Albert S. Kyle

The Flash Crash: High-Frequency Trading in an Electronic Market

We study intraday market intermediation in an electronic market before and during a period of large and temporary selling pressure. On May 6, 2010, U.S. financial markets experienced a systemic intraday event, known as the Flash Crash, when a large automated sell program was rapidly executed in the E-mini S&P 500 stock index futures market. Using audit trail transaction-level data for the E-mini on May 6 and the previous three days, we find that the trading pattern of the most active non-designated intraday intermediaries (classified as High Frequency Traders) did not change when prices fell during the Flash Crash.

Prospect Theory and Liquidation Decisions

We solve a liquidation problem for an agent with preferences consistent with the prospect theory of Kahneman and Tversky (1978). We find that the agent is willing to hold a risky project with a relatively inferior Sharpe ratio if the project is currently making losses, and intends to liquidate it when it breaks even. On the other hand, the agent may liquidate a project with a relatively superior Sharpe ratio if its current profits rise or drop to the break-even point. Our results capture the spirit of the disposition effect and the break-even effect documented in empirical and experimental studies.

Contagion as a Wealth Effect of Financial Intermediaries

This paper models financial contagion as a wealth effect of financial intermediaries in a market with two risky assets and three types of traders: noise traders who trade in one market, financial intermediaries who partially arbitrage away noise trading, and long-term investors who provide liquidity. Contagion is characterized as decreased liquidity, increased volatility in both markets, and increased correlation between returns on the two assets occurring simultaneously with financial intermediaries suffering losses on positions. When financial intermediaries have reduced capital as a result of trading losses, they have a reduced capacity for bearing risks. This motivates them to liquidate positions in both markets, resulting in reduced market liquidity, increased price volatility in both markets, and increased correlation. Through this mechanism, the wealth effect leads to contagion. Financial intermediaries are assumed to follow consumption and portfolio rules which make them look like a log-utility investor: the volatility of their portfolio equals the Sharpe ratio available in the market and the dividend rate (i.e., consumption rate) equals the rate of time preference. They trade in two markets with independent fundamentals and constant dollar total risk. As the financial intermediaries partially arbitrage away the effects of noise trading in one market, they take large risky arbitrage positions. Long-term investors provide some liquidity, which makes it possible for financial intermediaries to liquidate positions when they suffer losses. The equilibrium has two state variables, the wealth of financial intermediaries and noise trading. A system of two simultaneous partial differential equations is solved numerically using a projection method. This model cautions risk managers to evaluate risks using information about the capitalization and positions of other market participants.

Market Microstructure Invariance: Empirical Hypotheses

Using the intuition that financial markets transfer risks in business time, “market microstructure invariance” is defined as the hypotheses that the distributions of risk transfers (“bets”) and transaction costs are constant across assets when measured per unit of business time. The invariance hypotheses imply that bet size and transaction costs have specific, empirically testable relationships to observable dollar volume and volatility. Portfolio transitions can be viewed as natural experiments for measuring transaction costs, and individual orders can be treated as proxies for bets. Empirical tests based on a dataset of 400,000+ portfolio transition orders support the invariance hypotheses. The constants calibrated from structural estimation imply specific predictions for the arrival rate of bets (“market velocity”), the distribution of bet sizes, and transaction costs.

A Model of Portfolio Delegation and Strategic Trading

This article endogenizes information acquisition and portfolio delegation in a one-period strategic trading model. We find that, when the informed portfolio manager is relatively risk tolerant (averse), price informativeness increases (decreases) with the amount of noise trading. When noise trading is endogenized, the linear equilibrium in the traditional literature breaks down under a wide range of parameter values. In contrast, a linear equilibrium always exists in our model. In a conventional portfolio delegation model under a competitive partial equilibrium, the managers effort of acquiring information is independent of a linear incentive contract. In our strategic trading model, however, a higher-powered linear contract induces the manager to exert more effort for information acquisition. The Author 2011. Published by Oxford University Press on behalf of The Society for Financial Studies. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com., Oxford University Press.

Large Bets and Stock Market Crashes

For five stock market crashes, we compare price declines with predictions from market microstructure invariance. During the 1987 crash and the sales by Soci?et?e G?en?erale in 2008, prices fell by magnitudes similar to predictions from invariance. Larger-than-predicted temporary price declines during two flash crashes suggest rapid selling exacerbates transitory price impact. Smaller-than-predicted price declines for the 1929 crash suggest slower selling stabilized prices and less integration made markets more resilient. Quantities sold in the three largest crashes suggest fatter tails or larger variance than the log-normal distribution estimated from portfolio transitions data.

Market Microstructure Invariants: Empirical Evidence from Portfolio Transitions

The hypothesis of “market microstructure invariance” — based on the intuition that the size and costs of transferring risk in “business time” is constant across assets and time — is tested using a database of 400,000 portfolio transition trades. Defining trading activity W as the product of dollar volume and returns standard deviation, microstructure invariance predicts that order size, market impact costs, and bid-ask spread costs (adjusted for volume and volatility) are proportional to W^{-2/3}, W^{1/3}, and W^{-1/3}, respectively. Estimated exponents of -0.63, 0.33, and -0.39 are close to the predicted values of -2/3, 1/3, and -1/3 respectively. The distribution of order size as a fraction of volume conforms closely to a log-normal with log-variance of 2.50. Calibration estimates for a benchmark stock with expected daily volume of

Liquidity with High-Frequency Market Making

40 million and volatility of 2% imply that the median order size is 0.34% of average daily volume, market impact cost of trading one percent of daily volume is 2.89 basis points, and the bid-ask cost is 7.90 basis points.

Trading Game Invariance in the TAQ Dataset

We study a simple model of market making in which high-frequency market makers can cancel limit orders quickly after receiving an adverse signal. The resulting winners curse induces low-frequency market makers to widen bid-ask spreads. Liquidity in the market may deteriorate unless high-frequency market makers fully replace low-frequency market makers in liquidity provision. Our result suggests that some restrictions on high-frequency trading, such as minimum resting times, may improve market liquidity by leveling the playing field among market makers with different speeds.

Intraday Trading Invariance in the E-mini S&P 500 Futures Market

The trading game invariance hypothesis of Kyle and Obizhaeva (2011a) is tested using the Trades and Quotes (“TAQ”) dataset. Over the period 1993-2001, the estimated monthly regression coefficients of the log of trade arrival rate on the log of trading activity has an almost constant value of 0.690, slightly higher than the value of 2/3 predicted by the invariance hypotheses. Over the period 2001-2008, the coefficient estimates rise almost linearly, with an average value of 0.787. Average trade size, normalized for trading activity, falls dramatically over the period 1993-2008. The distribution of trade size adjusted for trading activity resembles a log-normal more closely in 1993 than in 2001 or 2008, with truncation below the 100-share odd-lot boundary becoming a more prominent feature over time. These results suggests that the 2001 reduction in minimum tick size to one cent and the subsequent increase in algorithmic trading have resulted in more intense order shredding in actively traded stocks than inactively traded stocks. The invariance hypothesis explains 91% of the cross-sectional variation in print arrival rates and average print size.