Anna A. Obizhaeva

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.

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

Optimal Investment Decisions

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

A discrete investment model of a production project is considered. Stoppage and recovery of production are allowed. The project is scrapped if the maintenance costs exceed some limit. The optimal maintenance cost threshold is calculated.

Liquidity Estimates and Selection Bias

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.

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

Since traders often employ price-dependent strategies and cancel expensive orders, conventional estimates tend to overestimate available liquidity. This paper studies trading costs using the sample of portfolio transition trades. The known exogeneity of these trades eliminates the selection bias problem. We estimate a piece-wise linear price impact functions with the intercept corresponding to fixed spread costs and the slope corresponding to variable price impact costs. Buy orders are more expensive than sell orders due to specific institutional features of portfolio transitions. For high-volume stocks, small trades are executed at a discount relative to a piece-wise linear specification. Since the size of this discount is comparable to bid-ask spread, we attribute documented non-linearity to ability of portfolio transition managers sometimes to earn bid-ask spread instead of paying it by providing liquidity to other market participants.

Market Microstructure Invariance: A Dynamic Equilibrium Model

The intraday trading patterns in the E-mini S&P 500 futures contract between January 2008 and November 2011 are consistent with the following invariance relationship: The return variation per transaction is log-linearly related to trade size, with a slope coefficient of -2. This association applies both across the pronounced intraday diurnal pattern and across days in the time series. The documented factor of proportionality deviates sharply from prior hypotheses relating volatility to transactions count or trading volume. Intraday trading invariance is motivated a priori by the intuition that market microstructure invariance, introduced by Kyle and Obizhaeva (2016c) to explain bets at low frequencies, also applies to transactions over high intraday frequencies.

Invariance of Buy-Sell Switching Points

We derive invariance relationships for a dynamic infinite-horizon model of market microstructure with risk-neutral informed trading, noise trading, market making, and endogenous production of information. Equilibrium prices follow a martingale with endogenously derived stochastic volatility. The invariance relationships for bet sizes and transaction costs are obtained under the assumption that the effort required to generate one discrete bet does not vary across securities and time. The invariance relationships for pricing accuracy and market resiliency require the additional assumption that private information has the same signal-to-noise ratio across markets. Since bets are based on the arrival of discrete chunks of information, the structural model describes how the invariance relationships reflect differences in the granularity of information flows across markets. The model links proportionality coefficients in invariance relationships to fundamental parameters.

A Practitioner’s Guide to Market Microstructure Invariance

Define the number of buy-sell “switching points” as the number of times that individual traders change the direction of their trading. Based on the hypothesis that switching points take place in business time, market microstructure invariance predicts that the aggregate number of switching points is proportional to the 2=3 power of the product of dollar volume and volatility. Using trading data from the Korea Exchange (KRX) from 2008 to 2010, we estimate the exponent to be 0.675 with standard error of 0.005. Invariance explains about 93% of the variation in the logarithm of the number of switching points each month across stocks. Most of the variation represents changes in the number of accounts trading the stock and not the number of switching points per account.