Statistical Properties of the Roll Serial Covariance Bid/Ask Spread Estimator

Exact small sample population moments of the standard serial covariance and variance estimators are derived under the assumptions of the Roll bid/ask spread model. Noise explains why serial covariance estimates are often positive in annual samples of daily and weekly returns. Small sample estimator bias partially explains why weekly estimates are more negative than daily estimates. Noise causes the Roll spread estimator to be severely biased by Jensen's inequality. The French-Roll adjusted variance estimator is unbiased but noisy. Empirical tests confirm the major implications.     

A MODIFIED METHOD FOR INFERRING THE EFFECTIVE BID-ASK SPREAD FROM SECURITY RETURNS

This paper presents a modified method for inferring the effective bid-ask spread from security returns in an eMicient market. The Modified Method removes from security returns the systematic effect of market movements and makes use of the equivalence properties of the moving average process and serial covariance function. The Modified Method is tested with the CRSP daily, weekly, and monthly returns data. The results show that the spread estimates are non-negative and sample time-interval independent. The results are compared with those of Roll (1984) and Amihud and Mendelson (1986).     

PERFORMANCE OF STOLL's SPREAD COMPONENT ESTIMATOR: EVIDENCE FROM SIMULATIONS,TIME-SERIES,AND CROSS-SECTIONAL DATA

Stoll (1989) introduces an intuitive procedure to estimate the basic components of the bid-ask spread (order-processing cost, inventory cost, and adverse-selection cost). He also provides reasonable estimates of the magnitudes of the order-processing, inventory, and adverse-selection costs of making markets for a large cross-section of NASDAQ/NMS stocks. Empirical applications of Stoll's model produce widely different estimates of the bid-ask spread components. We derive the sampling properties of Stoll's estimator of the realized bid-ask spread, i.e., the sum of the order-processing and inventory components. We test Stoll's model in simulations, using the ideal conditions implied by the model. We conclude that noise in serial covariance estimates causes estimates of the realized spread to be severely biased and highly unreliable in short time-series and small cross-sectional samples.     

Estimating the bid-ask spread in a heteroskedastic market: The case of foreign currency futures

Because the bid-ask spread often defies direct measurement, a serial covariance-based approach is frequently used to estimate it. We develop a new serial covariance estimator that exploits the relation of time-varying volatility to trading activity to obtain more precise estimates. The performance of Roll's (1984) estimator and the new estimator are compared using intraday data for four foreign currency futures. The new estimator finds currency futures spreads to be of economic significance—usually two to three ticks, or $25.00 to $37.50 per contract. A distinct maturity effect is present, with the lowest spreads occurring one to three months from expiration. While no evidence is found that the intraday spread changes near closing, the spread is larger near opening for some contracts four to six months from expiration.The University of Texas at Austin. We appreciate the comments of Katherine Daigle, Scott Irwin, Dan Quan, Barry Schachter, workshop participants at the University of Houston, and three anonymous referees. Part of this work was completed while Laux was visiting the Commodity Futures Trading Commission, and the support of the Commission is appreciated.     

Bid,ask and transaction prices in a specialist market with heterogeneously informed traders

The presence of traders with superior information leads to a positive bid-ask spread even when the specialist is risk-neutral and makes zero expected profits. The resulting transaction prices convey information, and the expectation of the average spread squared times volume is bounded by a number that is independent of insider activity. The serial correlation of transaction price differences is a function of the proportion of the spread due to adverse selection. A bid-ask spread implies a divergence between observed returns and realizable returns. Observed returns are approximately realizable returns plus what the uninformed anticipate losing to the insiders.     

AN IMPLICIT MEASURE OF THE EFFECTIVE BID-ASK SPREAD: A NOTE

We extend Roll's study of the effective bid-ask spread in an efficient market environment by allowing for serially correlated order arrival and quote behavior. This extension results in a more general effective bid-ask spread measure, which precludes imaginary spreads and includes Roll's measure as a special case when the serial correlation is zero. This new measure is related to the length of the measurement interval due to the serial correlation, and thus has the potential to explain the previously observed differential between weekly and daily derived spreads.     

Measurement effects and the variance of returns after stock splits and stock dividends

This article examines the relation between two factors affectingstock returns, the bid-ask spread and price discreteness, andthe increase in return variance after ex-dates of stock splitsand stock dividends. Controlling for these effects, the varianceof daily returns still increases significantly. The varianceof weekly returns also increases significantly, and the varianceof returns for a control sample of nonsplitting firms showsno significant increase. Variance ratio tests show that bid-askerrors are small for these stocks and therefore cannot explainthe large increase in variance. Spreads and price discretenessdo not explain increased variance after stock distributions.     

EMPIRICAL EVIDENCE ON THE IMPACT OF THE BID-ASK SPREAD ON THE CHARACTERISTICS OF CRSP DAILY RETURNS

It is widely recognized that Center for Research in Security Prices (CRSP) returns may differ from “true” returns because of the bid-ask effect. Using a large sample of New York Stock Exchange and American Stock Exchange securities, I confirm a discernible bid-ask effect, the magnitude and importance of which decrease with the security's price level (increase with the spread). I find volatility estimates using CRSP returns to be greater than those based on quote returns. However, market model properties, such as β and R², are generally unaffected. Bid-ask effects are clearly apparent in event studies, but because of certain offsetting effects commonly used test statistics remain unaffected. Low-priced stocks (below $2.00) do not conform to these patterns. Finally, the evidence raises the possibility that the existing literature on filter rule tests may underestimate the bid-ask spread component of transaction costs.     

Short-run Returns around the Trades of Corporate Insiders on the London Stock Exchange

Previous work examined the long-run profitability of strategies mimicking the trades company directors in the shares of their own company, as a way of testing for market efficiency. The current paper examines patterns in abnormal returns in the days around these trades on the London Stock Exchange.
We find movements in returns that are consistent with directors engaging in short-term market timing. We also report that some types of trades have superior predictive content over future returns. In particular, medium-sized trades are more informative for short-term returns than large ones, consistent with Barclay and Warner's (1993) 'stealth trading' hypothesis whereby informed traders avoid trading in blocks.
Another contribution of this study is to properly adjust the abnormal return estimates for microstructure (spread) transactions costs using daily bid-ask spread data. On a net basis, we find that abnormal returns all but disappear.     

Volatility increases Subsequent to NYSE and AMEX Stock Splits

The post-split increase in daily returns volatility is less for AMEX stocks than for NYSE stocks. The exchange trading location is a significant factor in explaining the volatility shift even after stock price and firm size are considered. Furthermore, when measured on a weekly basis, there is no increase in AMEX stocks' returns volatility. These results suggest that measurement errors created by bid-ask spreads and the 1/8 effect, and also one or more of the elements that make the NYSE different from the AMEX, explain why the estimated volatility of daily stock returns increases after the ex split date.     

WINNERS AND LOSERS ON NYSE: A RE-EXAMINATION USING DAILY CLOSING BID-ASK SPREADS

We study a sample of NYSE stocks that experienced a large one-day price change during 1992 and were reported as daily largest percentage gainers and largest percentage losers in the Wall Street Journal. The sample indicates significant reversals during the immediate post-announcement period. We test for market efficiency by using bid-ask spreads obtained from the transactions data for the days immediately after the announcement. The overall results indicate that the returns during the reversal period are less than the average bid-ask spread during the same time. We also find that major losers, firms with ?20 percent to ?50 percent event-date abnormal returns, experience price reversals generating returns that are significantly greater than the average bid-ask spread during that period. We interpret this result as consistent with the overreaction hypothesis. A test of a trading rule to exploit this overreaction is not profitable, providing support for weak-form market efficiency.     

Forecasting volatility of the U.S. oil market

We examine the information content of the CBOE Crude Oil Volatility Index (OVX) when forecasting realized volatility in the WTI futures market. Additionally, we study whether other market variables, such as volume, open interest, daily returns, bid-ask spread and the slope of the futures curve, contain predictive power beyond what is embedded in the implied volatility. In out-of-sample forecasting we find that econometric models based on realized volatility can be improved by including implied volatility and other variables. Our results show that including implied volatility significantly improves daily and weekly volatility forecasts; however, including other market variables significantly improves daily, weekly and monthly volatility forecasts.     

Estimating daily volatility in financial markets utilizing intraday data

This study proposes a new approach to the estimation of daily realised volatility in financial markets from intraday data. Initially, an examination of intraday returns on S&P 500 Index Futures reveals that returns can be characterised by heteroscedasticity and time-varying autocorrelation. After reviewing a number of daily realised volatility estimators cited in the literature, it is concluded that these estimators are based upon a number of restrictive assumptions in regard to the data generating process for intraday returns. We use a weak set of assumptions about the data generating process for intraday returns, including transaction returns, given in den Haan and Levin [den Haan, W.J., Levin, A., 1996. Inferences from parametric and non-parametric covariance matrix estimation procedures, Working paper, NBER, 195.], which allows for heteroscedasticity and time-varying autocorrelation in intraday returns. These assumptions allow the VARHAC estimator to be employed in the estimation of daily realised volatility. An empirical analysis of the VARHAC daily volatility estimator employing intraday transaction returns concludes that this estimator performs well in comparison to other estimators cited in the literature.     

Intraday Return Volatility Process: Evidence from NASDAQ Stocks

This paper presents a comprehensive analysis of the distributional and time-series properties of intraday returns. The purpose is to determine whether a GARCH model that allows for time varying variance in a process can adequately represent intraday return volatility. Our primary data set consists of 5-minute returns, trading volumes, and bid-ask spreads during the period January 1, 1999 through March 31, 1999, for a subset of thirty stocks from the NASDAQ 100 Index. Our results indicate that the GARCH(1,1) model best describes the volatility of intraday returns. Current volatility can be explained by past volatility that tends to persist over time. These results are consistent with those of Akgiray (1989) who estimates volatility using the various ARCH and GARCH specifications and finds the GARCH(1,1) model performs the best. We add volume as an additional explanatory variable in the GARCH model to examine if volume can capture the GARCH effects. Consistent with results of Najand and Yung (1991) and Foster (1995) and contrary to those of Lamoureux and Lastrapes (1990), our results show that the persistence in volatility remains in intraday return series even after volume is included in the model as an explanatory variable. We then substitute bid-ask spread for volume in the conditional volatility equation to examine if the latter can capture the GARCH effects. The results show that the GARCH effects remain strongly significant for many of the securities after the introduction of bid-ask spread. Consistent with results of Antoniou, Homes and Priestley (1998), intraday returns also exhibit significant asymmetric responses of volatility to flow of information into the market.     

Effects of the volatility smile on exchange settlement practices: The Hong Kong case

The well-documented volatility smile phenomenon in the US options market has affected the option settlement practices of other markets. To settle Hang Seng Index (HSI) options, the Hong Kong Stock Exchange artificially builds in a piecewise linear “smile” or “sneer” volatility function, which is determined daily by market makers rather than directly by market forces. In this study, we investigate the time-varying settlement function and find the following economic determinants of the volatility function: lag parameters, current-day HSI returns, the distribution of HSI returns, transaction costs as proxied by the bid-ask spread, and the “Monday effect”. For evaluation purposes, we use as a benchmark the estimated piecewise linear volatility function as directly driven by market forces. The comparison analyses show that base volatilities set by market makers run somewhat high, while downside slopes are not steep enough. This results in the overpricing of the lion’s share of traded options. An economic determinants analysis of market-force-driven parameters reveals that market makers can better align artificial volatility parameters both by reducing reliance on the function parameters of prior days and by more precisely accounting for current-day HSI returns, option time-to-maturity, bid-ask spreads and buying pressure.     

Inferring the Components of the Bid-Ask Spread: Theory and Empirical Tests

The relation between the square of the quoted bid-ask spread and two serial covariances—the serial covariance of transaction returns and the serial covariance of quoted returns—is modeled as a function of the probability of a price reversal, π, and the magnitude of a price change, ?, where ? is stated as a fraction of the quoted spread. Different models of the spread are contrasted in terms of the parameters, π and ?. Using data on the transaction prices and price quotations for NASDAQ/NMS stocks, π and ? are estimated and the relative importance of the components of the quoted spread—adverse information costs, order processing costs, and inventory holding costs—is determined.     

TRANSACTION COSTS AND DAY-OF-THE-WEEK EFFECTS IN THE OTC/NASDAQ EQUITY MARKET

A potential explanation is examined here for the observed day-of-the-week effect in equity returns—systematic daily patterns in percentage bid-ask spreads. Using OTC/NASDAQ data over 1973–1985, strong return day-of-the-week effects are documented while mean dealer percentage spreads are essentially unchanged over the week. These results provide evidence that systematic percentage spread changes do not contribute to the observed return anomaly.     

FX spreads and dealer competition across the 24-hour trading day

This study examines the impact of competition on bid-ask spreadsin the spot foreign exchange market. We measure competitionprimarily by the number of dealers active in the market andfind that bid-ask spreads decrease with an increase in competition,even after controlling for the effects of volatility. The expectedlevel of competition is time varying, highly predictable, anddisplays a strong seasonal component that in part is inducedby geographic concentration of business activity over the 24-hourtrading day. Our estimates show that the expected addition ofone more competing dealer lowers the average quoted spread by1.7%     

Trading Mechanisms and Stock Returns: An Empirical Investigation

This paper examines the effects of the mechanism by which securities are traded on their price behavior. We compare the behavior of open-to-open and close-to-close returns on NYSE stocks, given the differences in execution methods applied in the opening and closing transactions. Opening returns are found to exhibit greater dispersion, greater deviations from normality and a more negative and significant autocorrelation pattern than closing returns. We study the effects of the bid-ask spread and the price-adjustment process on the estimated return variances and covariances and discuss the associated biases. We conclude that the trading mechanism has a significant effect on stock price behavior.     

Trading Behavior and the Unbiasedness of the Market Reaction to Dividend Announcements

This article examines the price formation process during dividend announcement day, using daily closing prices and transactions data. We find that the unconditional positive excess returns, first documented by Kalay and Loewenstein (1985) , are higher for small-firm and low-priced stocks. Price volatility and trading volume also increase during this period. Examination of trade prices relative to the bid-ask spread and volume of trades at bid and asked prices shows that the excess returns cannot be attributed to measurement errors or to spillover effects of tax-related ex-day trading. Rather, the price behavior is related to the absorption of dividend information.