High-Frequency Trading and Systemic Risk: A Structured Review of Findings and Policies

2.1 Theoretical Models on HFT

To start with, there have been an important number of attempts to model HFT, on a theoretical basis, and its impact on societal welfare.

Hoffmann (2014) develops a stylised model of trading in a limit order market where market participants can trade at two different speeds (slow and fast). In a comparison with an equilibrium with only one speed of trading, he finds that HFT have two opposing effects: (i) their ability to revise quotes after news arrivals reduces the existing inefficiency (increasing trading), but (ii) the speed advantage of HFT generates a new type of inefficiency, as other market participants tend to strategically submit limit orders with a lower execution probability (reducing trading). Additionally, there is shift in market power between HFT and other market participants, with the latter always worse-off in equilibrium. So in terms of welfare, the introduction of HFT reduces it when compared with a hypothetical setting with only one trading speed. Finally, he finds that HFT are more likely to act as market-makers in equilibrium.

Biais et al. (2015) develop a model of trading at different speeds, which considers also general welfare and allows for policy analysis. They point towards an overinvestment in technology by HFT, derived from the fact that they do not internalise the externalities they produce for slower investors (adverse selection). In terms of policies, their model suggests that welfare is maximised when slow and fast traders co-exist in a single market and there is a Pigouvian tax on investment in technology.

Foucault et al. (2016) propose a model of trading on news where they look at the optimal trading strategies of an informed fast speculator (who can trade ahead of incoming news) and of slower investors. They find that the fast speculator’s trades represent a larger fraction of trading volume and are more correlated with short-run price changes. Fast speculators make a large proportion of their profits from trading on long-term price changes. Besides, both types of investors decrease their expected profit with news informativeness, but at a lower rate in the case of fast speculators. So, the relative gain of fast speculators increases with news informativeness. They also predict that the profitability of directional HFTs should be inversely related to news informativeness, but, at the same time, stocks with more informative news are more likely to attract directional HFTs.

In the model of Foucault et al. (2017), arbitrage opportunities arise when prices adjust to new information with a lag. These arbitrage opportunities are labelled as toxic because they expose dealers to the risk of trading at stale quotes. Their model also predicts that a technological change making arbitrageurs relatively faster should reduce the duration of arbitrage opportunities. Using data on triangular arbitrage, they find that illiquidity is higher on days when the fraction of toxic arbitrage opportunities and arbitrageurs’ relative speed are higher (usually at a timescale of milliseconds). That would be consistent with the idea that price efficiency gains of HFT come at the cost of increased adverse selection risk.

Bongaerts and van Achter (2016) develop a model to analyse the impact on market stability of the liquidity provision by HFT. In their model, orders are limited and there is informed trading and endogenous entry and exit, with liquidity provided by both traditional market-makers and HFT. The latter trade at a higher speed through the use of higher information processing technologies. They find that speed technology leads to an efficient allocation of resources and maximises liquidity while information processing technologies can generate minor issues related to information asymmetries. However, the combination of the two can lead to inefficient speed technology, oligopolistic rents and increased issues related to information asymmetries.

Jain et al. (2016) use the launch of Arrowhead by the Tokyo Stock Exchange as a quasi-natural experiment to gauge the impact of high-frequency quoting (HFQ) and HFT on financial markets. While they find that the introduction of Arrowhead and the related increase in latency and speed of trading improved market liquidity, they are concerned about the increase in systemic risk, mainly in the form of autocorrelation and cross-correlation in the order flow (which can lead to an amplified propagation of shocks) and of more frequent “flash crashes” during periods of stressful market conditions. They use several measures of systemic risk developed in the academic literature and conclude that the introduction of Arrowhead led to increases in all of them.

From the perspective of trading venues, the model by Pagnotta and Philippon (2018) considers that trading venues invest in technology in order to attract investors who value speed and to whom they can charge higher fees. In principle, this competition among venues may be beneficial by increasing investor participation, trading volumes and efficiency. They also find that regulations that protect transaction prices (in a nutshell, investors have access to a single asset via two markets with a unique price) lead to greater fragmentation and faster speeds but might reduce efficiency. In terms of welfare, they conclude that a regulator would find it optimal to impose a minimum speed requirement but not a maximum speed limit. When considering price protection policies, their consequences in terms of welfare depend crucially on the impact on entry decisions of venues. When protection increases entry, the impact of price protection on welfare is typically positive. In some cases, the implicit subsidy embedded in price protection can allow entry by a slower venue, stimulate competition and result in higher investor participation and greater allocative efficiency. However, when price protection does not increase entry, it typically has a small negative impact on welfare derived from lower price competition and efficiency.

Keeping the focus on speed at exchange level, Menkveld and Zoican (2017) examine whether markets improve when trading platforms reduce their latency. They find that increasing speed can reduce liquidity. They identify two channels by which speed affects the bid-ask spread and the increase or decrease in liquidity depends on which channel dominates. The first channel implies that when an exchange increases its speed, then HFT can more quickly update their quotes, reducing the competitive spread. According to the second channel, when an exchange increases speed, HFT acting as market-makers become more exposed to speculative HFT every time new information is released. A faster exchange would then increase the spread. In terms of dominance, the first channel tends to dominate when the news rate is high, whereas the second channel is strong when there is intense competition among HFT.

More recently, Baldauf and Mollner (2020) consider the impact of HFT (and possible policy responses) in trading through the trade-off between liquidity and information production. Their model features random latency, multiple exchanges, and a single security that is traded by liquidity investors, information investors and HFT. They find that (i) faster trading leads HFT to be more successful at order anticipation (narrowing spreads and decreasing the cost of information); (ii) order anticipation pushes outcomes inside the frontier of this trade-off, representing an inefficiency of HFT; and (iii) this inefficiency stems from aggressive trading strategies. On the latter, they argue that some trading mechanisms can be designed to eliminate the inefficiency by preventing aggressive-side order anticipation. Among these mechanisms, they refer to non-cancellation delay mechanisms and frequent batch auctions.

Moving to the area of market design, Budish et al. (2015) argue that the development of HFT is a signal of flawed market design and they call for the setting of frequent auctions as a solution. Using millisecond-level data, they find that, at high-frequency time horizons, correlations completely break down, which introduces arbitrage opportunities, and that competition has not affected the size or frequency of the arbitrage opportunities. In the model they develop, they argue that these mechanical arbitrage opportunities stem from the continuous-time serial processing of orders. The rents which can be extracted from these arbitrage opportunities hinder the provision of liquidity and provide incentives to market participants to engage in a never-ending arms race for speed, which does not have any positive effect on welfare. As a policy response to this, they argue that the introduction of frequent auctions would transform competition in speed to a competition in prices, removing arbitrage opportunities and enhancing liquidity in markets.

2.2 Academic Literature on the “Flash Crash” of 6 May 2010

After a revision of some relevant theoretical work on HFT, it is useful to refer to the literature analysing the “flash crash” of 6 May 2010, as that event drew the attention of policymakers towards HFT. The “flash crash” lasted just 36 min and most of the losses were recovered soon afterwards. In its short lifespan, stock prices (as well as futures, options and ETFs) collapsed and rebounded very rapidly. For example, the Dow Jones Industrial Average dropped 998.5 points (about 9% from the opening), within minutes, and later recovered a large part of the loss. Some stock prices dropped to just 0.01 $ and the prices of others jumped to 100,000 $ in a matter of seconds.

Kirilenko et al. (2017) examine intraday trading between 3 May 2010 and 6 May 2010 in the E-mini S&P 500 stock index futures market, which was found to be at the origin of the “flash crash”. They study the second-by-second co-movement of inventory changes of (non-HFT) market makers and of HFT and, consistent with the findings in the literature, find that inventory changes of HFT positively co-move with contemporaneous (and lagged) prices but that co-movement is negative in the case of (non-HFT) market markers. Interestingly, such relationship between inventories and prices changed for (non-HFT) market makers during the “flash crash” in comparison with the previous days but did not change for HFT. In the case of HFT, it has been suggested that when certain traders are able to react faster than others to a signal, they enter into a kind of “latency arbitrage”, to the expense of slower traders. This behaviour of HFT would contrast with that of (non-HFT) market makers, mostly in line with the theoretical findings of Glosten and Milgrom (1985). In this vein, they find that, between 3 and 5 May, stock prices for which HFT were net buyers in a given second increased in the following second and remained higher for 20 s more, with a similar qualitative behaviour also observed on 6 May.

Easley et al. (2011) also analysed in detail the trading activities about various markets during 6 May 2010. They argue that the events on that day were the result of new dynamics in the financial markets and highlight the prominent role played by order toxicity in hampering liquidity provision. Order toxicity occurs when the order flow adversely selects non-HFT market makers who may be unaware that they are providing liquidity at a loss (Easley et al. 2012). If order toxicity rises unexpectedly, due to a larger portion of trades being originated from informed traders, then non-HFT market makers would face losses. The subsequent process of adjustment of non-HFT market makers, which now become consumers of liquidity, would add volatility to the markets, as was the case with the “flash crash”.

Lastly, Golub et al. (2012) analyse all the mini “flash crashes” in the US equity markets between 2006 and 2011. Together with the impact created by market regulation, they argue that the existing market structure with many trading venues is fragmenting overall liquidity, being “flash crashes” the consequence of it. HFT play a crucial role in this development as imbalances in liquidity across trading venues create opportunities for HFT to profit from them.

3.1 Adverse Selection in Orders and Market-Making

The first vulnerability refers to adverse selection in orders, understood as a situation where market participation is affected by asymmetric information with HFT acting as “informed” traders (Aoyagi 2018; Biais and Woolley 2012; Biais et al. 2015; Brogaard et al. 2014; Carrion 2013; Easley et al. 2011; Foucault et al. 2016, 2017).^[3] The informational disadvantage of some market participants explains then the risk premium market makers charge, as they need to compensate that “information” risk (Glosten and Milgrom 1985). Following Haldane (2011) and O’Hara (2015), adverse selection in a HFT context needs not to be interpreted as access to a richer set of information on the fundamentals of an underlying security, but rather in terms of faster reactions to new pieces of information. The distinction should be made between fast and slow traders, not between informed and uninformed traders. Hence, the importance for HFT of being as fast as possible and the important investments they undertake in co-location, IT equipment, software and infrastructure.

Adverse selection becomes an issue of particular relevance when a market operates with HFT market-makers and non-HFT market makers, as the latter may be trading with a counterparty better informed (faster) than they are. There is evidence in the academic literature that HFT can also follow and even dominate market making strategies (Boehmer et al. 2018; Brogaard et al. 2015; Hoffmann 2014; Malceniece et al. 2019). In financial markets with a strong presence of HFT, this can lead to what Easley et al. (2012) define as order toxicity (Foucault et al. 2017, use the term “toxic arbitrage” with a similar definition). In a period of uncertainty about prices, which can be driven by multiple automatic transactions by HFT (like in the “flash crash” of 2010), the information risk that non-HFT market makers face impedes them to fulfil their expected role and generates substantial losses to them. Non-HFT market makers cannot keep pace with the incoming flow of information about price developments. Consequently, these non-HFT market makers cease to operate as market makers, because they are not able to keep speed with HFT (i.e. they are slow) and they would then be forced to charge a higher premium for the information risk they are facing (Haldane 2011; Menkveld and Zoican 2017). In such circumstances, the information embedded in prices decreases substantially and slower non-HFT market makers are crowded out from the market (Bongaerts and van Achter 2016; Huh 2014). Market making functions are left fully to HFT and their automatic trading. The ultimate consequence of this could be a dysfunctional and self-induced process of price formation, like the one observed on 6 May 2010. This mechanism was already described, under a different configuration of financial markets, by Glosten and Milgrom (1985), who also considered the self-fulfilling mechanism leading to wide bid-ask spreads and, eventually, to the closure of the market.

In an stylised way, the price (P) of a stock z at time t + 1 can be assumed to be a function of the past observed price at t and of the change in the available information about that stock (Itz), with a third term component covering all other residual factors affecting the stock price (utz):

With short time intervals, the difference between prices is expected to be insignificant, unless major news arise or uncertainty raises materially. The longer the time interval, though, the larger would be the influence of available information and other factors in the price of the stock. For HFT, the units in which time is measured are probably milliseconds, whereas for non-HFT market makers (and other types of investors) time can be measured in seconds. Despite this difference in the time scale, in calm times, the third component of Equation (1) above is expected to remain low, so the difference in the time scale used by HFT and non-HFT market makers does not substantially affect the setting of prices in the next period. However, in times of stress in financial markets, the information risk which non-HFT market makers face may become too large, derived from the second and third components of Equation (1) and from the fact that, just immediately before t + 1, the last price they observed, at time t (measured in seconds), may be a stale price, not representative of the real price. Therefore, they are not able to make a sound estimate of the price in the next period (Pt+1z) and would need to charge a large information premium to compensate for the risk they are taking. Ultimately, they may decide to quit the market, since they know that faster traders can make them assume substantial losses. The decision of non-HFT market makers to abandon the market may impair the price discovery process (assuming that all market makers would qualify, in principle, as informed traders), which could be entirely in the hands of HFT market makers.

The findings in Chakrabarty et al. (2019) seem to confirm the link between adverse selection and HFT. In an analysis of the impact of the SEC’s naked access ban, a policy that slowed down some of the most aggressive HFTs, they conclude that trading costs declined driven by reduced adverse selection cost. Similarly, Brogaard et al. (2018) find that HFTs typically provide liquidity during episodes of extreme price movements when only one stock is affected. In situations when several stocks are under extreme price movements, position risk of HFTs is larger than during normal times, triggering internal controls in the area of liquidity management, resulting in an excess of liquidity demand. Using the staggered entry of Chi-X in 12 European equity markets, Malceniece et al. (2019) find that HFTs provide less liquidity during times of market stress. Similar findings are reached by Huh (2014), who concludes that HFT provide less liquidity when markets are volatile, because information asymmetry tends to be higher in those times. On the other hand, Brogaard et al. (2015) find that fastest traders in the NASDAQ OMX market (those subscribing to optional speed upgrade) behave primarily as market makers, improving the liquidity provision to slow and faster traders. They explain these findings as the speed upgrade is used to improve inventory management rather than for trading on short-lived information.

3.2 Correlation and Herd Behaviour

A second identified vulnerability of HFT refers to the diversity in financial markets, touching upon correlation and herd behaviour. As a starting point, Chaboud et al. (2014) find evidence of correlation in HFT strategies in the FX markets, and Smith (2010) has documented a high level of correlation in transactions involving 1500 shares or less. Similarly, Lafarguette (2016) finds common statistical patterns in HFT quotes. Boehmer et al. (2018) examine a group of 31 HFT in Canadians markets and identify an important heterogeneity in HFT strategies. However, they also find that 78% of the trades made by HFT can be explained by just three common strategies, suggesting an important correlation in the order flow of HFT. Malceniece et al. (2019) argue that HFT increase the co-movement of stocks returns, attributing more than half of that increase in co-movement to correlated trading strategies by HFT. Intuitively, the optimisation of algorithms in HFT would remove the human component (often, comprising irrational behaviour) in trading, leading, in principle, towards more homogenous strategies and reactions to new events (Linton and O’Hara 2011). In essence, the growing importance of HFT would imply that factors closely linked to human behaviour would not have a large weight on financial markets.

The impact on systemic risk from this vulnerability can be twofold. First, starting with the more unlikely, a shock simultaneously affecting several HFT may have negative consequences for them in terms of solvency, given the fact that HFT usually have very thin capital positions, ultimately leading to widespread failures of HFT (Biais and Woolley 2012). Such a scenario could have undesired effects for systemic risk in terms of interconnectedness and contagion, as it would be difficult to identify who is exposed to the failed HFT. Actually, counterparty risk acquires a new dimension in a scenario where HFT absorb an important part of the transactions. However, on the other hand, overnight inventories of HFT tend to be small (Jovanovic and Menkveld 2010), so their counterparty risk in case of a failure should be manageable.

Second, in normal trading times, the fact that HFT dominate the “active” trading (with passive investors just following them) coupled with certain convergence amidst all HFT strategies (Haldane 2011) could in principle lead to over-reaction to new information, in particular if that information is unexpected or of particular importance (Brogaard et al. 2014; Caivano 2015). Returning to Equation (1), this over-reaction to new pieces of information would be reflected in significant variations in the term Δ(Itz) over a short time period. In other words, it could lead to financial markets where movements in prices have a shorter and more acute nature. Indeed, Jiang et al. (2014) find that HFT increase volatility in the US Treasury market during, shortly before and after the announcement of macroeconomic news.

The over-reaction to new pieces of information could ultimately lead to herd behaviour and higher probabilities of tail events or flash crashes (Biais and Foucault 2014; Jain et al. 2016). Menkveld and Yueshen (2018) conclude that a breakdown of cross-market arbitrage activity increases the fragility of markets and could result in price crashes, using the “flash crash” to support their statement. In relation to flash crashes, Johnson et al. (2013) have documented 18,520 crashes and spikes between 2006 and 2011 with durations below 1.5 s. They directly relate these events to the increasing importance of computers in trading.

3.3 Market Power and Barriers to Entry

The third vulnerability stemming from the expansion of HFT in financial markets refers to market power and barriers to entry. In the empirical literature, it has been observed that a small number of HFT usually account for a very large proportion of the orders posted into a stock exchange (Clark 2012; Hagströmer and Nordén 2013; Kaya 2016; Kirilenko et al. 2017). Most of these orders are ultimately cancelled, but they allow HFT to determine the inside quotes on a particular security (Biais and Woolley 2012). Financial market participants are then divided in two groups depending on their ability to trade fast (Cartlidge and Cliff 2012; Haldane 2011; Virgilio 2017). The first, and less numerous, group enjoys several advantages from their privileged position, while the slower group does not. Concerns derived from a two-tiered financial markets have been usually mentioned when discussing policies to address HFT (Bhupathi 2010; Hoffmann 2014). In principle, financial markets regulation must ensure that all financial market participants have equal access to information and prices. However, HFT may be changing this perception, as it operates at time ranges which are not accessible to all market participants (Johnson and Zhao 2012).

General economic theory would argue that if HFT is so beneficial, then slower traders would make an effort to become HFT and, ultimately, the privileges enjoyed by HFT would disappear. However, in reality, there are frictions in financial markets and the costly technology used by HFT can create a barrier to entry for new participants. For example, and simply referring to one aspect of the many fixed costs in HFT, the Hibernia Express transatlantic cable between London and New York, which has a tested latency of less than 58.95 ms, is expected to have costed more than 300 million USD (Hasbrouck 2016). Similarly, Laughlin et al. (2014) have estimated a cost, including operations and infrastructure, exceeding 500 million USD for the 3 ms improvement in communication between Chicago and New York.

To better understand the barrier to entry created by the necessary technology to use HFT strategies, it is useful to consider the concept of capability, used in engineering. Following Kumiega et al. (2014) and Van Vliet (2017), the capability of a single HFT strategy (C) would be defined as follows:

where µ_n is the average expected return per trade, σ_n is the standard deviation of expected returns per trade, and c is the average fixed cost necessary to operate as a HFT. Accordingly, HFT would operate if the capability ratio of Equation (2) is larger than one, although a value of 1.33 is usually set as a threshold in engineering literature (Kumiega et al. 2014). In an environment of increasing technological costs for HFT, higher returns per trade or lower volatility would be required in order to be able to keep pace with HFT. For potential market participants, Equation (2) implies that they should be able to design highly profitable strategies to be able to compensate for the elevated fixed costs.

From a different perspective, HFT would have strong interests in maintaining the technological advantage over other financial market participants and this could lead to certain over-investment in technology, as signalled by Ye et al. (2013) and Biais et al. (2015). Hirshleifer (1971) shows the existence of significant incentives to trade on private information. When applied to HFT, HFT may overinvest in technology (c in Equation (2) would be excessively large) in the search for additional profits from trading with private information, far from the social optimum (Hoffmann 2014; Ye et al. 2013). The extent to which the investment in technology by HFT reflects mere competition or an unproductive arms race ultimately depends on the assessment of the contribution of HFT to price discovery (Jones 2013).

3.4 Contribution to Price Discovery

Indeed, the fourth vulnerability arising from HFT refers to the degree its various strategies contribute to price discovery, raising ethical concerns in some circumstances. Price discovery is understood to be the process of determining the price of an asset in a market through the interactions of buyers and sellers. The role played by HFT in this process has been found to be positive by, among others, Carrion (2013), Brogaard et al. (2014) and Benos et al. (2017), while Lafarguette (2016) finds a positive relation between HFT and price discovery, but only in normal times.

More nuanced conclusions are reached by Weller (2018), as he finds that algorithmic trading increases price efficiency with respect to acquired information but it reduces the available information to which prices respond. In terms of social welfare, he argues that the net effect from informational channels is almost surely a loss. Similarly, according to the model by Jarrow and Potter (2012), HFT may lead to mispricing of stocks (understood as deviations from their fundamental value), derived from collective and independent responses from HFT to common signals. Similar findings are presented by the model of Yang and Zhu (2020), where HFT detect slower investors’ order flow in period one and then compete with these orders in period two in order to exploit this information for their own benefits. They also conclude that this behaviour by HFT poses a risk to the market.

These findings support the argument that the answer to the question whether HFT contributes to the price discovery process depends much on the strategies followed by HFT themselves (Benos and Sagade 2016). Following the identification by the Dutch Authority for the Financial Markets (2010) and Miller and Shorter (2016), HFT strategies can be classified into three main groups:

1. Market making strategies. In this situation, HFT sets the price in a venue of a stock which is also quoted on another venue. HFT would then gain the spread between the prices in the two venues. If this mechanism is expanded to several venues, HFT engage in what is called cluster trading. Option trading is a traditional field for this kind of strategies.

2. Statistical arbitrage. This strategy is based on finding arbitrage opportunities using statistics. For example, if stock prices temporarily stop behaving as could be expected based on statistical assumptions, this can be used as a signal for action by HFT, as it is possible to make sound forecasts about where the price will end up.

3. Aggressive strategies. Their underlying rationale is to be faster than the rest of the participants in the financial market, so these strategies depend mostly on having the fastest systems or the fastest connection to the trading venues. Some examples of aggressive strategies are (i) searching out limit orders of small and slower investors by placing immediate or cancel orders (so the investor will always pay the maximum price for an order, earning the HFT the difference), (ii) analysing how other algorithms work so that the HFT can carry out arbitrage on them, (iii) placing small gradual orders to slowly move the market and benefit from the ensuing volatility through an option contract previously arranged, or (iv) anticipating orders from large investors so that the HFT can trade ahead of it and earn a profit.^[4]

The positive contribution of market making strategies to price discovery seems to be clear (Huh 2014; Menkveld 2013), since HFT exploits mispricing and allows new information to be incorporated into prices. However, concerns about the role of HFT in the price discovery process start to emerge regarding statistical arbitrage and, particularly, aggressive strategies (Baldauf and Mollner 2020; Menkveld and Zoican 2017; Ye et al. 2013). Aggressive strategies, in particular, can lead to situations where the price moves away from the fundamental value of the stock (Egginton et al. 2016; Manahov 2016). The purpose of aggressive strategies to provoke a price increase or decrease and to generate a profit from establishing a long or short position on that price would not seem to improve the price discovery process. For example, Egginton et al. (2016) argue that episodic spikes in quoting activity by HFT (stemming from low latency strategies) lead to decreased liquidity, higher trading cost and increased short term volatility.

In this vein, the Dodd–Frank Act forbid in 2010 certain aggressive strategies and some others have been contested for a long-time. It is on this basis that O’Hara (2015) has claimed that financial markets are currently faster, but also less fair and more complex.