Decimalization of the U.S. stock exchanges has incurred a large number of contemporaneous researches during the past decades. Harris (1994) uses data from a time when the minimum tick size is eighths and estimates the frequency of spreads at the minimum by fitting a regression model. Using this relationship, Harris estimates that the impact of reducing the minimum tick size to sixteenths would be accompanied by both lower bid-ask spreads and lower quoted depth. His results are therefore also consistent with the notion that optimal tick size is related to the size of a
1 Specifically, the NYSE lowered the minimum tick size to a penny for seven securities on August 28, 2000, 57 more securities on September 25, 2000, and an additional 94 securities on December 5, 2000.
All remaining securities began trading in decimals on January 29, 2001.
trade. He indicates that small traders would almost certainly benefit from smaller tick sizes, but that large traders might be hurt if the depth of the market falls sufficiently.
Unlike Harris (1994), Chakravarty, Panchapagesan, and Wood (2003) examine the effect of decimalization on institutional investors by using proprietary data.
They find no evidence that decimalization increases trading costs for institutions. In fact, institutional trading costs appear to decline by about 23 basis points (or, roughly 5 cents per share) after decimalization. In economic terms, this decrease roughly translates to an average monthly saving of $133 million in institutional trading costs.
Estimations involving robust multivariate techniques that condition on order, manager and market characteristics yield roughly similar reductions as well. They find significant changes in order routing practices overall because of increase usage of alternate brokers (represented by ECNs and crossing networks such as Instinet) for easy-to-fill (i.e., smaller) orders and independent research brokers for orders that are difficult to fill (i.e., larger size orders).
Goldstein and Kavajecz (2000) analyze the NYSE’s reduction in tick size from eighths to sixteenths and address the relationship between minimum tick size, bid-ask spread, and market liquidity. What is unique about this study is that these authors not only look at the depth reported at the best bid and ask prices, they also collect data on liquidity available at some distance away from the best bid and ask prices. This complete collection of prices and available depth is called the limit order book.
They find that not only depth at the best bid and ask declines, but also cumulative depth similarly declines throughout the limit order book after the reduction in minimum tick size on the New York Stock Exchange (NYSE). Using implied average price of a trade derived from the limit order book, these authors find that
large traders are not better off under the smaller tick sizes and are worse off for infrequently traded stock.
Chakravarty, Van Ness and Van Ness (2005) examine adverse selection costs around decimalization and relationship between adverse selection costs and trade size by using a sample of NYSE stocks around the implementation of decimalization.
They find a significant reduction in adverse selection costs after decimalization on the NYSE. This decline in adverse selection costs occurs for all stocks except the very small stocks. They further try to understand the source of this decrease in adverse selection costs. They find that both the number of trades and trading volume in medium and large trade size fall significantly after decimalization on the NYSE while those in small trade size increases significantly. On estimating the adverse selection component by trade size classes, they find a decline in adverse selection costs in trades of all sizes, with the strongest evidence coming from medium size trades, followed by small and large size trades. One implication of their findings is that there appears to be less stealth trading following complete decimalization and less institutional trading overall.
Furfine (2003) examine the impact of decimalization on the liquidity of NYSE stocks. Analyzing transaction data for a sample of 1,339 stocks listed on the NYSE over a five-week period. He find that decimalization lead to a narrowing of average bid-ask spreads. The largest declines in spreads are found for the most actively traded stocks, where the average decline in spread was over 35 percent. The decline in depth is also most pronounced for the most actively traded stocks. Because previous findings suggest that decimalization has an ambiguous impact on market liquidity using spreads and depth as proxies for liquidity, Furfine estimates the price impact of a trade for each stock in his sample and then find that actively traded stocks generally experience an increase in liquidity after decimalization.
Bessembinder (2003) assesses trade execution costs and market quality for NYSE and NASDAQ stocks before and after the change to decimal pricing in 2001.
Quoted bid-ask spreads declined substantially on each market, with the largest declines for heavily traded stocks. The percentage of shares receiving price improvement increases on the NYSE, but not on NASDAQ. However, those trades completed at prices within or outside the quotes are improved or disimproved by smaller amounts after decimalization, and trades completed outside the quotes reveal the largest reduction in trade execution costs. Effective bid-ask spread as a percentage of share price which is the measure of execution costs for smaller trades is averaged 0.33% on a volume-weighted basis after decimalization for both NYSE and NASDAQ stocks.
Bollen and Busse (2003) measure changes in trading costs of equity mutual fund for two changes in tick size on NASDAQ and NYSE: the switch from eighths to sixteenths and the switch from sixteenths to decimals. They estimate trading costs by comparing a mutual fund’s daily returns with the daily returns of a synthetic benchmark portfolio that matches the fund’s holdings but has zero trading costs by construction. They find that index fund performance is unaffected by the switch to pennies. In contrast, actively managed funds underperform their benchmark by an additional one percent of fund assets per year after decimalization.
Chakravarty, Wood, and Van Ness (2004) find that both quoted and effective bid-ask spreads and depths decline significantly after decimalization on the NYSE.
Both trades and trading volume significantly decline in all trade size and stock size categories. Stock return volatility reveals an initial increase but a latter decline during the longer period, probably when traders become more comfortable under their new regime.
Henker and Martens (2005) find that market efficiency increases and the arbitrage link between index futures and the stock market strengthens after the reduction of minimum change for stock prices and quotes from an eighth to sixteenth on Jane 24, 1997. They find a substantial increase in the number of arbitrage trades reported to the Securities and Exchange Commission after the change. The average number of stocks traded and the average dollar amount underlying each arbitrage trade increases and decreases respectively. The average mispricing error that triggers arbitrage reduces and reverts to zero more quickly.
3.2 Non-linear Adjustment Mechanisms
In the recent time-series literature, the examination of non-linear adjustment
mechanisms has attracted a growing numbers of research. The ideal of threshold cointegration is introduced by Balke and Fomby (1997). Deviations may exhibit unit root behavior within the transactions cost band because no adjustment takes place.The process for deviations is mean-reverting out side the band because adjustment takes place. This phenomenon is referred to as a threshold cointegration. Stoll and Whaley (1986) and MacKinlay and Ramaswamy (1988) discuss the impact of transaction costs on index-futures arbitrage strategy, starting with the forward-contract pricing relation. The impact of transaction costs is to permit the futures price to fluctuate within a band around the formula value. The width of the band derives from round-trip commissions in the stock and futures markets and the market impact costs of putting on the trade initially.
Many empirical studies find evidence on the presence of nonlinear equilibrium relations on cost-of-carry model. For example, Martens, Kofman and Vorst (1998) use a threshold autoregressive model and a threshold VECM to explore the existence of different arbitrage regimes. First, they investigate the location of possible
thresholds indicating a change in the pattern of mispricing error and possibly also in the relations between the index and futures returns and the error-correction term.
They show that indeed different regimes exist for the S&P500 and that in fact the US markets respond to arbitrage opportunities in just a few minutes. Second, they estimate an error-correction model in each regime. By estimating transaction costs they also indicate which thresholds could indicate the band around the theoretical futures price in which arbitrage is not profitable. Dwyer, Locke, and Yu (1996) indicate that the thresholds are signals for index arbitrage, which can affect the speed of convergence of the basis to its equilibrium value. Further, their results indicate that nonlinear dynamics are important and are related to S&P500 index-futures arbitrage, and suggest that arbitrage is associated with more rapid convergence of the basis to the cost of carry than would be indicated by a linear model.
Other studies concerning economic behaviors affected by asymmetric transaction costs and institutional rigidities reveal that many economic variables and relations display asymmetry and nonlinear adjustment. Michael, Nobay, and Peel (1997) find a nonlinear adjustment process toward purchasing power parity (PPP).
Hansen and Seo (2002) and Enders and Siklos (2001) applies nonlinear models to the term structure model of interest rates and finds strong evidence for the asymmetric mature of error correction among interest rates of different maturities. Chung, Ho, and Wei (2005) follow the Hansen and Seo’s (2002) model to develop a multivariate threshold VECM. The model is employed to estimate the threshold parameters, to construct asymptotic confidence intervals for the threshold parameters, and to develop new tests for the threshold effects of ADRs and their underlying stocks prices. Their study provides strong evidence to show that threshold effect does exist in the prices of ADRs and their underlying stocks.