Implied Lévy volatility

We study the cause of large fluctuations in prices on the London Stock Exchange. This is done at the microscopic level of individual events, where an event is the placement or cancellation of an order to buy or sell. We show that price fluctuations caused by individual market orders are essentially independent of the volume of orders. Instead, large price fluctuations are driven by liquidity fluctuations, variations in the market's ability to absorb new orders. Even for the most liquid stocks there can be substantial gaps in the order book, corresponding to a block of adjacent price levels containing no quotes. When such a gap exists next to the best price, a new order can remove the best quote, triggering a large midpoint price change. Thus, the distribution of large price changes merely reflects the distribution of gaps in the limit order book. This is a finite size effect, caused by the granularity of order flow: in a market where participants place many small orders uniformly across prices, such large price fluctuations would not happen. We show that this also explains price fluctuations on longer timescales. In addition, we present results suggesting that the risk profile varies from stock to stock, and is not universal: lightly traded stocks tend to have more extreme risks.     

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.     

Order submission strategies,liquidity supply,and trading in pennies on the New York Stock Exchange

We use NYSE system order data to conduct a controlled experiment examining changes in trader behavior, displayed liquidity supply, and execution quality around the reduction in the minimum price variation to $0.01. Although traders do not substantially reduce their use of traditional limit orders in favor of market orders or non-displayed orders, they do decrease limit order size and cancel limit orders more frequently after decimals than before. These changes in order submission strategy appear to result in less displayed liquidity throughout the limit order book more than 15 cents from the quote midpoint. This reduction in displayed liquidity, however, does not manifest itself in poor execution quality. Even for large system orders, traditional execution quality is not worse with decimals than with fractions.     

Does stock exchange consolidation improve market liquidity? A study of stock exchange acquisition in Russia

The last couple of decades have witnessed significant institutional and structural changes in financial sector within a worldwide trend toward consolidation. In the segment of organized trading stock exchanges merge and develop into large and diversified publicly traded companies. These processes are rather complicated in case of a transition economy like Russia. In December 2011 MICEX, the first largest and state-controlled stock exchange acquired RTS, the second largest and privately owned stock exchange primarily designed for foreign investors. We empirically investigate whether the acquisition resulted in improved liquidity of the Russian stock market which was one of the declared acquisition objectives. We use the Kolmogorov–Smirnov and the Wilcoxon tests to compare market-wide liquidity in several discrete periods pre and post acquisition. A deep and thorough insight into liquidity performance is ensured by assessing liquidity from limit order book data of tick frequency along three dimensions (tightness, immediacy, and elasticity).     

Limit Order Book and Commonality in Liquidity

We show that the liquidity provided by an individual stock's limit order book comoves significantly with the market aggregate limit order book liquidity. A closer look at the inside and outside liquidity provided by different parts of limit order book suggests that inside liquidity is mainly influenced by market volatility, while idiosyncratic volatility has a larger impact on outside liquidity. Hence, limit order book inside liquidity exhibits higher commonality than outside liquidity. We also show that the comovement between the stock‐level and market‐aggregate limit order book liquidity measures is related to the commonality in the overall stock market liquidity.     

Stock Liquidity Risk and the Cross‐sectional Earnings‐Returns Relationship

We argue that a higher sensitivity to aggregate market‐wide liquidity shocks (i.e., a higher liquidity risk) implies a tendency for a stock's price to converge to fundamentals. We test this intuition within the framework of the earnings‐returns relationship. We find a positive liquidity risk effect on the relationship between return and expected change in earnings. This effect on the earnings‐returns relationship is distinct from the negative effect observed for stock illiquidity level. Notably, the liquidity risk effect is evident (absent) during periods of neutral/low (high) aggregate market liquidity. We also show that the liquidity risk effect is dominant in firms that: (a) are of intermediate size; (b) are of intermediate book‐to‐market; and (c) are profit making.     

Limit order books and trade informativeness

In the microstructure literature, information asymmetry is an important determinant of market liquidity. The classic setting is that uninformed dedicated liquidity suppliers charge price concessions when incoming market orders are likely to be informationally motivated. In limit order book (LOB) markets, however, this relationship is less clear, as market participants can switch roles, and freely choose to immediately demand or patiently supply liquidity by submitting either market or limit orders. We study the importance of information asymmetry in LOBs based on a recent sample of 30 German Deutscher Aktienindex (DAX) stocks. We find that Hasbrouck's (1991) measure of trade informativeness Granger causes book liquidity, in particular that required to fill large market orders. Picking-off risk due to public news-induced volatility is more important for top-of-the book liquidity supply. In our multivariate analysis, we control for volatility, trading volume, trading intensity and order imbalance to isolate the effect of trade informativeness on book liquidity.     

Systematic liquidity risk and stock price reaction to shocks

This study examines the relationship between systematic liquidity risk and stock price reaction to large 1‐day price changes (or shocks). We base our analysis on a yearly updated constituents list of the FTSE All share index. Our overall results are consistent with the price continuation hypothesis, which suggests that positive (negative) shocks will be followed by positive (negative) abnormal returns. However, further analysis indicates that stocks with low systematic liquidity risk react efficiently to both positive and negative shocks, whereas stocks with high systematic liquidity risk underreact to both positive and negative shocks. Our results are valid irrespective of various robustness tests such as size of the shock, size of the firm, month‐of‐the‐year and day‐of‐the‐week effects. We conclude that trading on price patterns following shocks may not be profitable, as it involves taking substantial liquidity exposure.     

Liquidity supply in electronic markets

We examine the supply of liquidity by proprietary trading desks and hedge funds (PTDH) versus mutual funds, index funds, and insurance companies (MII) across ten bid (ask) steps of the limit order book. We document that institutional investors simultaneously supply liquidity at multiple prices in the limit order book. We also find that PTDHs are more price aggressive liquidity suppliers than MIIs, consistent with hypothesized responses to observed changes in the cost and risk of non-execution. We investigate whether these findings are robust to fast versus slow markets, the volatility of daily returns, and aggregate depth relative to daily volume.     

Reprint of: Market liquidity in the financial crisis: The role of liquidity commonality and flight-to-quality

We examine the dynamics and the drivers of market liquidity during the financial crisis, using a unique volume-weighted spread measure. According to the literature we find that market liquidity is impaired when stock markets decline, implying a positive relation between market and liquidity risk. Moreover, this relationship is the stronger the deeper one digs into the order book. Even more interestingly, this paper sheds further light on so far puzzling features of market liquidity: liquidity commonality and flight-to-quality. We show that liquidity commonality varies over time, increases during market downturns, peaks at major crisis events and becomes weaker the deeper we look into the limit order book. Consistent with recent theoretical models that argue for a spiral effect between the financial sector’s funding liquidity and an asset’s market liquidity, we find that funding liquidity tightness induces an increase in liquidity commonality which then leads to market-wide liquidity dry-ups. Therefore our findings corroborate the view that market liquidity can be a driving force for financial contagion. Finally, we show that there is a positive relationship between credit risk and liquidity risk, i.e., there is a spread between liquidity costs of high and low credit quality stocks, and that in times of increased market uncertainty the impact of credit risk on liquidity risk intensifies. This corroborates the existence of a flight-to-quality or flight-to-liquidity phenomenon also on the stock markets.     

Market liquidity in the financial crisis: The role of liquidity commonality and flight-to-quality

We examine the dynamics and the drivers of market liquidity during the financial crisis, using a unique volume-weighted spread measure. According to the literature we find that market liquidity is impaired when stock markets decline, implying a positive relation between market and liquidity risk. Moreover, this relationship is the stronger the deeper one digs into the order book. Even more interestingly, this paper sheds further light on so far puzzling features of market liquidity: liquidity commonality and flight-to-quality. We show that liquidity commonality varies over time, increases during market downturns, peaks at major crisis events and becomes weaker the deeper we look into the limit order book. Consistent with recent theoretical models that argue for a spiral effect between the financial sector’s funding liquidity and an asset’s market liquidity, we find that funding liquidity tightness induces an increase in liquidity commonality which then leads to market-wide liquidity dry-ups. Therefore our findings corroborate the view that market liquidity can be a driving force for financial contagion. Finally, we show that there is a positive relationship between credit risk and liquidity risk, i.e., there is a spread between liquidity costs of high and low credit quality stocks, and that in times of increased market uncertainty the impact of credit risk on liquidity risk intensifies. This corroborates the existence of a flight-to-quality or flight-to-liquidity phenomenon also on the stock markets.     

Stock liquidity and corporate tax avoidance

We show that firms with higher stock liquidity engage less in extreme (i.e., overly aggressive or overly conservative) tax avoidance. The effect of stock liquidity on tax avoidance is economically meaningful and robust across alternative measures of tax avoidance and stock liquidity. The findings also hold after controlling for potential endogenous effects. We further document that the effect of stock liquidity on tax avoidance is amplified for firms with high proportions of activist shareholders and attenuated for firms with high levels of stock price informativeness. Overall, our findings suggest that stock liquidity mitigates extreme tax avoidance by enhancing shareholders’ monitoring over firm management.

     

Liquidating large security positions strategically: a pragmatic and empirical approach

This article investigates static liquidation strategies for large security positions in illiquid markets. Under the assumption that the liquidation horizon is given exogenously, a discretionary liquidity trader solves for the optimal sales trajectory so as to maximize an objective function that considers the expected liquidation revenues and their standard deviation. Although existing literature tends to focus on theoretical aspects with the intention of deriving closed-form solutions for special types of market impact functions, this article considers a framework that is able to capture important empirical phenomena in the stock market, such as the intraday U-shaped pattern of price impact and the resiliency of the order book. The new model is very flexible since it allows for liquidation intervals of varying length and foregoes the assumption of constant speed of trading. Examples with real-world order book data demonstrate how the setup can be implemented numerically and provide deeper insight into relevant properties of the model.     

How effective are trading pauses?

Exploiting Nasdaq order book data and difference-in-differences methodology, we identify the distinct effects of trading pause mechanisms introduced on US stock exchanges after May 2010. We show that the mere existence of such a regulation makes market participants behave differently in anticipation of a pause. Pauses enhance price discovery during the break but have adverse effects on price stability and liquidity after the pause. We find that pauses ultimately do not “cool off” markets but cause extra volatility. This implies a regulatory trade-off between the protective role of trading pauses and their adverse effects on market quality.     

Liquidity,volume and price efficiency: The impact of order vs. quote driven trading

As equity trading becomes predominantly electronic, is there still value to a traditional, intermediated dealer system? We address this question by comparing the impact of the organization of trading on volume, liquidity, and price efficiency in a quote-driven dealer market and in an order-driven limit order book. Small order price impacts are higher and large order price impacts are lower in a dealer market. Prices are more efficient in the limit order book, except when the level of informed trading is high. Volume is higher in a limit order market, making this system most attractive for trading venues.     

Competition for Order Flow and Smart Order Routing Systems

We study the rivalry between Euronext and the London Stock Exchange (LSE) in the Dutch stock market to test hypotheses about the effect of market fragmentation. As predicted by our theory, the consolidated limit order book is deeper after entry of the LSE. Moreover, cross‐sectionally, we find that a higher trade‐through rate in the entrant market coincides with less liquidity supply in this market. These findings imply that (i) fragmentation of order flow can enhance liquidity supply and (ii) protecting limit orders against trade‐throughs is important.     

Stock price synchronicity and liquidity

We argue and provide evidence that stock price synchronicity affects stock liquidity. Under the relative synchronicity hypothesis, higher return co-movement (i.e., higher systematic volatility relative to total volatility) improves liquidity. Under the absolute synchronicity hypothesis, stocks with higher systematic volatility or beta are more liquid. Our results support both hypotheses. We find all three illiquidity measures (effective proportional bid-ask spread, price impact measure, and Amihud's illiquidity measure) are negatively related to stock return co-movement and systematic volatility. Our analysis also shows that larger industry-wide component in returns improves liquidity. We find that improvement in liquidity following additions to the S&P 500 Index is related to the stock's increase in return co-movement.     

The impact of short-selling and margin-buying on liquidity: Evidence from the Chinese stock market

We propose a framework based on limit order book to analyze the impact of short-selling and margin-buying on liquidity. We show that when short-sellers are perceived as informed, adverse selection may lead to uninformed traders withdrawing their limit orders. Given that the Chinese stock market has strong information asymmetry and a high proportion of uninformed traders, we predict that the pilot program launched in March 2010, which lifts restrictions on short-selling and margin-buying for a designated list of stocks, may have a negative impact on liquidity. We perform difference-in-differences tests and show evidence that allowing for short-selling and margin-buying indeed has a significantly negative impact on liquidity for stocks on the designated list. In particular, the negative impact on liquidity is more pronounced for stocks with high information asymmetry. Nevertheless, when short-selling volume dries up due to regulation changes in August 2015, i.e., the “T+1” trading rule on short-selling, we show that consistent with model predictions, lifting restrictions on short-selling and margin-buying has a positive effect on liquidity.     

Statistical properties of stock order books: empirical results and models

Abstract

We investigate several statistical properties of the order book of three liquid stocks of the Paris Bourse. The results are to a large degree independent of the stock studied. The most interesting features concern (i) the statistics of incoming limit order prices, which follows a power-law around the current price with a diverging mean; and (ii) the shape of the average order book, which can be quantitatively reproduced using a ‘zero intelligence’ numerical model and qualitatively predicted using a simple approximation.