Execution in an aggregator

An aggregator is a technology that consolidates liquidity—in the form of bid and ask prices and amounts—from multiple sources into a single unified order book to facilitate ‘best-price’ execution. It is widely used by traders in financial markets, particularly those in the globally fragmented spot currency market. In this paper, I study the properties of execution in an aggregator where multiple liquidity providers (LPs) compete for a trader’s uninformed flow. There are two main contributions. Firstly, I formulate a model for the liquidity dynamics and contract formation process, and use this to characterize key trading metrics such as the observed inside spread in the aggregator, the reject rate due to the so-called ‘last-look’ trade acceptance process, the effective spread that the trader pays, as well as the market share and gross revenues of the LPs. An important observation here is that aggregation induces adverse selection where the LP that receives the trader’s deal request will suffer from the ‘Winner’s curse’, and this effect grows stronger when the trader increases the number of participants in the aggregator. To defend against this, the model allows LPs to adjust the nominal spread they charge or alter the trade acceptance criteria. This interplay is a key determinant of transaction costs. Secondly, I analyse the properties of different execution styles. I show that when the trader splits her order across multiple LPs, a single provider that has quick market access and for whom it is relatively expensive to internalize risk can effectively force all other providers to join her in externalizing the trader’s flow thereby maximizing the market impact and aggregate hedging costs. It is therefore not only the number, but also the type of LP and execution style adopted by the trader that determines transaction costs.     

Optimal liquidation in dark pools

We consider a large trader liquidating a portfolio using a transparent trading venue with price impact and a dark pool with execution uncertainty. The optimal execution strategy uses both venues continuously, with dark pool orders over-/underrepresenting the portfolio size depending on return correlations; trading at the traditional venue is delayed depending on dark liquidity. Pushing up prices at the traditional venue while selling in the dark pool might generate profits. If future returns depend on historical dark pool liquidity, then sending orders to the dark pool can be worthwhile simply to gather information.     

Optimal Liquidity Trading

A liquidity trader wishes to trade a fixed number of shares within a certain time horizon and to minimize the mean and variance of the costs of trading. Explicit formulas for the optimal trading strategies show that risk-averse liquidity traders reduce their order sizes over time and execute a higher fraction of their total trading volume in early periods when price volatility or liquidity increases. In the presence of transaction fees, traders want to trade less often when either price volatility or liquidity goes up or when the speed of price reversion declines. In the multi-asset case, price effects across assets have a substantial impact on trading behavior.We are grateful to Prajit Dutta and Larry Glosten for numerous conversations and comments and to Marc Lipson for help with the Plexus data. Comments and suggestions of the referee and the editor, Josef Zechner, helped us improve the paper. We also thank the participants of the Chicago Board of Trade 13th Annual European Futures Research Symposium 2000 and the participants of the EFA Annual Meetings 2001.     

Market or limit orders?

In this paper we investigate the problem of optimal order placement of an asset listed on an exchange using both market and limit orders in a simple model of market dynamics. We seek to understand under which settings it is optimal to place limit or market orders. Limit orders typically lower transaction costs but increase the risk of incomplete order execution, whereas market orders typically have higher transaction costs but are guaranteed to be executed. Rather than considering order book dynamics to determine if a limit order is executed we rely on price dynamics for this. We look at implementation shortfall in this setup with market impact of trading and propose a dynamic program to find the optimal placement of both market and limit orders for risk-neutral and risk-averse traders. With this we find a bound on the expected cost of trading and show that a trader who behaves optimally should always expect to pay less to trade less. We then solve the dynamic program numerically and examine optimal order placement strategies. We find that the decision between market and limit orders is sensitive to price volatility, risk aversion, and trading costs.     

Trader Leverage and Liquidity

Does trader leverage drive equity market liquidity? We use the unique features of the margin trading system in India to identify a causal relationship between traders’ ability to borrow and a stock's market liquidity. To quantify the impact of trader leverage, we employ a regression discontinuity design that exploits threshold rules that determine a stock's margin trading eligibility. We find that liquidity is higher when stocks become eligible for margin trading and that this liquidity enhancement is driven by margin traders’ contrarian strategies. Consistent with downward liquidity spirals due to deleveraging, we also find that this effect reverses during crises.     

A theory of the interday variations in volume, variance, and trading costs in securities markets

In an adverse selection model of a securities market with oneinformed trader and several liquidity traders, we study theimplications of the assumption that the informed trader hasmore information on Monday than on other days. We examine theinterday variations in volume, variance, and adverse selectioncosts, and find that on monday the trading costs and the varianceof price changes are highest, and the volume is lower than onTuesday. These effects are stronger for firms with better publicreporting and for firms with more discretionary liquidity trading.     

Depth improvement and adjusted price improvement on the New York stock exchange

Traditional price improvement improperly assesses large orders’ execution quality by ignoring additional liquidity depth-exceeding orders receive at the quoted price and viewing orders that “walk the book” as “disimproved”. Ignoring this additional liquidity is particularly problematic when assessing execution quality in markets with significant non-displayed liquidity. To correct this deficiency, we modify the price benchmark used to determine whether an order is price improved by making the benchmark a function of the order's size relative to the quoted depth. We document that the differences between conventional price improvement and our measure, adjusted price improvement, can be dramatic and show that the difference depends on trading volume, stock price, and volatility.     

Optimal execution in Hong Kong given a market-on-close benchmark

For stocks traded on the Hong Kong Exchange, the median of five prices taken over the last minute of trading is currently chosen as the closing price. We introduce a stochastic control formulation to target such a median benchmark in an empirically justified model which takes the key microstructural features into account. We solve this problem by providing an explicit and efficient algorithm which even has applications beyond this paper as it can be used for the dynamic linear approximation of any square-integrable random variable. Implementing the algorithm on the stocks of the Hang Seng Index, we find an average improvement of around 6% in standard deviation of slippage compared to an average trader’s execution. We conclude by providing a novel decomposition of the trading risk into that which is intrinsic to the median benchmark and that due to execution.     

Asset market equilibrium with liquidity risk

This paper derives an equilibrium asset pricing model with endogenous liquidity risk. Liquidity risk is modeled as a stochastic quantity impact on the price from trading, where the size of the impact depends on trade size. Under a strong set of assumptions, we prove that a unique equilibrium liquidity cost process and a unique equilibrium price process exists for our economy. We characterize the market’s state price density, which enables the derivation of the risk-return relation for the stock’s expected return including liquidity risk. We derive a generalized intertemporal CAPM and consumption CAPM for these markets. In contrast to the traditional models without liquidity risk, there is an additional systematic liquidity risk factor which is related to the stock return’s covariation with the market’s stochastic liquidity cost. Traditional transaction costs are a special case of our formulation.     

Price signatures

Price signatures are statistical measurements that aim to detect systematic patterns in price dynamics localised around the point of trade execution. They are particularly useful in electronic trading because they uncover market dynamics, strategy characteristics, implicit execution costs, or counter-party trading behaviours that are often hard to identify, in part due to the vast amounts of data involved and the typically low signal to noise ratio. Because the signature summarises price dynamics over a specified time interval, it constitutes a curve (rather than a point estimate) and because of potential overlap in the price paths it has a non-trivial dependence structure which complicates statistical inference. In this paper, I show how recent advances in functional data analysis can be applied to study the properties of these signatures. To account for data dependence, I analyse and develop resampling-based bootstrap methodologies that enable reliable statistical inference and hypothesis testing. I illustrate the power of this approach using a number of case studies taken from a live trading environment in the over-the-counter currency market. I demonstrate that functional data analysis of price signatures can be used to distinguish between internalising and externalising liquidity providers in a highly effective data driven manner. This in turn can help traders to selectively engage with liquidity providers whose risk management style best aligns with their execution objectives.     

The Impact of Information Diffusion on Comparisons among Various Trading Mechanisms

The information environment and investor order strategy are both important determinants when comparing the market performance of trading mechanisms. However, less is known about what happens when trading mechanisms are compared. In this paper, we link the information environment, trading mechanisms, investor order strategy and market performance to form a model of the securities market. The primary goal of this study is to examine the impact of various call markets in an agency market on liquidity, price volatility and market efficiency under various information regimes. The results indicate that an optimal transaction frequency appears at the trade-off of liquidity, volatility and market efficiency.     

Stock market dynamics with rational liquidity traders

In the Kyle (1985) finite horizon model of stock market dynamics with a trader who holds long-lived information, informed trading intensities rise with time, and the slopes of the equilibrium price schedules fall. This paper shows that this result depends crucially on the irrational liquidity trader assumption. We replace the irrational noise traders with a sequence of rational, risk averse, liquidity traders who receive endowment shocks to their holdings of the risky asset. We demonstrate that unless liquidity traders are sufficiently risk averse, the slope of equilibrium price schedule rises over time, while informed trading intensities fall. In particular, Kyle's result holds only when liquidity traders are so risk averse that they ‘over-rebalance’ their portfolio's holdings of the risky asset, so that their final holdings of the risky asset have the opposite sign of their initial position.     

Trading performance and market efficiency: Evidence from algorithmic trading

In India, National Stock Exchange directly identifies algorithmic trading participation. Algorithmic traders possess intraday market timing skills. Results are not motivated by extreme short-term signals or transitory price trading. Magnitude of market timing performance in cross-sectional group of traders shows that they earn profit across all the cases, and maximize while providing liquidity. Volume-weighted-average-price decomposition analysis reports algorithmic traders earn profits through intraday market timing performance for five-minute and one-minute intervals, and it is higher compared to short-term market timing performance across all trader groups. Order imbalance and price delay regressions show that algorithmic trading significantly improves price efficiency.     

High-frequency trading: a literature review

The relatively recent phenomenon of high-frequency trading has had a profound impact on the micro-structure of financial markets. Several authors hailed it as a provider of liquidity and a mechanism for controlling volatility, two highly welcome features, especially beneficial to retail traders, whereas other authors view the situation generated by algorithmic trading as damaging for both small and institutional traders, and the orderly functioning of the markets. This paper analyzes the impact of high-frequency trading in respect of the main parameters affecting market quality: volatility, transaction costs, liquidity, price discovery, penalization of slower traders, and impact on sudden financial crises, the notorious flash crashes. As often happens within the financial community, different views stand to each other and no conclusive agreement on the value of most parameters has been reached as yet. A section on the apparently falling profits of high-frequency traders, as denounced in recent times, completes the review.

     

Predatory Trading

This paper studies predatory trading, trading that induces and/or exploits the need of other investors to reduce their positions. We show that if one trader needs to sell, others also sell and subsequently buy back the asset. This leads to price overshooting and a reduced liquidation value for the distressed trader. Hence, the market is illiquid when liquidity is most needed. Further, a trader profits from triggering another trader's crisis, and the crisis can spill over across traders and across markets.     

An empirical investigation of large trader market manipulation in derivatives markets

Using account-level transaction data in options and futures markets, we investigate the existence of market manipulation, which is the ability of large traders to trade strategically, impacting prices and making abnormal profits. First, large trader’s option positions have a quantity impact on the underlying asset’s price. Second, large traders generate significantly positive alphas from trading options and futures. Among the different investor types, proprietary dealers generate the largest positive alphas. Third, these abnormal returns are consistent with strategic trading and cross-market manipulation. The evidence supports market manipulation across the options and futures markets, but not within the futures market itself.     

Perfect hedging under endogenous permanent market impacts

We model a nonlinear price curve quoted in a market as the utility indifference curve of a representative liquidity supplier. As the utility function, we adopt a \(g\)-expectation. In contrast to the standard framework of financial engineering, a trader is no longer a price taker as any trade has a permanent market impact via an effect on the supplier’s inventory. The P&L of a trading strategy is written as a nonlinear stochastic integral. Under this market impact model, we introduce a completeness condition under which any derivative can be perfectly replicated by a dynamic trading strategy. In the special case of a Markovian setting, the corresponding pricing and hedging can be done by solving a semilinear PDE.     

Dancing in the dark: post-trade anonymity,liquidity and informed trading

We analyze the impact of post-trade anonymity on liquidity and informed trading in an order driven stock market. The German stock market introduced the Central Counterparty (CCP) in March 2003 for German equities traded on its anonymous electronic trading platform Xetra leading to a major change in its existing transparency regime. Before the introduction trader IDs were revealed to the counterparties of a trade, with the introduction of the CCP even after the transaction the traders remain anonymous. Previous theoretical and empirical research documents that pre-trade anonymity results in increased liquidity, while results on post-trade anonymity are mixed. We find a significant increase in liquidity measured through a reduction of 25% in implicit transaction costs. We also document that the arrival rate of informed traders is reduced in the anonymous setting. Following recent findings of Bloomfield et al. (J Finan Econ 75:165–199, 2005) that informed traders take on the role of liquidity providers we interpret our findings as indication that informed traders change their behavior in providing liquidity more aggressively in an anonymous environment.     

Price dispersion in OTC markets: A new measure of liquidity

In this paper, we model price dispersion effects in over-the-counter (OTC) markets to show that, in the presence of inventory risk for dealers and search costs for investors, traded prices may deviate from the expected market valuation of an asset. We interpret this deviation as a liquidity effect and develop a new liquidity measure quantifying the price dispersion in the context of the US corporate bond market. This market offers a unique opportunity to study liquidity effects since, from October 2004 onwards, all OTC transactions in this market have to be reported to a common database known as the Trade Reporting and Compliance Engine (TRACE). Furthermore, market-wide average price quotes are available from Markit Group Limited, a financial information provider. Thus, it is possible, for the first time, to directly observe deviations between transaction prices and the expected market valuation of securities. We quantify and analyze our new liquidity measure for this market and find significant price dispersion effects that cannot be simply captured by bid-ask spreads. We show that our new measure is indeed related to liquidity by regressing it on commonly-used liquidity proxies and find a strong relation between our proposed liquidity measure and bond characteristics, as well as trading activity variables. Furthermore, we evaluate the reliability of end-of-day marks that traders use to value their positions. Our evidence suggests that the price deviations from expected market valuations are significantly larger and more volatile than previously assumed. Overall, the results presented here improve our understanding of the drivers of liquidity and are important for many applications in OTC markets, in general.     

Very fast money: High-frequency trading on the NASDAQ

This paper provides evidence regarding high-frequency trader (HFT) trading performance, trading costs, and effects on market efficiency using a sample of NASDAQ trades and quotes that directly identifies HFT participation. I find that HFTs engage in successful intra-day market timing, spreads are wider when HFTs provide liquidity and tighter when HFTs take liquidity, and prices incorporate information from order flow and market-wide returns more efficiently on days when HFT participation is high.