of the main index. We observe a high similarity in quoted spreads across markets, and as expected, the transaction costs for non-index stocks are substantially higher than those of their index-constituent counterparts.

Margins refer to the minimum amount of money a trader must deposit in their margin trading account to fund the notional exposure of their portfolio. These margins serve as a collateral deposit and minimize credit risk. Specifically, exchanges typically define both an initial margin (IM) and maintenance margin (MM). The IM is the collateral required as a proportion of the total traded value to open a new leveraged position. The MM is the minimum collateral a trader must retain to maintain their open position. For example, a $100 buy order may require an IM of 5% (or $5). Appreciation in the bought asset, say to $110, results in the value of the margin account increasing by $10. However, reductions in price will be deducted from the margin account. For a MM of 2.5%, the trader's position is automatically closed if the price falls below $97.5 (leaving only the minimum 2.5% margin).

We collect the daily IM requirements for equity index futures contracts for multiple indices. We obtain these data directly from regulatory information available on each exchange's webpage. 8 Typically, exchanges report margin as the dollar amount required to trade a contract. 9 For example, the margin to buy one S&P 500 futures contract that has a notional exposure of approximately $840,000 is reported as $31,500 at the start of our sample period. Table 3 , Panel A, contains descriptive statistics for the dollar margin for each contract for a pre-pandemic and a post-pandemic period around the WHO's declaration of a pandemic on March 11, 2020. The pre-pandemic period spans from February 11 to March 10, 2020 and the post-pandemic period spans from March 11 to April 11, 2020.

Because the notional value for equity index futures contracts differs significantly across markets, the reported dollar margin can be hard to interpret. Accordingly, While the figures reported in Panel B allow for an intuitive comparison across exchanges, a change in percentage margin can occur due to a change in the notional exposure (caused by a change in price), rather than a change in the dollar margin. Thus, to avoid any potential contamination of margin changes due to changes in the underlying price (or notional exposure), we use the dollar margin per contract, rather than the percentage margin, for our analysis in the following sections. 10 However, to allow for a comparison across each contract, we present the summary statistics for the dollar margin requirement on each day, relative to the average daily margin requirement in January,

Because we are unable to obtain margin data for the Nordic markets, for reasons outlined in Section 4 and Subsection 6.2, we rely on the systemic increase in global margins to proxy for the margin requirements in these markets.

To understand the impact of the pandemic on margin levels, in Figure 2 we plot the margin requirements for equity index futures in markets for which we are able to obtain margin data: Canada, Hong Kong, U.K., and U.S. The figure shows that the margin requirements remain reasonably constant throughout January and February, 2020, but rapidly increase around the WHO's announcement of a pandemic on March 11, 2020, reaching over 300% of pre-pandemic levels in the case of Canada. Because of the systemic increase in global margin requirements in March, 2020, it is reasonable to assume that other markets for which we do not have margin data (i.e., Norway and Sweden), also experienced similar jumps in margin requirements, which we discuss further in Subsection 6.2.

10 Our results are robust to either the dollar or percentage measure of margin.

J o u r n a l P r e -p r o o f

The sudden dramatic jump in margin for equity index futures is likely to affect stock liquidity in several ways. First, while we are unable to obtain data on individual stock margins, it is reasonable to assume that stock margins experienced similar jumps, 11 thereby directly imposing binding constraints on leveraged traders, who subsequently withdraw from the market. Second, a jump in the margin requirements for equity index futures is likely to affect leveraged sophisticated investors and cross-market arbitrageurs, who typically hedge their underlying equity positions via equity derivative products, such as index futures. Thus, these sophisticated investors could also withdraw from equity markets if they are unable to effectively manage their risk via the futures markets.

We argue that HFMMs are more sensitive to margin requirements than traditional traders due to their unique trading style. HFMMs operate over short time horizons, and typically carry no overnight inventory risk (Hasbrouck and Saar, 2013; Bartlett and McCrary, 2019; Shkilko and Sokolov, 2020) . Accordingly, their positions are unlikely to precipitate a margin call, as large adverse price moves are unlikely to occur during their short holding periods. For this reason, HFMMs require less "buffer" in their margin accounts and can effectively trade on higher leverage ratios closer to the binding margin limits than other market participants. Moreover, HFMMs are often propriety trading firms, with smaller balance sheets than large institutional investors that use leveraged derivative positions to hedge price risk.

A key component of the health of any market is liquidity. Figure 3 illustrates the evolution of liquidity during the pandemic. We document the changes across two key metrics: quoted spread (the anticipated cost of liquidity provision) and effective spread (the cost of traded liquidity).

Panel A shows the quoted spread relative to the average daily levels during January, 11 In Appendix C, we confirm that margins for equity index futures are likely to be highly correlated with the margin requirements for their underlying stocks.

J o u r n a l P r e -p r o o f Journal Pre-proof 2020. We observe that quoted spreads, which measure the marginal cost charged by a liquidity provider for an additional unit of liquidity, begin rising around the beginning of March. However, after the WHO's declaration of a pandemic on March 11, 2020, we observe a significant increase in this measure of transaction costs. 12 For Canada and the U.K., the quoted spread increases from around 200% of January levels in the beginning of March to upwards of 500% by the end of March. All other markets show a similar response, with significant increases from pre-pandemic levels. This sharp increase in quoted spreads supports the notion that liquidity providers became more cautious in their liquidity provision once it became clear that COVID-19 would become a global issue. By early May 2020, these costs had fallen to a more typical level, but still remain between 125% and 200% of their pre-pandemic levels.

Panel B documents the evolution of effective spreads, representing the transaction cost of liquidity demanders when liquidity is consumed. Unlike the quoted spread, which measures the cost of trading an additional share, the effective spread measures the cost of liquidity in the size demanded-large market orders are likely to walk the book, increasing their actual cost. Rapid, correlated "fire sales" by market participants are likely to exhaust available market liquidity, increasing the transaction costs borne by market participants. Panel B shows that effective spreads follow a similar evolution to quoted spreads, with the cost of demanding liquidity in the U.K. increasing the most, peaking at 450% of January levels during March 2020.

One feature of the models proposed by Morris and Shin (2004) and Brunnermeier and Pedersen (2009) is that volatile markets may result in increased capital margin requirements. These increased margins may constrain the ability of market makers, arbitrageurs, and speculators to provide liquidity exactly when it is needed. This constraint can result in reduced liquidity, further increasing volatility, resulting in a negative "liquidity spiral" or "liquidity black hole." The COVID-19 pandemic provides a fertile field to test these theoretical arguments in an equity market setting.

This section presents our main results. In Subsection 6.1, we examine a unique case of two ETFs tracking the S&P 500 Index. While these ETFs track the same underlying asset, the ETFs trade on different markets, which experience different changes in their margin requirements during March 2020. We exploit this unique setting to test the relation between margin requirements and market liquidity. In Subsection 6.2, we extend the analysis to the world's major equity markets. We argue that changes to margin requirements affect stocks that are index constituents more than stocks that are outside the index due to a higher concentration of margin sensitive high-frequency market makers (HFMM) in index constituents. Using a difference-in-differences analysis, we find a larger fall in liquidity for stocks that are index constituents than non-index constituents, following a margin increase. Last, in Subsection 6.3, using the order to trade ratio as a proxy for HFMM activity, we test whether HFMMs withdraw more from index stocks, relative to non-index stocks, when margin requirements increase.

We investigate liquidity differentials between two ETFs that track the same underlying index and test if these differentials are correlated to changes in margin requirements.

Specifically, we investigate SPY, an ETF tracking the S&P 500 that trades on the NYSE (the U.S. ETF), and CPSX.L, an ETF that also tracks the S&P 500, but trades on the London Stock Exchange (the U.K. ETF). Accordingly, these two ETFs trade on different exchanges and are subject to their respective exchange margins, but track the same underlying asset. Thus, while not fungible, the ETFs are synthetically identical and primarily differ only by the margin required to trade them. Because the ETFs are synthetically identical, any shock to the fundamental value of the S&P 500 should equally affect both ETFs. For this reason, we can control for any common changes to liquidity in 14 J o u r n a l P r e -p r o o f these ETFs due to falling prices or increased volatility of the S&P 500 using a differencein-differences framework.

While all exchange margins increased around the time of the WHO's declaration of a pandemic (Figure 2 ), some markets experienced larger increases in margins, relative to other exchanges. Exploiting this phenomenon, we use a difference-in-differences framework to isolate the effect of an idiosyncratic margin increase on market liquidity. We note, however, due to data limitations, we are unable to obtain the exact margin for the two ETFs. Thus, we proxy the respective ETF margin by using the margin corresponding to the main equity index future for each market. We proxy the margin requirement for the U.K. ETF using the margin for the FTSE 100 Index futures, which are traded on the Intercontinental Exchange (ICE). Similarly, we proxy the margin requirement for the U.S. ETF margin using the margin for the S&P 500 Index futures, which are traded on the Chicago Mercantile Exchange (CME). 13 Figure 4 illustrates the differential increase in U.K. and U.S. ETF margin proxies.

Panel A shows a large jump in the U.K. margin proxy (dotted line), relative to the U.S. margin proxy (solid line) on March 11 (indicated with a vertical line). To illustrate the difference in margin changes more distinctly, Panel B shows the margin differential, which is the difference between the U.K. and U.S. margin proxies. Panel B shows a clear increase in the margin differential for the period March 11 to March 16: over this period, the U.K. margin proxy increases more substantially, relative to the U.S. margin proxy. For this reason, we select the March 11 to March 16 period as the post-period for the difference-in-differences estimation, to test the prediction from Brunnermeier and Pedersen (2009) that binding margin constraints lead to deterioration in market liquidity.

Because the U.K. margin proxy increased earlier, and by more than the U.S. margin proxy, we expect market liquidity to deteriorate more in the U.K. market than in the U.S. market. Turning to the two ETF contracts, Figure 5 shows the evolution of the 13 In Appendix C, we provide evidence that a market's equity index futures margin is a suitable proxy for both ETF and individual stock margins traded in the market's primary exchange.

J o u r n a l P r e -p r o o f effective spread in the U.K. ETF (grey markers) and the U.S. ETF (black markers).

We see a much larger increase in the effective spread for the U.K. ETF, relative to the U.S. ETF, which is consistent with the theoretical prediction from Brunnermeier and Pedersen (2009) and Morris and Shin (2004) .

To formalize these observations, we perform a difference-in-differences estimation using the pre-and post-periods indicated in Figure 4 . The pre-period covers the February 5 to February 10, 2020 period, and Figure 4 shows there is no material deviation in the margin differential over this period. Our post-period covers the March 11 to March 16, 2020 period, which corresponds to the jump in margin differential described earlier.

Importantly, we observe a 43% margin differential in the post-period while the margin differential is only 1% in the pre-period. 14 We run the following difference-in-differences regression model:

where Liquidity i,t is one of the following liquidity variables: quoted spread, effective spread, realized spread or price impact. Each liquidity variable is averaged over hourly intervals. U.K. i,t is an indicator variable equal to 1 if the ETF trades in the U.K., and 0 otherwise. Margin increase t is an indicator variable equal to 1 for the post-period from March 11 to March 16, 2020 and 0 for the pre-period from February 5 to February 10, 2020. The interaction term U.K. × Margin increase isolates the effect of the margin increase on stock liquidity. To control for differences between trading conditions in the U.K. and U.S., we include Return i,t and V olatility i,t , where Return i,t is computed as

over one-hour intervals. For Return and Volatility, we use index levels for the FTSE 100 14 In Appendix D, we report similar results using a smaller two-day window around the March 11 event.

J o u r n a l P r e -p r o o f and S&P 500 for the U.K. and U.S. markets, respectively. 15 Table 4 reports the results from the difference-in-differences regression models. Consistent with the theoretical predictions of Morris and Shin (2004) and Brunnermeier and Pedersen (2009), our results show a decrease in liquidity for the U.K. ETF after the jump in the U.K. margin proxy, relative to the U.S. margin proxy. Across all model specifications, U.K. × Margin increase is positive and significant, indicating that transaction costs (i.e., quoted, effective, and realized spreads) increase for the U.K ETF after the margin differential widens between the U.K. and U.S. markets. Further, the price impact of trades for the U.K. ETF increases after the margin differential widens. Prior empirical studies show that increases in margin correspond to a deterioration in market quality for commodity futures markets (Daskalaki and Skiadopoulos, 2016) and CDS and bond markets (Aramonte and Szerszeń, 2020). Our results complement these studies by showing that the relation between increasing margins and deterioration in market quality extends to equity markets.

While the U.K. initially experiences a larger jump in margins relative to the U.S., shortly after, on March 17, 2020, the U.S. margin also jumps, and the difference between the U.K. and U.S. margins narrows (see Figure 4 ). Our second test exploits this narrowing in the margin differential. Because there is a narrowing in the margin differential between the U.K. and U.S. markets, there should be a reduction in the market quality differences between the markets. That is, we expect spreads on the U.K. market to decrease, relative to spreads on the U.S. market.

For this experiment, we use a similar difference-in-differences framework to equa-15 Our regressions contain 56 observations. We have 24 observations for the pre-period, which consists of 4 trading days, each with 3 × 1 hour observations when both the U. (1): (2) where Margin narrowing t is an indicator variable equal to 1 for the post-period from March 17 to March 21, 2020 and 0 for the pre-period from March 12 to March 16, 2020.

The remaining variables are defined in the same way as for equation (1). In Appendix E, we show that the average margin differential is 43% for the pre-period, which declines to 14% for the post-period. 16 Based on the predictions of Gârleanu and Pedersen (2011), we expect to see a negative and significant coefficient on U.K. × Margin narrowing. Table 5 shows the results for the difference-in-differences regression around the March 17, 2020 margin narrowing event. Consistent with our expectations, we find that the interaction term U.K. × Margin narrowing is negative and significant across all model specifications. Complementing the results of equation (1) for the widening of the margin differential in Subsection 6.1, Table 5 shows that the narrowing of the margin differential is associated with an improvement in the market quality for the U.K. ETF, relative to the U.S. ETF, evidenced through tighter quoted, effective and realized spreads, and lower price impacts.

Above, we use a difference-in-differences approach, which relies on an indicator variable to define the post-period, when the margin differential between the U.K. and U.S. markets increased (Subsection 6.1) or reduced (Subsection 6.1.1). Based on the difference-indifferences approach, we are unable to capture the actual daily margin differences between the two ETFs. To provide additional robustness, we repeat the prior experiment using 16 We use a five-day pre-and post-window to maintain consistency with the results in Subsection 6.1. In Appendix D, we show that our results are robust to a shorter two-day window around the margin narrowing event.

J o u r n a l P r e -p r o o f an alternative approach, which captures the granularity of the daily differences in the margin proxies. For the daily analysis, we estimate the following regression:

where ΔX t is defined as X U.K.,t −X U.S.,t , or the difference between the U.K. and U.S. variable on day t. X i,t represents one of the variables defined in equation (1) The results in Table 6 show that ΔMargin t is positive and significant for all but one model specification. Importantly, consistent with our findings in Subsection 6.1, we show that when the margin on the U.K. ETF increases (decreases) more than the margin on the U.S. ETF, we observe a relative deterioration (improvement) in the liquidity measures for the U.K. ETF.

In Subsection 6.1, we exploit a period when the U.K. margin proxy increases by more than the U.S. margin proxy. However, during this interval, there were also significant falls in the underlying S&P 500. To provide further confidence that our results are driven by the widening of the margin differential, rather than the fall in the S&P 500,

we conduct a similar analysis over an interval when the market fell without a change in margins. Because there is no change in the margin differential, we do not expect to observe changes to market quality between the two markets.

For this investigation, we identify the period with the largest fall in stock price, without a corresponding change in the margin differential. 18 Specifically, we identify 17 In unreported results, our findings are robust to alternate sample windows. 18 We have data on margin requirements for both the U.K. and U.S. markets from January 2015.

J o u r n a l P r e -p r o o f the August 19 to August 25, 2015 period, when the S&P 500 Index fell by more than 10%. Importantly, the margins for both the U.K. and U.S. markets remained stable during the interval. We re-estimate equation (1), where Margin increase t is equal to 1 for the post-period from August 19 to August 25, 2015 and 0 for the pre-period from August 12 to August 18, 2015. Because the stock price fall is not associated with a corresponding change in margin, we expect the interaction term U.K. × Margin increase to be insignificant in our model specifications. Table 7 reports the results for the falsification test. Importantly, we find that U.K.

× Margin increase is insignificant for all but one of the model specifications. 19 These findings show that market quality between the U.K. and U.S. markets does not change when there is no change to the margin differential. Based on these findings, the change in market quality reported in Subsection 6.1 is likely due to the change in the margin differential, rather than the fall in stock prices.

In Appendix F, we report the results of additional falsification tests, in which we repeat the difference-in-differences analyses from Subsections 6.1 and 6.1.1 using data from March 2019, the year before the COVID-19 shock. Again, based on these falsification tests, we do not detect significant changes in market quality between the U.K. and U.S. ETFs when there is no change in the margin differential in 2019.

Taken together, our evidence provides strong empirical support for the prediction that an exogenous increase in margins leads to a decrease in market liquidity as proposed by Brunnermeier and Pedersen (2009) and Gârleanu and Pedersen (2011) . This result is further supported by a reduction in the margin differential on March 17, 2020. Our main result is also robust to several falsification tests over periods when there are no changes to the differential between the U.K. and U.S. margin proxies.

19 For the Effective spread regression, U.K. × Margin increase is weakly significant at the 10% level.

J o u r n a l P r e -p r o o f

In the previous subsection, we investigate two ETFs tracking the same underlying index, but trading on separate exchanges, where the exchanges implemented differential changes to their margin requirements during the COVID-19 pandemic. Exploiting this unique scenario, we find strong evidence that market quality declines more for the U.K. ETF, which experienced larger increases in margin requirements, relative to the U.S. ETF. In this subsection, to generalize our main findings and to provide additional robustness for our results, we extend our analysis to a larger cross-section of listed equities. However, due to the difficulty in identifying additional ETFs that track the same underlying index while trading on different exchanges with varying margins, we use an alternate experimental design focusing on factors that are likely to affect some stocks more than others.

Specifically, we argue that an increase in a market's margin requirements is likely to affect stocks that are index constituents (index stocks) more than stocks that are not index constituents (non-index stocks). This argument is based on the assertion that HFMMs are 1) more margin sensitive than traditional investors and 2) are more likely to be present in index stocks than non-index stocks. For reasons outlined in Section 4,

HFMMs are likely to be more margin sensitive due to their unique trading style, which focuses on trading across short time horizons and using leveraged derivatives to hedge price risk. Similarly, Brogaard et al. (2014) and Shkilko and Sokolov (2020) show that high-frequency traders are more prevalent in index stocks, which is also supported by our empirical tests in Subsection 6.3. Thus, because HFMMs are more likely to withdraw their liquidity from stocks in which they are most active, we expect larger liquidity declines for index stocks, relative to non-index stocks, when margin increases.

For this investigation, we conduct a difference-in-differences test using the systemic increase in global margin requirements after the WHO's declaration of COVID-19 as a pandemic on March 11, 2020 for identification. Our treatment group contains stocks with a higher level of HFMM participation (i.e., stocks within the market's primary index as 21 J o u r n a l P r e -p r o o f outlined in Table 1 ). Our control group contains stocks with a lower HFMM participation.

To control for stock liquidity, we select the most liquid stocks outside the primary index for the sample of low HFMM stocks. Specifically, to be included in the sample of low HFMM stocks, we require the stock to have at least 100 daily trades and to be above the median market capitalization of non-index stocks.

For this difference-in-differences test, We also note that due to data limitations, we are unable to observe margin require- Using this design, we estimate the following difference-in-differences regression:

where Liquidity i,t is one of the following liquidity variables (quoted spread, effective spread, realized spread, price impact) in stock i on day t as described previously. High margin is an indicator variable equal to 1 for the one-month period after the WHO declares the COVID-19 outbreak a pandemic (i.e., March 11 -April 11, 2020), and 0 for the onemonth period prior (i.e., February 11 -March 10, 2020). Index constituent is an indicator variable equal to 1 if the stock belongs to a major stock market index as listed in Table 1 .

The results in Table 8 support our main result that increased margin requirements contribute to the reduction in stock liquidity. Specifically, we find that the interaction term High margin × Index constituent is positive and significant for quoted, effective, and realized spreads, indicating that the increase in spreads for index stocks is larger than 21 While we can only obtain margin requirements for equity index futures for the majority of markets, we are able to obtain margin requirements for both the equity index futures and individual stock futures for the Hong Kong Exchange. and government bonds (Duffie, 2020), where inventory risk generated significant increases in transaction costs.

In the previous subsections, we show that market liquidity declines when stock exchange margins increase. Here, we analyze a potential channel contributing to the reduction in market liquidity. In Subsection 6.2, we assert that margin sensitive HFMM withdraw more liquidity from index stocks than non-index stocks and thus, we expect to see a larger reduction (or withdrawal) of their activity from index stocks after the increase in margin requirements. 2018), we use the order-to-trade ratio (OTR) as a proxy for the overall level of HFMM activity. As HFMMs withdraw from the market, we expect to see a decline in the OTR as high-frequency quote updates become less necessary. Further, this decline in the OTR is likely to be more pronounced for index stocks, which have a higher concentration of HFMM activity, relative to non-index stocks.

Following the empirical design from Subsection 6.2, we use a difference-in-differences regression framework to test whether HFMM activity falls more for index stocks, which are likely to have higher HFMM participation, versus non-index stocks. For this analysis, we replace the dependent variable in equation (4) with OTR:

OT R i,t = α 0 + β 1 High margin t + β 2 Index constituent i + β 3 High margin × Index constituent i,t 24 J o u r n a l P r e -p r o o f

where OT R i,t is the sum of the number of asks and bid updates at the top of the book, divided by the number of trades for stock i on day t. All other variables are defined as for equation (4).

The results in Table 9 support the assertion that index stocks, which have higher HFMM participation, experience a larger fall in HFMM activity, relative to non-index stocks with lower HFMM participation, after the increase in margin requirements. We find that the interaction term High margin × Index constituent is negative and significant, indicating that OTR falls more for index stocks, relative to non-index stocks, following the significant increase in exchange margin requirements.

To provide additional robustness to these results, we perform a falsification test to show that our results are due to increasing margins, rather than the falling stock price. For this test, we estimate equation (5) for a period in 2015. During August 2015, the S&P 500 fell by more than 10% with no corresponding changes to margin requirements, as discussed in Subsection 6.1.3. Importantly, our results for the falsification test in Appendix F show no differential changes in OTR for index stocks, relative to non-index stocks, for this period when margins did not increase.

Together, our findings from Tables 8 and 9 are consistent with the hypothesis that escalating margins during times of crises negatively impacts market liquidity via the withdrawal of margin sensitive HFMMs.

We show that the WHO's declaration of the COVID-19 pandemic in 2020 is associated with a sharp and sudden increase in margin requirements for exchanges worldwide. Using this change in margin requirements across a variety of developed equity markets globally, we test the theoretical predictions of Brunnermeier and Pedersen (2009) and document three main findings.

First, we show that an increase in capital requirements correlates with a decline in market liquidity. Using ETFs tracking the S&P 500 Index listed in the U.K. and U.S. markets, we find a larger deterioration in market liquidity for the U.K. ETF, which experienced a larger increase in margin, relative to the U.S. ETF.

Second, we demonstrate that stock liquidity decreases more for index stocks, which tend to have a higher proportion of liquidity provided by high-frequency market makers (HFMMs), than for non-index stocks. Due to their higher portfolio turnovers and shorter holding periods, HFMMs are more reliant on margin as they hold leveraged portfolios.

This finding is consistent with the notion that increases in margin requirements have a larger impact on the liquidity of stocks in which HFMMs are more active.

Third, our findings suggest that HFMMs withdrew more from index stocks in which they are typically more prevalent. Specifically, we document that the order to trade ratio (OTR) declined more for index stocks, relative to non-index stocks, when exchange margin requirements increased.

Our findings contribute to ongoing policy debates around systemic risk and the regu- The table reports the changes to liquidity measures around the widening of the margin differential for the CSPX.L (U.K.) and SPY (U.S.), which are ETFs that track the performance of the S&P 500, traded on the LSE and NYSE, respectively. Specifically, we report the results for the following difference-indifferences regression:

where Liquidity i,t is one of the following liquidity variables: Quoted spread, Effective spread, Realized spread or Price impact for the U.S. or U.K. ETF, i. The dependent variables are calculated over onehour intervals, and are expressed in basis points. U.K. i,t is an indicator variable equal to 1 if the ETF trades in the U.K., and 0 otherwise. Margin increase t is an indicator variable equal to 1 for the post-period from March 11 to March 16, 2020 and 0 for the pre-period from February 5 to February 10, 2020. V olatility i,t and Return i,t are based on the FTSE 100 and S&P 500 Index levels for the U.K. and U.S. markets, respectively. V olatility i,t and Return i,t are calculated over one-hour intervals as log(High Price i,t /Low Price i,t ) and log(Close Price i,t /Open Price i,t ), respectively. ***, **, and * denote statistical significance at the 1%, 5%, and 10% levels, respectively. J o u r n a l P r e -p r o o f The table reports the changes to liquidity measures around the narrowing of the margin differential for the CSPX.L (U.K.) and SPY (U.S.), which are ETFs that track the performance of the S&P 500, traded on the LSE and NYSE, respectively. Specifically, we report the results for the following difference-indifferences regression:

where Liquidity i,t is one of the following liquidity variables: Quoted spread, Effective spread, Realized spread or Price impact for the U.S. or U.K. ETF, i. The dependent variables are calculated over one hour intervals, and are expressed in basis points. U.K. i,t is an indicator variable equal to 1 if the ETF trades in the U.K., and 0 otherwise. Margin narrowing is an indicator variable equal to 1 for the period March 17 to March 21, 2020 and 0 for the period March 12 to March 16, 2020. V olatility i,t and Return i,t are based on the FTSE 100 and S&P 500 index levels for the U.K. and U.S. markets, respectively.

V olatility i,t and Return i,t are calculated over one-hour intervals as log(High Price i,t /Low Price i,t ) and log(Close Price i,t /Open Price i,t ), respectively. ***, **, and * denote statistical significance at the 1%, 5%, and 10% levels, respectively. J o u r n a l P r e -p r o o f 

The table reports the relation between the margin differential and the liquidity differential for the CSPX.L (U.K.) and SPY (U.S.), which are ETFs that track the performance of the S&P 500, traded on the LSE and NYSE, respectively. Specifically, we report the results for the following equation:

where ΔX t is computed as X U.K.,t − X U.S.,t or the difference between the U.K. and U.S. ETF variables on day t. X i,t represents one of the variables defined in equation (1) (Quoted spread, Effective spread, Realized spread, Price impact, Volatility and Return) for the U.S. or U.K. ETF, i, for day, t. ΔMargin t represents the difference between the U.K. and U.S. margin proxies. The U.K. margin is proxied using the margin for the FTSE 100 futures trading on the Intercontinental Exchange. The U.S. margin is proxied using the margin for the S&P 500 futures trading on the Chicago Mercantile Exchange. Variables are calculated daily for the period February 11, 2020 to April 11, 2020. ***, **, and * denote statistical significance at the 1%, 5%, and 10% levels, respectively. J o u r n a l P r e -p r o o f Table 7 : Difference-in-differences regression for U.K. and U.S. ETFs: Falsification test

The table reports the results to a falsification test in August 2015, when the S&P 500 fell over 10% with no corresponding change to exchange margin requirements. The CSPX.L (U.K.) and SPY (U.S.) are ETFs that track the performance of the S&P 500, traded on the LSE and NYSE, respectively. Specifically, we report the results for the following difference-in-differences regression:

where Liquidity i,t is one of the following liquidity variables: Quoted spread, Effective spread, Realized spread or Price impact for the U.S. or U.K. ETF, i. The dependent variables are calculated over one hour intervals, and are expressed in basis points. U.K. i,t is an indicator variable equal to 1 if the ETF trades in the U.K., and 0 otherwise. Margin increase is an indicator variable equal to 1 for the period August 19 to August 25, 2015 and 0 for the period August 12 to 18, 2015. V olatility i,t and Return i,t are based on the FTSE 100 and S&P 500 index levels for the U.K. and U.S. markets, respectively.

V olatility i,t and Return i,t are calculated over one-hour intervals as log(High Price i,t /Low Price i,t ) and log(Close Price i,t /Open Price i,t ), respectively. ***, **, and * denote statistical significance at the 1%, 5%, and 10% levels, respectively. 

The table reports the changes to liquidity measures around the COVID-19 pandemic for index and nonindex stocks in global markets. Specifically, we report the results for the following difference-in-differences regression:

where Liquidity i,t is one of the following liquidity variables: Quoted spread, Effective spread, Realized spread or Price impact for stock i on day t. The dependent variables are calculated daily, and are expressed in basis points. For each stock, the liquidity measure is normalized based on the average of January liquidity measures. High margin is an indicator variable equal to 1 for the period after the World Health Organization declares the COVID-19 outbreak a pandemic (March 11 -April 11, 2020), and 0 for the pre-pandemic period (February 11 -March 10, 2020). Index constituent is an indicator variable equal to 1 if the stock belongs in the main market index for the stock's listing market as outlined in Table 1 . Volume is the natural logarithm of the daily number of shares traded in the stock. Return is the percentage return for the main stock market index for the stock's listing market as outlined in Table 1 . The estimation uses data for Canada, Hong Kong, Norway, Sweden and U.K. ***, **, and * denote statistical significance at the 1%, 5%, and 10% levels, respectively. J o u r n a l P r e -p r o o f Table 9 : Changes in the order to trade ratio around the COVID-19 pandemic

The table reports changes to order to trade ratio (OTR) around the COVID-19 pandemic for index and non-index stocks in global markets. Specifically, we report the results for the following difference-indifferences regression:

where OT R i,t is the sum of the number of asks and bid updates at the top of book, divided by the number of trades for stock i on day t, normalized based on the average of January OTRs. High margin is an indicator variable equal to 1 for the period after the World Health Organization declares the COVID-19 outbreak a pandemic (March 11 -April 11, 2020) , and 0 for the pre-pandemic period (February 11 -March 10, 2020). Index constituent is an indicator variable equal to 1 if the stock belongs in the main market index for the stock's listing market as outlined in Table 1 . Volume is the natural logarithm of the daily number of shares traded in the stock. Return is the percentage return for the main stock market index for the stock's listing market as outlined in • The Realized Spread is defined as:

where m i,j+10sec is the quote midpoint ten seconds after the jth trade for stock i and q ji has the same definition used for Effective Spread. Realized Spread it is the volume-weighted average of all j trades for stock i on day t.

For the ETFs traded in the U.S. and the U.K., we calculate the same market quality metrics defined above at an hourly, rather than daily, frequency. Thus, rather than taking averages across all trade observations in the day, we compute hourly averages using only trades contained within each respective hour. We use hourly intervals for two reasons: This figure shows a histogram of the correlation in margins for stocks in the Hang Seng Index. We analyze data for the period January 1 to May 27, 2020. During this period, there are 33 days that the dollar margin changed for at least one index constituent. On these days, we calculate the correlation between the margin for all constituents in the index.

J o u r n a l P r e -p r o o f

In this Appendix, we conduct robustness tests to ensure our results in Tables 4 and 5 are insensitive to sample windows of different lengths. Specifically, we use a shorter twoday window for our pre-and post-periods to provide robustness for our primary findings around the widening and narrowing of the margin differential between the U.K. and U.S. markets. Table D .1 reports the results for the widening of the margin differential using a preperiod from February 5 to February 6, 2020 and a post-period from March 11 to March 12, 2020. Consistent with our primary findings, we find the interaction term (U.K.

× Margin increase) is generally positive and significant, which confirms the correlation between higher margins and lower market quality. Table D .2 reports the results for the narrowing of the margin differential using a preperiod from March 15 to March 16, 2020 and a post-period from March 17 to March 18, 2020. Again, consistent with our primary findings, we find the interaction term (U.K.

× Margin narrowing) is generally negative and significant. This finding confirms that market quality improves for the U.K. market (i.e., there is a decline in spreads), relative to the U.S. market, when the margin differential narrows.

J o u r n a l P r e -p r o o f The table reports the changes to liquidity measures around the widening of the margin differential for the CSPX.L (U.K.) and SPY (U.S.), which are ETFs that track the performance of the S&P 500, traded on the LSE and NYSE, respectively. Specifically, we report the results for the following difference-indifferences regression:

where Liquidity i,t is one of the following liquidity variables: Quoted spread, Effective spread, Realized spread or Price impact for the U.S. or U.K. ETF, i. The dependent variables are calculated over one hour intervals, and are expressed in basis points. UK i,t is an indicator variable equal to 1 if the ETF trades in the U.K., and 0 otherwise. Margin increase t is an indicator variable equal to 1 for the post-period from March 11 to March 12, 2020 and 0 for the pre-period from February 5 to February 6, 2020. V olatility i,t and Return i,t are based on the FTSE 100 and S&P 500 index levels for the U.K. and U.S. markets, respectively. V olatility i,t and Return i,t are calculated over one-hour intervals as log(High Price i,t /Low Price i,t ) and log(Close Price i,t /Open Price i,t ), respectively. ***, **, and * denote statistical significance at the 1%, 5%, and 10% levels, respectively. The table reports the changes to liquidity measures around the narrowing of the margin differential for the CSPX.L (U.K.) and SPY (U.S.), which are ETFs that track the performance of the S&P 500, traded on the LSE and NYSE, respectively. Specifically, we report the results for the following difference-indifferences regression:

where Liquidity i,t is one of the following liquidity variables: The table reports the changes to liquidity measures around the placebo widening of the margin differential for the CSPX.L (U.K.) and SPY (U.S.), which are ETFs that track the performance of the S&P 500, traded on the LSE and NYSE, respectively. Specifically, we report the results for the following differencein-differences regression:

Liquidity i,t = α 0 +β 1 U.K. i,t +β 2 Margin increase t +β 3 U.K. i,t ×Margin increase t +Volatility i,t +Return i,t +ε i,t ,

where Liquidity i,t is one of the following liquidity variables: Quoted spread, Effective spread, Realized spread or Price impact for the U.S. or U.K. ETF, i. The dependent variables are calculated over one hour intervals, and are expressed in basis points. UK i,t is an indicator variable equal to 1 if the ETF trades in the U.K., and 0 otherwise. Margin increase is an indicator variable equal to 1 for the period March 25 to March 29, 2020 and 0 for the period March 11 to March 15, 2020. V olatility i,t and Return i,t are based on the FTSE 100 and S&P 500 index levels for the U.K. and U.S. markets, respectively.

V olatility i,t and Return i,t are calculated over one-hour intervals as log(High Price i,t /Low Price i,t ) and log(Close Price i,t /Open Price i,t ), respectively. ***, **, and * denote statistical significance at the 1%, 5%, and 10% levels, respectively. The table reports the changes to liquidity measures around the placebo narrowing of the margin differential for the CSPX.L (U.K.) and SPY (U.S.), which are ETFs that track the performance of the S&P 500, traded on the LSE and NYSE, respectively. Specifically, we report the results for the following difference-in-differences regression:

Liquidity i,t = α 0 +β 1 UK i,t +β 2 Margin narrowing t +β 3 UK i,t ×Margin narrowing t +Volatility i,t +Return i,t +ε i,t ,

where Liquidity i,t is one of the following liquidity variables: Quoted spread, Effective spread, Realized spread or Price impact for the U.S. or U.K. ETF, i. The dependent variables are calculated over one hour intervals, and are expressed in basis points. UK i,t is an indicator variable equal to 1 if the ETF trades in the U.K., and 0 otherwise. Margin narrowing is an indicator variable equal to 1 for the period March 17 to March 21, 2019 and 0 for the period March 12 to March 16, 2019. V olatility i,t and Return i,t are based on the FTSE 100 and S&P 500 index levels for the U.K. and U.S. markets, respectively.

V olatility i,t and Return i,t are calculated over one-hour intervals as log(High Price i,t /Low Price i,t ) and log(Close Price i,t /Open Price i,t ), respectively. ***, **, and * denote statistical significance at the 1%, 5%, and 10% levels, respectively. The table reports changes to the order to trade ratio (OTR) for a period during August to September 2015, when global stock markets declined, with no corresponding change to exchange margin requirements. Specifically, we report the results for the following difference-in-differences regression:

OT R i,t = α 0 + β 1 High margin t + β 2 Index constituent i + β 3 High margin × Index constituent i,t

where OT R i,t is the sum of the number of asks and bid updates at the top of book, divided by the number of trades for stock i on day t, normalized based on the average of January OTRs. High margin is an indicator variable equal to 1 for the period after the market decline (August 25 -September 30, 2015), and 0 for the period immediately before the market decline (August 1 -August 24, 2015). Index constituent is an indicator variable equal to 1 if the stock belongs in the main market index for the stock's listing market as outlined in Table 1 . Volume is the natural logarithm of the daily number of shares traded in the stock. Return is the percentage return for the main stock market index for the stock's listing market as outlined in Table 1 . The estimation uses data for Canada, Hong Kong, Norway, Sweden, and U.K. ***, **, and * denote statistical significance at the 1%, 5%, and 10% levels, respectively. 

Dealer balance sheets and bond liquidity provision

Cross-market liquidity and dealer profitability: Evidence from the bond and CDS markets

Stock markets' reaction to covid-19: Cases or fatalities?

The Unprecedented Stock Market Reaction to COVID-19

How rigged are stock markets? Evidence from microsecond timestamps

Procyclical Capital Regulation and Lending

The decline of too big to fail

Bank liquidity creation following regulatory interventions and capital support

High-frequency trading and price discovery

Appendix A. 1 

We use trade-and-quote data from Refinitiv to construct standard measures of market quality. We calculate our market quality metrics using data from continuous trading sessions. Accordingly, we exclude trades that occur during the first and last 15 minutes of each trading day.• The Quoted Spread is the difference between the current best bid and ask in that venue's order book divided by the midpoint, m ji . The quoted spread is recalculated whenever the limit order book is updated. The daily Quoted Spread it for stock i on day t is the daily time-weighted average.• The Effective Spread is defined as:where q ji is an indicator variable that equals +1 for buyer-initiated trades and −1 for seller-initiated trades; p ji is the trade price; and m ji is the quote midpoint prevailing at the time of the trade. To determine whether an order is buyer or seller initiated, the transaction price is compared to the previous quote midpoint -if the price is above (below) the midpoint, we classify the order as buyer (seller) initiated.Effective Spread it is the volume-weighted average of all j trades for stock i on day t.• The Price Impact is defined as:where m i,j+10sec is the quote midpoint ten seconds after the jth trade for stock i and q ji has the same definition used for Effective Spread. Price Impact it is the 45 J o u r n a l P r e -p r o o f Figure C .1, we plot the margin for the ETF future and Index future over the sample period. The plots show a remarkable similarity between the margins of the ETF future and the Index future (correlation = 0.928), which provides confidence that the margin of the index future is a reasonable proxy for the margin of the ETF future. 23

Next, we conduct two tests to provide assurance that the margin for the index future is an appropriate proxy for the margin on individual equities trading in the market. First, we compare the margin of an equity index futures with the margin of a "synthetic" equity index, which we construct from the margin of individual stock futures. Second, we test that changes in margin are systematic across all stocks. 22 The underlying instrument for the ETF future and Index future are not identical, but both reflect trading on the Hong Kong Exchange.23 While we cannot obtain the margin requirements for the ETF trading on the Stock Exchange of Hong Kong, it is reasonable to assume that the margin requirements for the ETF future trading on the Hong Kong Futures Exchange are highly correlated as both exchanges are owned by the same parent company.

J o u r n a l P r e -p r o o f Appendix E. Margin narrowing illustration Figure E .1 illustrates the evolution of the differential between the U.K. and U.S. ETF margin proxies. We observe a sharp narrowing in the margin differential on March 17, 2020. Accordingly, we use the period just prior to this narrowing as our pre-period and the interval directly after the narrowing as our post-period, as indicated in the figure.

In this Appendix, we conduct falsification placebo tests over the same time intervals in the previous year to provide robustness to our main results. In our primary analysis, we investigate changes to market liquidity around the margin increase in March 2020.Accordingly, for our placebo margin increase test, we repeat the difference-in-differences using the full second and fourth trading weeks in March 2019 for our pre-and postperiods, respectively. In contrast to our main results, we observe that U.K. × Margin increase is insignificant across all model specifications for the placebo tests in 2019, when there is no change in the margin differential between the U.K. and U.S. markets.Next, we extend our falsification placebo tests to our analysis of the narrowing of the margin differential. Specifically, in our main results, we use a pre-period from March 12 to March 16, 2020 and a post-period from March 17 to March 21, 2020 to investigate the narrowing of the margin differential. For our falsification placebo tests, we use these same intervals during the previous year. In contrast to our main results, the placebo results in Table F 

In Subsection 6.1.3, we perform a falsification test to provide further confidence that our results are driven by the widening of the margin differential during the pandemic period, rather than a sudden fall in stock price. Specifically, we use a period in August 2015 when the S&P 500 fell by over 10% with no corresponding change to exchange margin requirements.In this Appendix, we conduct a similar falsification test during August 2015 to show that the reported change in OTR in Subsection 6.3 is associated with the change in margin, rather than a fall in stock price. Figure The results reported in Table G .1 show that OTR did not decline more for index stocks, relative to non-index stocks, as a result of the price decline in August 2015 (High margin × Index constituent is not negative and significant for any of the markets). This result provides support for the hypothesis that high-frequency market makers withdrew more liquidity from index stocks, relative to non-index stocks, as a result of rising margins,