نوسانات و ساختار بازار

This study examines volatility within three related intra-day series – transaction returns, quote midpoint returns, and limit order book midpoint returns – for a set of NYSE-listed stocks. We document statistically significant GARCH effects both overall and surrounding earnings announcements in all three series for the majority of stocks in the sample. We then compare the extent of volatility clustering among the series. In addition, the relation between volatility and market structure is examined via a set of cross-sectional regressions, and relations among the series over time are studied in a vector autoregressive framework.

The fact that the variance of stock returns changes over time is well documented in the finance literature. Much of the existing research describes the time-variation in volatility using some form of ARCH or GARCH model (Engle, 1982; Bollerslev, 1986).1 For example, French, Schwert, and Stambaugh (1987) find GARCH effects in monthly S&P returns and Cheung and Ng (1992) and Engle and Mustafa (1992) find ARCH effects in daily returns for individual stocks. While the existence of conditional heteroskedasticity in asset returns is well documented, this phenomenon is not well understood. In addition to documenting volatility clustering in financial series, the work in this area has focused on determining its cause. One commonly offered explanation is a similar clustering of news or information arrival. There is some evidence in support of this hypothesis (e.g. Engle et al., 1990); however, the underlying cause of the news clustering is not known. The possibility that changes in macroeconomic conditions affect volatility has also been investigated. For example, Campbell (1987) and Glosten et al. (1993) find a relation between volatility and interest rate levels. A third explanation, which has received less attention, relates conditional heteroskedasticity to micro-level factors. Lamoureux and Lastrapes (1990) find that the ARCH coefficient (α) is no longer significant when trading volume is incorporated into a GARCH model. Bollerslev and Domowitz (1991) examine the relation between price volatility and trading mechanisms in a futures market setting. They find that returns for transactions executed via the Globex futures trading system exhibit GARCH effects, while returns for transactions accomplished through an open outcry mechanism do not. Despite this extensive literature, little conclusive evidence has emerged regarding the underlying cause of volatility clustering. Consequently, we adopt a slightly different approach to increase our understanding of this phenomenon. Rather than directly studying a particular cause, we compare the degree of volatility clustering across a set of financial series that provide a natural controlled experiment. Specifically, we examine three distinct, yet related return series – a transaction series, a quote midpoint series, and a limit order book midpoint series – for each individual stock in our sample. As a result, we are able to examine the way in which the three series relate to one another and to isolate differences in their relation to the market structure. This comparison is unique because it analyzes the properties of conditional variance series for the same asset over the same time period. The only differences among the three series are the participants (liquidity providers versus liquidity demanders) and the private information they each possess. Our analysis documents conditional heteroskedasticity in all three return series overall, as well as surrounding earnings announcements. In other words, we find that both past shocks to the return series and lagged values of the variance affect the magnitude of the current variance. The extent to which current variance is impacted by lagged shocks to the return series and lagged variance is known as the asset's sensitivity and persistence levels respectively. In comparing the variances of the three series, we find that the sensitivity and persistence levels for the limit order book midpoint returns equal or exceed those in quote midpoint returns, which in turn surpass those in transaction returns. Moreover, we find that the transaction series is least affected by earnings announcements, while the limit order book series is most affected. Specifically, the sensitivity to shocks increases for the limit order book and decreases for the quote series, while the persistence parameters decrease significantly for both series during the announcement period. We also show that the level, sensitivity, and persistence of the conditional volatility series are related to the overall structure of the market. For each series, we estimate a set of cross sectional regressions relating volatility to liquidity measures. We find that the variance of each series is negatively related to trading volume and the average quoted spread and depth are positively related to the variance of quoted depth and to the stock's average trade size relative to quoted depth. In addition, a high relative trade size is associated with decreased persistence levels for transactions and the limit order book, but increased sensitivity levels for quotes. Higher trading volume is linked to a higher sensitivity to incoming information for the transaction variance series and a lower persistence for the limit order book series. Despite the prevalence of volatility clustering, a substantial minority of the stocks in our sample have constant conditional variance for at least one of the series. We find that stocks with constant conditional variances for the quote and limit order book series tend to be either low volume stocks or high volume stocks with high prices, while stocks with constant conditional transaction variances are evenly disbursed over the trading volume/price groups. Finally, we examine the time-series relations among the three volatility series for each stock using a vector autoregressive model. The results suggest that, while there is a strong relation between volatility clustering in quote and transaction returns, the relation among limit order book returns and the other series is substantially weaker. Overall, this paper provides the first description of the conditional variance series for limit order books and offers insight into the behavior of market participants. By comparing the three series, we highlight important differences between liquidity demanders and liquidity providers and how those differences are manifested in price volatility. Specifically, our results, which document varying degrees of conditional heteroskedasticity across the three series, are consistent with liquidity demanders and liquidity suppliers reacting to different stimuli and having different aptitudes for processing incoming information. In addition, we show that, although microstructure effects are related to volatility clustering, they are unable to explain it fully. Consequently, other considerations, such as the speed of information arrival, are likely to have a substantial impact on clustering as well. The remainder of the paper is organized as follows. Section 2 describes the data, the procedure used to estimate the limit order books, and the model employed in the analysis. Section 3 discusses volatility clustering in the transaction, quote, and limit order book return series both unconditionally and surrounding information events. Section 4 examines relations between volatility and the NYSE market structure, as well as the characteristics of stocks with constant conditional variance series. Section 5 uses a vector autoregression to relate volatility clustering among the three return series through time. Section 6 concludes.

By analyzing the volatility of three related yet distinct series – transaction returns, quote midpoint returns, and limit order book midpoint returns – we obtain insight into the impact of market structure on volatility and into the relations among the series. We document statistically significant GARCH effects in the transaction, quote, and limit order book series for the majority of the stocks in our sample. We further show that the sensitivity and persistence levels for the best prices on the limit order book equal or exceed those in quoted prices, which in turn surpass those in transaction prices. We extend the comparison by examining the impact of earnings announcements on the volatility of each series. The results demonstrate that the sensitivity to shocks (α) increases for the limit order book and decreases for the quote series surrounding earnings announcements, while the persistence parameters (α+β) decrease for both series during the announcement period. We examine the impact of market structure on volatility directly by estimating a set of cross-sectional regressions. We find that the average conditional variance is negatively related to trading volume and the quoted spread and depth, and is positively related to the variance of quoted depth and to relative trade size. Furthermore, the sensitivity of transaction variance to incoming innovations (α) is higher for actively-traded stocks and the persistence (α+β) of shocks decreases as the average trade size (relative to the quoted depth) increases for both transactions and the book. We also show that low volume stocks and high priced, high volume stocks have a greater tendency to exhibit conditional variance series that are not time-varying. Finally, we estimate a vector autoregressive model to analyze relations among the three series over time. The results suggest that, while there is a strong relation between volatility clustering in quote and transaction returns, the relation among limit order book returns and the other series is substantially weaker. The results summarized above document a number of facts about volatility clustering in equity markets that we believe will be valuable in many different contexts. First, the findings constitute the first detailed description of limit order book volatility in the literature. Consequently, the limit order book results can be viewed as interesting stylized facts. They also provide additional information regarding the role of limit order books, which could be beneficial in discussions of the optimal structure of equity markets. Second, the findings offer new insight into the behavior of market participants, as well as confirming some existing results. In particular, by comparing the three series, we are better able to understand the interplay between liquidity providers who place limit orders, the specialist and floor members, and liquidity demanders who place market orders. For example, our results may suggest that, while some information is impounded into prices through the trading process, a significant portion of transaction volatility stems from liquidity shocks. Furthermore, we find evidence that liquidity suppliers may be better able than liquidity demanders to quickly process and interpret incoming information in the period surrounding corporate announcements. Finally, as stated in the introduction, the underlying cause of volatility clustering in financial markets remains largely a mystery. Although this study in isolation cannot offer definitive conclusions about the source of volatility clustering in equity markets, the results constitute an important step towards improving our understanding of this phenomenon. Valuable insight can be gained by considering the relations among the series in conjunction with the differential effects of the market structure on each. For example, we find that both volatility levels and clustering are higher on the limit order book than in transactions, but that little of the clustering on the book can be linked to microstructure effects. Together, these facts suggest that other considerations, like the way in which information arrives and is incorporated into each series, have a substantial impact on clustering. We believe that additional research in this area will be fruitful and hope that this study has laid the groundwork for such work.