Advances in Quantitative Analysis of Finance and Accounting

The following sections are included:

• Preface to Volume 3

• Contents

• Introduction

• List of Contributors

The paper provides new results on the optimality of a centralized limit order book. In an environment in which traders optimally choose their trade quantity in response to the terms of trade they face, the analysis shows that a centralized limit order book is optimal in the following sense: the equilibrium in a limit order book corresponds to the welfare optimum for some set of welfare weights. The paper also provides a new analysis of a uniform price limit order book with endogenous trade.

The electronic limit order book has transformed securities markets. Advantages of speed, simplicity, scalability, and low costs drive the rapid adoption of this mechanism to trade equities, bonds, foreign exchange, and derivatives worldwide. But limit order book systems depend primarily on public limit orders to provide liquidity, raising natural questions regarding the resiliency of the mechanism under stress. This paper provides an analysis of the stochastic dynamics of liquidity and its relation to volatility shocks using data from a futures market. Aggregate market liquidity exhibits considerable variation, and is inversely related to volatility, as predicted by our model. However, liquidity shocks dissipate quickly, indicating a high degree of market resiliency. This fact has important practical implications, particularly as regards to institutional trading, and market protocols. We explore these practical issues in detail.

This paper provides a roadmap for building a contingent claims theory of limit order markets grounded in a simple observation: limit orders are equivalent to a portfolio of cash-or-nothing and asset-or-nothing digital options on market order flow. However, limit orders are not conventional derivative securities: order flow is an endogenous, nonprice state variable; the underlying asset value is a construct, the value of the security in different order flow states; and arbitrage trading or hedging of limit orders is not feasible. Fortunately, none of these problems is fatal since options on order flow can be conceptualized as bets implicit in limit orders, arbitrage trading can be replaced by limit order substitution, and plausible assumptions can be made about the endogeneity of order flow states and their associated asset values. The analysis yields two main results: Arrow–Debreu prices for order flow "states" are proportional to the slope of the limit order book and the limit order book at one time proves to be identical to that at an earlier time adjusted for the intervening net order flow when all information arrives via trades.

Previous studies of the limit order book report that low depths accompany wide spreads and that spreads widen and depths fall in response to higher volume, but some postulate a positive relationship between spreads and depth during normal trading periods. We calculate the option value of the limit order book at 11:00 a.m. for 10 actively traded firms listed on the Australian Stock Exchange. Simultaneously this approach enables us to consider the spread and depth of the limit order book. We find that 33.1% of the option value of the limit order book is provided at the best ask and 34.7% at the best bid. We find that the option value of the limit order book is greatest at the best bid price and the best ask price and is more stable through time than the option value of individual shares or share quantities in the book. Also, consistent with the arguments of Cohen et al. (1981), we find evidence of equilibrium in the supply and demand of liquidity.

In this paper, we analyze cross-sectional heterogeneity in the time-series variation of liquidity in equity markets. Our analysis uses a broad time-series and cross-section of liquidity data. We find that average daily changes in liquidity exhibit significant heterogeneity in the cross-section; the liquidity of small firms varies more on a daily basis than that of large firms. A steady increase in aggregate market liquidity over the past decade is more strongly manifest in large firms than in small firms. Absolute stock returns are an important determinant of liquidity. We investigate cross-sectional differences in the resilience of a firm's liquidity to information shocks. We use the sensitivity of stock liquidity to absolute stock returns as an inverse measure of this resilience, and find that the measure exhibits considerable cross-sectional variation. Firm size, return volatility, institutional holdings, and volume are all significant cross-sectional determinants of this measure.

This paper compares intraday volatility on two different market structures: specialist and multiple dealer. Return volatility based on 15-minute returns is compared for stocks trading on the NYSE and NASDAQ. It is hypothesized in the paper that the price continuity obligation of specialists will lead to lower volatility for stocks traded in that market structure. The results support the hypothesis. Regressions are performed to control for firm-specific variables. The results of the regressions do not alter the conclusions of the paper that a specialist-based market is associated with a lower level of volatility than a multiple dealer market.

Trading and quoting exhibit distinct intraday patterns. Using transaction data for a sample of NYSE stocks, we analyze the intraday probability of informed trading using a model developed by Easley, Kiefer, O'Hara, and Paperman (1996). We find a crude inverted U-shaped pattern in the probability of informed trading on an intraday basis. We find that trading activity, measured by the number of trades, is positively related to the probability of informed trading, and the amount of regional activity is inversely related to the probability of informed trading.

We study the returns to leasing a New York Stock Exchange (NYSE) seat during 1995–2005 and find that these returns are a weighted average of past leasing returns and a set of fundamental factors such as average NYSE quoted spreads, the dollar value of NYSE trading volume, and the return on the overall stock market. Our partial adjustment model explains 70–80% of the variation in leasing returns and 80–85% of this explanatory power is attributable to a simple AR(1) process. Quoted spreads, trading volume, and stock market returns are all significant factors that positively affect leasing returns, albeit to a lesser extent than past returns to leasing. In addition, NYSE seat lessors rely more heavily on past values of these fundamental factors rather than coincident or forward-looking values of spreads, volume, returns, etc. This is in contrast to previous results on exchange seat prices which find that only unexpected changes in fundamental factors such as those noted above have a significant impact on exchange seat prices. In addition, unlike previous research on seat prices, which report that these prices follow a random walk, we do not find that leasing returns behave in this manner.

We study the impact of decimalization on the New York Stock Exchange (NYSE). Empirical results indicate that spreads decrease significantly after decimalization, but the market depth and average volume per trade also decline significantly. It is likely that more front-runners are entering the market. We test the degree of front-running surrounding decimalization directly and confirm the conjecture. Furthermore, stocks with different characteristics have different reactions to decimalization. Our results lend support to multiple optimal tick sizes for stocks with different characteristics, instead of a uniform minimum tick size for all stocks.

With an aversion to losses, there are some traders in financial markets who are not overly aggressive in bidding too high and some traders who are not overly aggressive in selling at too low of a price. This paper shows in an evolutionary model of natural selection within the context of a futures market that as long as these conservative traders have some positive probability (however small) of making an accurate prediction of the spot price, their presence ensures the convergence to an efficient market. This result is distinct from previous related research. Furthermore, although such conservative traders are not aggressive nor do they always participate in the market, in the long run they not only survive but eventually increase their share of aggregate wealth.

Economists have long conjectured that movements in stock prices may involve speculative components, called bubbles. A bubble is defined as the difference between the market value of a security and its fundamental value. The topic of asset bubbles remains controversial because the existence of a bubble is inherently an empirical issue and no satisfactory test has yet been devised to estimate the magnitude of a bubble. This paper proposes a new methodology for testing for the existence of rational bubbles. Unlike previous authors, we treat both the dividend that drives the fundamental part and the nonfundamental process as part of the state vector. This new methodology is applied to the four mature markets of the US, Japan, England, and Germany to test whether a speculative component was present during the period of January 1951 to December 1998 in these markets. The paper also examines whether there are linkages between these national speculative components. We find evidence that the nonfundamental component in the US market causes the other three markets but we find no evidence for reverse causality.

The following sections are included:

• INDEX