Clustering in US Stock Prices after Decimalisation

Early in 2001, US equity markets transitioned from trading in discrete price fractions to a smoother decimal format with a tick size of one penny. Theory suggests in an unconstrained world, stock prices should be distributed uniformly, particularly if the cost of defeating time priority is low. This regime change provides a natural experiment to test whether investors prefer to trade at particular price points even when their choices are essentially unconstrained by regulation. Instead of uniformity, we find widespread evidence of price clustering at increments of five and ten cents (nickels and dimes); the overall magnitude of clustering is double in scale of what is otherwise expected. Previous studies which documented clustering around even‐eighths argued that these patterns were a rational market response to trading impediments. We report consistent findings, but also find that the overall level of post‐decimalisation clustering is far more extensive than is reasonably explained by prior hypotheses. The evidence instead suggests a more fundamental human bias for prominent numbers as discussed in the psychology literature. Contrary to previous studies, we find no difference in price clustering, ceteris paribus, between the Nasdaq and NYSE after decimalisation. Should regulators choose to revisit the notion of tick size, our evidence suggests that for many stocks there would be only minor impact between the transaction prices that prevail now and those that would occur if the tick size were increased to five cents.     

Stealth trading: The case of the Tokyo Stock Exchange

The stealth trading hypothesis asserts that informed traders trade strategically by breaking up their orders so as to more easily hide among the liquidity traders. Using data for the Tokyo Stock Exchange (TSE), a pure order-driven market, we find evidence that price changes are driven by small- and medium-size trades, with small trades making the greatest contribution to price change relative to their contribution to trading volume. We also find that large trades explain a greater portion of the cumulative price change on high volatility days. Hence, our results support the stealth trading hypothesis for the TSE.     

A market-clearing role for inefficiency on a limit order book

Limit order markets with stationary dynamics attract equal volumes of market orders and uncanceled limit orders, equalizing the supply and demand for liquidity and immediacy. To maintain this balance, market orders must share any benefit obtained by limit order traders from more efficient trading conditions, such as better order queuing policies. Therefore an efficient market places a low price on immediacy, producing small bid–ask spreads. Furthermore, when price-discreteness leads to a mainly constant spread, cutting the price tick raises surplus. This is modeled with a stochastic sequential game, using stationarity considerations to bypass direct analysis of traders’ intricate market forecasts.     

The Effect of Tick Size on Price Clustering and Trading Volume

Proposals have been made for some stock exchanges to reduce the size of their trading tick in order to lower transactions costs and, as a result, attract more trading volume and firm listings. We investigate the impact of tick size on price clustering and trading volume when the minimum price change varies with price level. Controlling the firm specific variables, we find that a smaller trading tick tends to exacerbate price clustering. Furthermore, a reduction in tick size is more likely to increase trading volume if the shares are heavily traded. These results suggest that previous studies on other stock markets may have overstated the benefits of a smaller trading tick to traders.     

An evolutionary multi‐objective optimization of trading rules in call markets

We evaluate an agent‐based model featuring near‐zero‐intelligence traders operating in a call market with a wide range of trading rules governing the determination of prices and which orders are executed, as well as a range of parameters regarding market intervention by market makers and the presence of informed traders. We optimize these trading rules using a multi‐objective population‐based incremental learning algorithm seeking to maximize the trading volume and minimize the bid–ask spread. Our results suggest that markets should choose a small tick size if concerns about the bid–ask spread are dominating and a large tick size if maximizing trading volume is the main aim. We also find that unless concerns about trading volume dominate, time priority is the optimal priority rule. Copyright © 2011 John Wiley & Sons, Ltd.     

The Impact of Pennies on the Market Quality of the Toronto Stock Exchange

Using detailed order flow data from the Toronto Stock Exchange, this paper finds no evidence that a smaller tick size lessens market liquidity for either small or large traders. Rather, there is evidence of lower trading costs, faster time to order execution, and greater price continuity. Consistent with a penny tick allowing a finer pricing grid search, there is an increase in the number of Change Former Orders and cancellations.     

Liquidity distribution in the limit order book on the stock exchange of Thailand

The liquidity distribution, or the shape of the limit order book, influences trading behavior and choice of order submission by public liquidity suppliers. The present study seeks to discover whether liquidity providers are concerned about being picked off by informed traders, and whether they are less willing to supply liquidity at the market or demand higher price spreads. The results show that liquidity at the market is a small portion of total liquidity, and that firm size, minimum tick size, volatility, and trading volume play significant roles in determining the liquidity distribution within an order book.     

Locals, foreigners, and multi-market trading of equities: Intraday evidence from Thailand

We study stock market orders and trades in a developing country, Thailand, where foreign ownership limits partially segment local and foreign investors into two distinct markets. Some foreigners forgo voting rights and distributions to trade on the “local board”, while some locals forgo such benefits and pay a price premium to trade on the “foreign board”. Regardless of nationality, these cross-market traders typically submit orders when liquidity is high, fill orders at relatively beneficial prices, exploit patterns in stock prices across markets, display profitable holding-period returns, and enhance price discovery. This suggests that skilled, informed trading that affects market quality does not depend on trader nationality.     

Evidence of oil market price clustering during the COVID-19 pandemic

We use hourly data on opening price, closing price, opening ask price, opening bid price, closing ask price and closing bid price to show that while oil prices are characterized by price clustering behavior, prices tend to cluster on numbers closer to zero than to one. Comparing the pre-COVID-19 sample with the COVID-19 sample, we find that evidence of price clustering is 8% more in the COVID-19 sample. We test the determinants of price clustering and find that as much as 30% of the price clustering behavior can be attributed to the COVID-19 pandemic. Finally, using a simple technical trading strategy, we do not find any evidence that the oil market is profitable in the COVID-19 period.     

Undisclosed orders and optimal submission strategies in a limit order market

Reserve orders enable traders to hide a portion of their orders and now appear in most electronic limit order markets. This paper outlines a theory to determine an optimal submission strategy in a limit order book, in which traders choose among limit, market, and reserve orders and simultaneously set price, quantity, and exposure. We show that reserve orders help traders compete for the provision of liquidity and reduce the friction generated by exposure costs. Therefore, total gains from trade increase. Large traders always benefit from reserve orders, whereas small traders benefit only when the tick size is large.     

Trader see,trader do: How do (small) FX traders react to large counterparties’ trades?

We show that information about the counterparty of a trade affects the future trading decisions of individual traders. The effect is such that traders tend to reverse their order flow in line with the better-informed counterparties. Informed traders primarily incorporate their own private as well as publicly available information into prices, whereas uninformed traders mainly magnify the effect of the informed. This pattern of interaction among traders extends to different order types: traders treat their own and others’ market orders as more informative than limit orders.     

Price clustering on the limit-order book: Evidence from the Stock Exchange of Hong Kong

We examine the clustering pattern in trade and quote prices on the electronic limit order book of the Stock Exchange of Hong Kong (SEHK). Earlier research into clustering focuses on transaction prices only. We study clustering on quote prices over a maximum of five queues on the limit order book. We observe an abnormally high frequency of even and integer prices in trade and quote prices for all tick size groups on the SEHK. The deeper quotes display stronger clustering than the best quotes, indicating that the farther away the quotes are from the best queue, the less information they carry. Our analysis further reveals that an extremely fine tick size itself works as a binding constraint to hinder the price resolution process. We also find that short sale prohibition imposed on the majority of stocks listed on the SEHK causes a significant bias in clustering towards the ask side of the limit order book. This implies that a short sale prohibition impairs efficient price discovery in the market.     

Trade size clustering and the cost of trading at the London Stock Exchange

For the London Stock Exchange, this paper investigates differences in trading costs between market maker (off-book) and order book trades, in the context of clustering in trade sizes and prices. We report several substantial findings. Even after controlling for differences in trade size, the realised spread measure is lower for off-book trades. For the order book, trade size clustering is not associated with differences in transaction costs nor with differences in the information content of trades. For the off-book market, trades in clustered (popular) sizes carry significantly more information than non-clustered trades. Despite the significant differences in the price impact estimates between the order book and off-book, we show that traders placing large orders off-book are still better off than trading via the order book as they benefit from a large discount from the current midpoint price. Additionally, we highlight that price and size clustering tend to occur simultaneously rather than being substitutes in this market setting.     

LIQUIDITY AND QUOTE CLUSTERING IN A MARKET WITH MULTIPLE TICK SIZES

We analyze market liquidity (i.e., spreads and depths) and quote clustering using data from the Kuala Lumpur Stock Exchange (KLSE), where the tick size increases with share price in a stepwise fashion. We find that stocks that are subject to larger mandatory tick sizes have wider spreads and less quote clustering. We also find that liquidity providers on the KLSE do not always quote larger depths for stocks with larger tick sizes. Overall, our results suggest that larger tick sizes for higher priced stocks are detrimental to market liquidity, although the adverse effect of larger tick sizes is mitigated by lower negotiation costs (i.e., less quote clustering).     

INFORMATION AND NOISE IN FINANCIAL MARKETS: EVIDENCE FROM THE E‐MINI INDEX FUTURES

I examine the informational contributions and effects on transitory volatility of trades initiated by different types of traders in three actively traded index futures markets. The results show that trades initiated by exchange member firms account for more than 60% of price discovery during the trading day. These institutional trades appear to be more informative than trades of individual exchange members or off‐exchange traders. I also find that off‐exchange traders introduce more noise into the prices than do exchange members. My findings provide new evidence on the role of different types of traders in the price formation process.     

SLIPPAGE AND THE CHOICE OF MARKET OR LIMIT ORDERS IN FUTURES TRADING

Retail futures traders face uncertainty regarding the price they will obtain when trading. This price "surprise," known as slippage, can be substantial. Using unique data from an introducing brokerage for Chicago Board of Trade (CBOT) wheat, corn, and soybean futures contracts, we quantify time-to-clear and the magnitude of slippage. We then identify factors that affect these trade quality measures. Finally, we analyze individual trader choice between market and limit orders and find that the likelihood of placing limit orders, where regulations protect traders from slippage, is greater when order and market characteristic indicate that adverse slippage is likely.     

The Relationship Among Market-Making Revenue, Payment for Order Flow, and Trading Costs for Market Orders

We study the division of market-making revenue among dealer, broker, and trader. When Knight Securities, a major Nasdaq dealer, interacts with market orders in actively traded stocks during the fourth quarter of 1996, we estimate that its revenue is $0.057 per share. Knight pays brokers at least $0.025 per share (44% of revenue) for orders. To examine whether brokers appear to share these payments with traders, we compare net trading costs (trade price net of commissions) for traders using brokers routing Knight orders with estimated net trading costs for traders using the only discount broker we can determine did not directly receive market-making revenue. We find that the net trading cost of the broker refusing order-flow payments does not dominate the net trading cost of all brokers selling order flow to Knight. This finding suggests that order-flow payments do not unambiguously harm traders and challenges the conclusions of extant studies using only trade prices to assess market quality.     

Trading Mechanisms in Securities Markets

This paper analyzes price formation under two trading mechanisms: a continuous quote-driven system where dealers post prices before order submission and an order-driven system where traders submit orders before prices are determined. The order-driven system operates either as a continuous auction, with immediate order execution, or as a periodic auction, where orders are stored for simultaneous execution. With free entry into market making, the continuous systems are equivalent. While a periodic auction offers greater price efficiency and can function where continuous mechanisms fail, traders must sacrifice continuity and bear higher information costs.     

Order Flow and Liquidity around NYSE Trading Halts

We study order flow and liquidity around NYSE trading halts. We find that market and limit order submissions and cancellations increase significantly during trading halts, that a large proportion of the limit order book at the reopen is composed of orders submitted during the halt, and that the market-clearing price at the reopen is a good predictor of future prices. Depth near the quotes is unusually low around trading halts, though specialists and/or floor traders appear to provide additional liquidity at these times. Finally, specialists appear to 'spread the quote' prior to imbalance halts to convey information to market participants.     

Locals,foreigners, and multi-market trading of equities: Intraday evidence from Thailand

We study stock market orders and trades in a developing country, Thailand, where foreign ownership limits partially segment local and foreign investors into two distinct markets. Some foreigners forgo voting rights and distributions to trade on the “local board”, while some locals forgo such benefits and pay a price premium to trade on the “foreign board”. Regardless of nationality, these cross-market traders typically submit orders when liquidity is high, fill orders at relatively beneficial prices, exploit patterns in stock prices across markets, display profitable holding-period returns, and enhance price discovery. This suggests that skilled, informed trading that affects market quality does not depend on trader nationality.