Modelling time-varying asymmetric information component of transaction costs

ABSTRACT

The main purpose of this paper is to model time-varying asymmetry information costs. To do this, first, we use two classical reduced-form microstructure models defined in a Bayesian hierarchical framework. In this scenario, we consider adverse selection as a random unobserved state variable and we use the Markov chain Monte Carlo (MCMC) estimator. And second, we evaluate whether time-varying asymmetric information cost estimates reflect the existence of periodicity (intraday patterns, time-of-day effects) and mean reversion in one stock. This procedure is applied to tick-by-tick quote and trade data on 15 SIBE-listed stocks over the 126 trading days since January–June 2005, estimating the unobserved time-varying costs for different hourly intervals. The main results indicate that our model captures periodicity between trading sessions and time-varying adverse selection costs showing the U-shape intraday pattern and mean reversion.

 

El propósito principal de este trabajo es modelar los costes de información asimétrica variables en el tiempo. Para ello, en primer lugar, se utilizan dos modelos clásicos de microestructura de forma reducida y definidos en un esquema jerárquico bayesiano. En este escenario consideramos que la selección adversa es una variable aleatoria de estado no observada y se utiliza el método Markov Chain Monte Carlo (MCMC). En segundo lugar, evaluamos si las estimaciones de costes de información asimétrica variables en el tiempo reflejan la existencia de periodicidad (patrones intradía, efectos de la hora del día) y reversión a la media en un activo. Este procedimiento se aplica a datos tick a tick de 15 acciones listadas en el SIBE durante 126 días de negociación desde enero a junio de 2005, estimando los costes variables no observados en el tiempo para diferentes intervalos horarios. Los principales resultados indican que nuestro modelo captura la periodicidad entre sesiones de negociación y los costes de selección adversa variables en el tiempo muestran el patrón intradía en forma de U y la reversión a la media.

KEYWORDS:

• Quote revision models
• adverse selection costs
• Bayesian estimates

PALABRAS CLAVE:

• modelos de revisión de precios
• costes de selección adversa
• estimación bayesiana

JEL CLASSIFICATION:

• C11
• C15
• C22
• G14

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. Information cost models emerge when dealers adjust prices in response to the existence of private information (Bagehot, 1971; Copeland & Galai, 1983; Glosten & Milgrom, 1985; Kyle, 1985; among others).

2. For example, in Admati and Pfleiderer (1988), liquidity traders are better off in clustering their trades over the trading time. The concentration of liquidity trades over time has two main effects. First, it attracts the information-motivated trading because it offers the opportunity to better disguise insider information. Second, it engages competitiveness in providing liquidity which, in turns, reduces the liquidity trader’s gain.

3. For example, Foster and Viswanathan (1993) show patterns in the interday trading costs in the NYSE market. Madhavan et al. (1997) indicate that adverse selection costs are not uniformly distributed throughout the day, but decrease towards the end of the session. Barclay and Hendershott (2004) show that adverse selection costs are highest early in the morning, decrease as the open approaches, remain relatively constant during the trading day and increase again immediately after the close. Other authors like Ranaldo (2002) and Pascual et al. (2004), among others, have descriptively analysed the intra-daily distribution of the information risk to see how the adverse selection change over trading day for Swiss and the NYSE markets, respectively.

4. Hasbrouck (1999a) proposes a structural model incorporating stochastic quote exposure costs and asymmetric rounding of bid and ask quotes by maximising a likelihood function using a non-linear state space filtering approach. Hasbrouck (1999b) also proposes a structural model maximising an approximate likelihood function for bid and ask quotes which cast the estimation in a Bayesian framework using a Gibbs sampler approach to compute posterior densities, which is more computationally efficient.

5. By their nature, inventory costs exist only in quote-driven markets, where operators are institutionally required to supply liquidity continuously (De Jong & Rindi, 2009). On the other hand, adverse selection and order processing costs may exist in any financial market. Because SSE is an order-driven market with specialists for some stocks, there can be inventory costs.

6. Hasbrouck (1991) models trade impact due to asymmetric information. More recently, following Hasbrouck (1991)’s model for trades and quotes, Pérez-Rodríguez (2011) estimates the expectation of a trade on the basis of a prior information set and, therefore, obtains the probability of an incoming order for a given stock, constructing a probabilistic neural network that assumes Bayesian learning.

7. The market model is anonymous both in the order book and in negotiations, because the aim is to maintain the strategies of the market members, to facilitate the purchasing of blocks of shares, to compete with alternative systems for dealing in shares and to compare it with other international financial markets (fixed income, currencies, derivatives, etc.) which are also anonymous. A market order is an order that an investor makes through a broker or brokerage service to buy or sell immediately at the best available current price. A limit order is an order placed with a brokerage to buy or sell a set number of shares at a specified price or better. Finally, a market to limit order is submitted as a market order to execute at the current best market price. If the order is only partially filled, the remainder of the order is cancelled and resubmitted as a limit order with the limit price equal to the price at which the filled portion of the order executed.

8. We have also used other econometric methods such as Kalman filter estimates to evaluate other parameter estimation methods. However, this method has provided erratic results. Therefore, we cannot draw conclusions by comparing the Kalman filter and Bayesian methods. For this reason, no results are shown. On the other hand, we have also used OLS methods to estimate time-varying adverse selection costs but many results are not statistically significant. Therefore, we claim for the Bayesian regression modelling.

9. Although testing for mean reversion can be done is several ways: unit root tests, Hurst exponent, variance ratio test, among others; we employ the former. Mathematically, a continuous mean-reverting time series can be represented by an Ornstein–Uhlenbeck stochastic differential equation, in contrast to a random walk (Brownian motion), which has no ‘memory’ of where it has been at each particular instance of time. This mean-reverting property of a time series can be exploited in order to produce profitable trading strategies.

10. Using Spanish Stock Exchange data during a similar analysed period and without taking into account time-varying cost estimates, Pérez-Rodríguez and Gómez-Déniz (2015) have found that order processing cost is around 80%, in average.

Additional information

Funding

This work was supported by the Ministerio de Economía y Competitividad: [Grant Number ECO2013-47092]; and Spanish Ministry of Science and Technology [Grant Number ECO2011-23189].