The Effects of Decimalization on the Components of Bid–Ask Spreads: Evidence from ETFs on the AMEX
Chang-Wen Duan*
Assistant Professor, Department of Banking and Finance, Tamkang University
Jung-Chu Lin
Associate Professor, Department of Banking and Finance, Takming University of Science and Technology
Abstract
This paper modifies the traditional approach to evaluating bid–ask spread. We use equal-weighted and volume-weighted average spread as proxies for bid–ask spread and model some spread components using options concepts. We are about to observe the effects of decimalization of AMEX on bid–ask spreads and their components of the two kinds of exchange-traded fund (ETF) products: DIA and QQQ. While the literature holds that the bid–ask spreads of ETF products, which possess advantages of diversification and lower risks, are smaller than those of individual stocks, the work presented here finds that the bid–ask spreads of ETFs declined significantly after decimalization. The magnitude of this decline is greater for the QQQ, which, with its higher trading volume, implies that higher trading volume has the effect of significantly reducing the spread.
After decimalization, the trading volumes of both ETFs increased and hence order processing costs declined, and inventory holding costs evaluated by option pricing theory declined, but adverse selection costs increased. On the other hand, the impact of order processing costs on spreads increased while the influence of inventory holding costs and adverse selection costs decreased, revealing that decimalization could reduce the effects of inventory holding costs and adverse selection costs on spreads, but augment the quantity of adverse selection costs in the spread components.
Keywords: Bid–Ask Spreads, Order Processing Costs, Inventory Holding Costs, Adverse Selection Costs, Exchange-Traded Funds (ETFs)
* We acknowledge the financial support from National Science Council of R.O.C. (Grant No: NSC 94- 2416-H-032-017). Please address all correspondence to Chang-Wen Duan, Department of Banking and Finance, Taipei Campus, Tamkang University, No. 5, Lane 199, Kinghua St., Taipei 106, Taiwan. Tel:
+886-939-117211; Fax: +886-2-2395-9040. Email: 107800@mail.tku.edu.tw.
Introduction
In a quote-driven market, market makers often play an important role in maintaining market equilibrium. For example, dealers and specialists are the major market makers grooming the market. Through quoting, they long positions where investors intend to short them and short positions where investors intend to take long positions, thus creating a market. The bid–ask spread is a kind of profit for market makers, providing liquidity and compensating for internal costs incurred in making the market. Demsetz (1968) characterized the bid–ask spread as compensation for order processing costs1 as market makers provided stable order transactions to satisfy investor trading needs. The bid–ask spread, then, constituted the compensation investors paid to the market maker, and order processing costs were regarded as justification for the existence of the bid–ask spread.
Stoll (1978b) decomposed bid–ask spread costs generated by the quotes of market makers during a transaction into order processing costs, inventory holding costs, and adverse selection costs. Tinic (1972) further took the market maker’s market competition factor in the market into consideration while studying bid–ask spread components.
As the tick sizes of bid–ask quotes and trading prices must be integer multiples of the minimum tick sizes defined by exchanges, the quotes will induce price discreteness. If the tick size is greater than the average movement of price, the change in stock price will be restricted by the tick size. On the contrary, if the tick size is smaller than the average movement of price, theoretically it will have no effect on the stock price. The minimum changing unit is to reveal the fixed costs the market maker incurred while making the market. In a market with no restriction in tick size, the supply and demand of market liquidity could determine the bid–
ask spread and the equilibrium bid–ask spread would thereby be determined by the market. However, a restriction in tick size will impact the equilibrium share price and lead the equilibrium bid–ask spread to be adjusted at least as much as the magnitude of the minimum tick size, if the tick size is larger than the equilibrium bid–ask spread. This will result in increased trading costs and the market competitiveness of that market maker will become impaired. Therefore, any restriction in tick size by an exchange is bound to affect the transaction costs and investment behavior of investors.
In recent years, many well-known exchanges gradually adopted measures that reduced minimum tick size. For example, the NYSE, AMEX, and NASDAQ have all reduced minimum tick size many times.
Harris (1994) discovered that, after AMEX and NYSE reduced minimum tick sizes, both the bid–ask spread and quote were simultaneously reduced
1 Such as commission fees.
and daily trading volumes increased, indicating that reducing tick size effectively increases market transaction efficiency. Hence he formulated that the minimum tick size for market transactions would affect the bid–ask spread and the spread components. Ahn, Cao, and Choe (1996), Bollen and Whaley (1998), as well as Bessembinder (2000) reached similar conclusions.
Summarizing the results of existing research and considering the effects of price discreteness induced by minimum tick size, order processing costs, inventory holding costs, adverse selection costs, and competition of market makers, Bollen, Smith and Whaley (2004) proposed a spread structure model in which the inventory holding and adverse selection cost components are modeled as an option with a stochastic time to expiration. This model was tested empirically using NASDAQ stocks to observe changes in quote spread and its components after reducing tick size three times. The results showed that after three reductions in minimum tick size, the bid–ask spread and spread components were further reduced, indicating that the exchange’s adjustments of minimum tick size do indeed influence the quote spreads of market makers.
Exchange-traded funds (ETFs) are a kind of mutual fund that is designed to track various indices but that are traded on exchanges like stocks. They have the advantages of both stocks and funds, including diversifying the investment to reduce risk, lower fund management and transaction costs, and high liquidity. But precisely because of the trading convenience that ETFs possess, their trading is more frequent. Therefore, traders tend to be more cognizant of transaction costs, particularly the bid–
ask spread.
However, past studies of bid–ask spread and spread components generally focused on individual stocks in the market. There is still no concrete empirical evidence demonstrating that these research models are applicable to ETFs. This is particularly so in that the ETF itself represents a diversified portfolio, theoretically implying that the loss from information asymmetry to the market makers will be less, hence the bid–ask spread will be smaller than those of individual stocks (Subrahmanyam, 1991; Gorton and Pennachi, 1993; Hedge and McDermott, 2004).
Secondly, since ETF quotes are usually proposed by a single market maker, whether the bid–ask spread is determined by the same factors as those determing the bid–ask spread of individual stocks deserves an empirical study on the bid-ask spread of ETFs..
Thirdly, it is evident that ETFs with larger trading volume have transaction costs that are generally lower than their individual component stocks, and the bid–ask spreads do represent the major transaction costs in the trading of ETFs. Therefore, to study the bid–ask spread and its components of ETFs is of vital empirical importance. In view of these three
considerations stated above, our study extends the spread structure model of Bollen et al. (2004) to calculate bid–ask spread using an equal–
weighted-average method and evaluates spread components using options concepts in order to observe the relationship between an ETF’s bid–ask spread and its spread components. At the same time, the effects from adjusting minimum tick size on the relationship between bid–ask spread and its components were also examined.
In summary, this paper offers three contributions to the literature:
First, while existing analysis of the influences of tick-size adjustment focuses on individual stocks, this paper examines ETF products, which are diversified portfolios,—in order to measure the influence of reducing minimum tick size on their bid–ask spreads. Next, modifying the traditional bid–ask spread evaluation method, this study adopts a weighted spread for estimation purposes. Finally, we evaluate the spread components from the viewpoint of options in order to determine whether there was any increase in market efficiency after AMEX implemented decimal pricing.
Whereas past empirical results showed that bid–ask spreads for the ETF market were smaller than those of their component stocks, in this study we found that AMEX’s adoption of decimal pricing reduced bid–ask spreads for ETFs obivously. The magnitude of reduction in bid–ask spreads, based on a QQQ sample characterized by higher trading volume, was larger, indicating that the increase in trading volume in itself further reduced the bid–ask spread. We also found that order processing and inventory holding costs declined, but that adverse selection components increased. Finally, from our structural model, it was discovered that both the influences of inventory holding and adverse selection on spreads declined if we excluded the results of the DIA’s volume-weighted effective spread (VWES) sample, and the main factor impacting on spreads was trading volume via order processing costs.
The remainder of this paper is structured as follows: Section 2 discusses the bid–ask spread and its components; Section 3 describes the data and methodology employed; Section 4 sets forth the empirical results;
and Section 5 concludes.
Spread and its Components
If an investor longs securities at the ask-price and thereafter shorts them immediately at the bid-price, he or she will realize a book loss equal to the bid–ask spread when the spread is positive. This spread represents a transaction cost. Traditionally, the bid–ask spread is measured by the quoted spread given by the market maker, and can be expressed as follows:
quoted spread ask price bid price . (1)
This spread measurement assumes that investors cannot trade within the quoted spread, and that only market makers set the prevailing quote and stand on the other side of investors to trade. More recent investigations of spread in the securities markets have focused on effective spread. The effective spread measurement assumes that, if a trade takes place above the bid–ask price midpoint, then it is a buy order, and if it takes place below the bid–ask price midpoint, it is a sell order. Thus, the absolute difference between trading price and the bid–ask price midpoint can be interpreted as the trading cost incurred by the investor, or the profit obtained by the market maker. On a round-turn trade, the effective spread (ES) can be measured as follows:
2 | |
ES trade price midpoint . (2) If all trades take place at the prevailing bid and ask quotes, the effective spread is equal to the quoted spread. If trades take place within the spread, the effective spread will be smaller than the quoted spread; and the product of one-half the effective spread times the trading volume can be viewed as the profit of the market maker. In terms of investor trading cost, though the effective spread seems a better measure than the quoted spread, it still cannot tell whether the trades are executed between investors, or between investors and the market maker. If the trade is executed between investors, the average effective spread will be zero.
Most of the existing literature focuses its examination of the determinants of the bid–ask spread on stock spreads, and empirically determines the components of spreads by observing which variable best captures cross-sectional variation in spreads. Stoll (1978b) thought that the bid–ask spread was induced by processing orders, inventory holding, and information asymmetry; for the market maker to provide liquidity, if any of these three factors increases (decreases), it will face higher (lower) costs and will then widen (narrow) the bid–ask spread. However, Tinic (1972) pointed out that competition among market participants could also have an effect on a market maker’s bid–ask spread.
Stoll (1989) investigated the spread components of NASDAQ stocks and found that the quoted spread consisted of about 47% order processing costs, 10% inventory holding costs, and 43% adverse selection costs; and the proportion of realized spread to average quoted spread was 57%. Huang and Stoll (1994) used both two-way and three-way decomposition methods to estimate the spread components; the two-way decomposition method revealed that 89% of the bid–ask spread was comprised of order processing costs, and 11% was inventory holding costs combined with adverse selection costs. Moreover, after controlling for trade clustering, the three- way decomposition method showed that 62.7% of the bid–ask spread was
comprised of order processing costs, 28.7% inventory holding costs, and 9.6% adverse selection costs. Based on these empirical results, order processing costs, inventory holding costs, and adverse selection costs are regarded as the three major spread components. Next, we describe these cost components of the market maker’s bid–ask spread and review how past researchers have measured these costs.
1. Order Processing Costs
Order processing costs are those costs directly associated with providing a trading service on the market and include such items as commission fee, taxes, floor rent fee, computer user fee, information service costs, labor costs, opportunity costs of the market maker, etc. Taking the rate of transactions, number of stockholders, and the number of stock listing exchanges as empirical factors, Demsetz (1968) found that the more actively traded the security, the lower the waiting and trading costs, resulting in a lower bid–ask spread as well. Benston and Hagerman (1974) and McInish and Wood (1992) also found that a higher transaction rate would lead to increased economy of scale so as to reduce transaction costs, which implies a negative relationship between trading frequency and bid–
ask spread.
In the short run, since order processing costs are constant, the larger the trading volume, the lower the order processing costs of each unit for the market maker. In addition, in order to attract more participants into the market, market makers will shrink their bid–ask spread and thereby promote trading liquidity.
2. Inventory holding Costs
Inventory holding costs are those costs that a market maker incurs while carrying positions acquired for the purpose of supplying investors with immediacy of exchange and liquidity of market. Inventory holding costs include the opportunity costs of holding inventory and the premium for the uncertainty of price movements. Demsetz (1968) found that spread per share tended to increase in proportion to an increase in the price per share so as to equalize the cost of transacting per dollar exchanged. This led him to view price per share as a proxy for the opportunity cost of funds. With respect to the volatility of price movements, Tinic (1972), Stoll (1978b) and Harris (1994) used similar measurements for the price risk of holding inventory.
Market makers carry inventory in the course of supplying liquidity, and hence bear the risk of price volatility. The size of the spread therefore must include compensation for bearing the risk of price volatility; through quoting, market makers may adjust the amount of inventory held so as to balance the supply and demand in the market. Garman (1976) suggested
that market makers should connect pricing decision rules to inventory conditions in order to avoid market failure. Using a dynamic model for the behavior of spread, Amihud and Mendelson (1980) pointed out that market makers actively adjust their quotes in response to inventory levels. They found that there was a negative relationship between the optimal bid/ask price and the inventory level. In other words, if inventory level increases (decreases), the quoted price will fall (rise), allowing market makers to adjust the level of inventory by changing their quotes.
Bollen et al. (2004) indicated that the market maker’s bid–ask spread must include a premium to compensate for the expected inventory holding costs. If a market maker expects that the holding period will be transient, then it would be reasonable for him to infer that this period is risk-free and that there will not be very large changes in the price of the security. If the market maker takes a long position in a share of stock as a result of accommodating an investor’s sell order, then he will incur inventory holding risk. To reduce this risk, the market maker could short underlying futures or options for hedging until the long stock position is unwound with an investor’s buy order. However, market makers would not be willing to incur a large hedging cost merely for the small return of the position they hold. Especially in the ETF market, trading costs of index futures are very high. Because of the lack of a viable hedging instrument, the market maker faces price volatility risk from inventory holding, for which he must be paid compensation, known as the inventory holding premium (IHP).
If a market maker has no inventory to accommodate a customer’s order by buying at the bid, then before buying the stock, the market maker must protect against the price falling below his purchase price by longing an at- the-money put written on this stock; conversely, he needs to protect against the price rising over his sell price by longing an at-the-money call written on this stock. So for the purpose of hedging, the premiums of calls and puts that market makers buy can be viewed as costs of holding inventory.
According to Bollen et al. (2004), Black and Scholes (1973) and Merton (1973) an options valuation framework provides an easy way to measure the IHP.
3. Adverse Selection Costs
Adverse selection costs arise from the fact that market makers, in supplying liquidity, may trade with individuals who are better informed about the expected price movements of the underlying security, causing market makers to incur losses. For an individual stock, if certain individuals possess inside information2 and thus trade it at a profit, then market makers will incur losses as a result. These losses are so called adverse selection costs arising from information asymmetry.
2 Such as advance news of earnings, restructurings, and management changes.
Bagehot (1971), Copeland and Galai (1983), and Glosten and Milgrom (1985) point out that there exist informed and uninformed traders in any securities market, in which informed traders know the true values of some stocks, and who can exactly predict their movements. Such informed traders utilize the private or public information they own in their trading.
Thus, market makers expect losses when trading with informed traders, which causes them to expand the quoted spread in order to profit from uninformed traders, compensating for the losses incurred from trading with informed traders. Therefore, the more serious the information asymmetry problem, the larger the bid–ask spread. Glosten and Milgrom (1985) indicated that adverse selection is an important determinant that affects the magnitude of the bid–ask spread.
In summary, inside information has a positive relationship with bid–
ask spread, and is highly related to the numbers of informed and liquidity traders.
The existing literature on adverse selection consistently shows that after decimalization, adverse selection costs increase. For example, Gibson, Singh, and Yerramilli (2003) found that the effects of decimalization on the behavior of informed traders were opaque, which indicated that the probability of the occurrence of adverse selection would rise after decimalization. Bollen, Smith, and Whaley (2004) also found that the degree of influence of adverse selection on spreads increased after decimalization when using options theory to estimate the spread components of dealers making markets on NASDAQ. Zhao and Chung (2006), and Chakravarty, Van Ness, and Van Ness (2005), using a sample of NYSE stocks, also found that adverse selection components increased in importance after decimalization.
However, it is difficult to measure adverse selection costs. Branch and Freed (1977) used the number of securities for which a dealer makes markets as a proxy for adverse selection; that is, the larger the number of securities managed, the less informed the dealer is, and hence higher adverse selection costs arise. Stoll (1978a) used turnover3 as his proxy and found that the higher the turnover, the greater the adverse selection costs.
Glosten and Harris (1988) used the concentration of ownership by insiders as their proxy and found that the higher such concentration, the greater the possibility of adverse selection. Harris (1994) used the market values of shares outstanding as his proxy, and found that the larger and more well known the firm, the lower the possibility of adverse selection. Easley, Kiefer, O’Hara, and Paperman (1996) investigated NYSE stocks and found that the higher the trading volume, the greater the activity of uninformed traders relative to informed traders and the lower the adverse selection costs.
3 Trading value divided by market value of capital.
Copeland and Galai (1983) pointed out that the cost components of dealer bid–ask spreads could be viewed as a “free” straddle. They modeled their approach on the concept that market makers lose from trading with informed traders on the one hand, and profit from trading with liquidity traders, who aim to complete trades immediately, on the other hand. Since informed traders possess inside information with which to trade, their main goal is profit. If the real price lies between the bid and ask prices, liquidity traders will deal, and the profit of market makers would be equal to ask price minus real price, or real price minus bid price; otherwise informed traders would deal, and the losses of market makers would be equal to real price minus ask price, or bid price minus real price, which are one kind of adverse selection cost. The payoff for market makers could be viewed as a combination of a call and a put whose exercise prices are different from each other. Copeland and Galai (1983) characterized that combination as a free straddle in which market makers are provided with a free-trading option to buy at the ask price or to sell at the bid price. The option’s life begins once a quote is hit and remains open for the expected length of time between offsetting trades. This combination is composed of an out-of-the- money call and an out-of-the-money put.
Data and Methodology
This paper extends the Bollen et al. (2004) bid–ask spread model to examine the changes in ETF bid–ask spread and its components after AMEX adjusted its minimum tick size from 1/16 to decimal pricing on January 29, 2001. In order to analyze the quoting behavior, we used high frequency intraday data obtained from NYSE’s Trade and Quote (TAQ) database. Since we used an options concept to estimate spread components, we selected those ETFs that have issued corresponding options for our sample. Thus, there are two kinds of ETFs, Diamond (DIA) and QQQ (Cube),4 in our sample.
In order to exclude anomalous data arising from the events of September 11, 2001, we set the sample period from AMEX’s decimalization implementation of January 29, 2001 to September 10, 2001, 156 trading days in all. Therefore the sample period before AMEX’s decimalization must also include 156 trading days, encompassing the period June 15, 2000 to January 28, 2001.
1. Estimation of Volatility
According to Garman and Klass (1980), while estimating volatility, if only the closing prices are taken into account, other useful information that could increase the efficiency of estimation would be overlooked. Thus, they included highest, lowest, opening, and closing prices from each
4 SPDR is not included as one kind of ETF sample in our study since there are no corresponding SPDR options traded in American options markets during our study period.
sample trading day in their estimation in order to construct a more efficient estimator as follows:
2 2 2
ˆt 0.51(Ht Lt) 0.019[OC Ht( t Lt) 2H Lt t] 0.383OCt
, (3)
where H, L and OC are the logarithms of the highest, lowest, and opening minus closing prices for each sample trading day, respectively. Since this equation was complex in estimating process, Garman and Klass (1980) removed the cross-multiplying term, which yielded a simplified equation of equal efficiency, as follows:
2 1 2 2
ˆ ( ) (2ln 2 1)
t 2 Ht Lt OCt
(4) We apply this equation to estimate volatility in this paper.
2. Bid–Ask Spread
Researchers often apply quoted spread and effective spread when estimating the bid–ask spread. According to Harris (1994), on AMEX and NYSE, empirical results could avoid being influenced by the outlier effect if the average bid–ask spread for each transaction was evaluated.
Therefore, to prevent disturbance from outliers within intraday data, we adopt the volume-weighted effective spread5 (VWES), and the equal- weighted effective spread (EWES) for each day as the spread proxy variable.
We used the ratio of the trading volume of a trade in some trading day to total volume for that trading day as the weighting factor to evaluate the VWES:
, ,
t i
t t i
i t
VWES ES q
Q , (5) where ES is the effective spread, q and Q are transaction volume of one trade and total transaction volume, respectively, for each trading day.Subscript i is the number of transactions during the trading day. We used the ratio of the average trading volume to total volume for each trading day as weighting factor to evaluate the EWES. The estimation equation is:
, ,
t i
t t i
i t
EWES ES q
Q , (6) where qt i, Qt
i.3. Spread Components (1). Order Processing Costs
Order processing costs are those costs directly related to the services provided by the market maker. Copeland and Stoll (1990) pointed out that order processing costs represent the cost of employees employed during the
5 As the occurrences of many trading are struck between the previous quote, using effective spread to evaluate the profit rate of market makers has more accurate performance. Bollen et al. (2004) also has similar view. Therefore, we all adopt effective spread as the bid–ask spread.
transaction, dealer time costs, and the costs of equipment needed to complete the transaction. Since processing costs are fixed, every unit order processing cost would be reduced with an increase in trading volume.
Therefore, the larger is the volume of transactions and the more active the trading, the larger are the opportunity costs of waiting to deal, and thus will the bid–ask spread be reduced so as to allow for the order processing cost to be reduced. In this way, it is possible to observe the size of order processing costs by looking at the trading volume. Hence, we use the inverse of trading volume (InvTV) as a proxy variable for order processing costs. When trading volume increases, the inverse of trading volume is reduced and therefore order processing costs are reduced; and vice versa.
(2). Inventory H olding Premium (IHP)
Supposing that the market maker needed to long call for hedging, as described in Bollen et al. (2004), the IHP could be estimated using the option formula from Black and Scholes (1973), and Merton (1973). When the option is at-the-money, the IHP based on the option pricing formula can be simplified to:
( t) t 2 (0.5 t t( )) 1
E IHP S N E , (7) where S, and τ are the underlying asset price, annualized return volatility, and the number of minutes between trades, respectively, while the market maker is holding positions. N(.) is the accumulated probability of standard normal distribution. E( ) is the expected value of the square root of the time between trades. We adopt the average of each trading day’s all trade prices of the ETFs as the underlying asset price, and the square root of the time between trades as the expected value of the square root of the number of minutes between offsetting trades.
Bollen et al. (2004) indicated that if the market maker had no inventory to accommodate a customer’s buy order at the ask, then the expected IHP would be the value of an at-the-money call. Therefore, the market maker not only could be protected when the security price rose unexpectedly but also could earn a profit when the security price dropped.
However, using at-the-money options to estimate the IHP is based on the fact that the moving direction of future prices is what the market maker prefers. Hence the value of IHP could be overestimated. In a perfectly competitive market, part of this speculative privilege would be bid away by speculators, just as the market maker shorts an out-of-the-money put so that his ability to make profit in the future through holding valuable inventory becomes smaller. Therefore, the value of IHP will be the value of the at- the-money call, less the value of an out-of-the-money put, or a COLLAR value. In a complete and frictionless market, bid and ask prices are equal to each other, such that the exercise prices of the call and the put would be the same. That is, the IHP (the COLLAR value) should be equal to zero.
However, it is not possible for the real world to be complete and frictionless. Therefore, while the bid–ask spread is not zero, the exercise prices of the call and the put would not be equal on condition that it would not affect hedging costs.
Therefore, in addition to applying an at-the-money call to evaluate IHP, we also used COLLAR value to observe the IHP. Since COLLAR value is equal to at-the-money call value minus out-of-the-money put value, we assume the out-of-the-money put had an exercise price of 0.01%
and 0.02%, respectively away from the current underlying asset price in order to observe the influence of the degree of out-of-the-money on the measurement of IHP, and thus on the spread.
(3). Adverse Selection Costs
According to Copeland and Galai (1983), the adverse selection component of the bid–ask spread could be modeled as a straddle in which the exercise price of call was the ask price and the exercise price of put was bid price. While the trading price lies between the bid and ask prices, this straddle acts as a kind of out-of-the-money option. Bollen et al. (2004) employed a similar method of measuring adverse selection costs.
To observe the effects of various trading prices on the magnitude of adverse selection costs to the market maker, we use the first decile (Q1), second decile6 (Q2), and the third decile (Q3) to simulate trading price.
Thus, if the market is a buyer’s market, the trading price should lie in the third decile, which is close to the ask price. On contrary, if the market is a seller’s market, the trading price should lie in the first decile, close to the bid price.
4. Structural Model
As the spread components represent outcomes from the spread decomposition, here we further observe the influence created by the individual spread component on the bid–ask spread. In the structural model, we treat the spread component as an independent variable and run the regression model as follows:
0 1 2
i i i i
SPRD InvTV IHP , (8) where SPRD, InvTV, and IHP are the proxy variables of the bid–ask spread, inverse trading volume for evaluating order processing costs, and inventory holding premium, respectively.
Let us examine the independent variable InvTV in the model. As the order processing costs of market makers is fixed, the smaller the InvTV, which is used as the proxy variable for order processing cost, the less the cost to market makers for processing orders; the quote spread is then expected to be lowered and coefficient value α1 should be positive. The existing literature shows that during high-trading-volume periods, the unit
6 I.e., the middle price between bid and ask price.
order processing cost would approach zero and the relationship between bid–ask spread and InvTV could not be observed through the coefficient of structural model.
To reiterate, variable IHP is the inventory holding premium expected by the market maker. When there is high IHP cost, the market maker will expand his ask–bid quotes. Hence it is expected that there is a positive relationship between both, and that coefficient α2 is positive. The higher the value of coefficient, the higher is the influence generated on the bid–ask spread when inventory holding costs change. First, we estimate the expected inventory holding premium using the at-the-money option. Next, considering that market makers would sell out these options with appreciation potential to minimize IHP, we further use COLLAR to estimate market makers’ expected IHP and compare the influences of changes in IHP during pre-/post-decimal pricing on spreads in structural models. Finally, we also classified estimated adverse selection costs as IHP and let IHP be an independent variable of the structural model in order to observe its influence on spreads surrounding decimalization.
Empirical Results
Table 1 and Table 2 each present basic summary statistics of the DIA and QQQ, respectively, before and after adjusting the minimum tick size from fractional pricing to decimal pricing as of January 29, 2001. These tables show that the average trading prices of DIA and QQQ were
$107.183 and $82.3589, respectively, during the pre-decimalization period, and during the post-decimalization period they were $105.037 and
$45.0484, respectively; both were in decline. Trading volumes per day during the post-decimalization period increased for both DIA and QQQ, with that of DIA climbing from 1,092,397 to 2,275,647, up by 108.32%;
and that of QQQ rising from 23,589,227 to 31,746,576, up by 34.58%.
Easley et al. (1996) pointed out that high trading volume would lead to smaller spreads. Comparing the spreads of DIA and QQQ, we discover that, for the higher-volume trading QQQ, all proxy variables of the bid–ask spread were smaller than those of DIA, indicating that the high trading volume could lower order processing costs and the probability of occurrence of adverse selection, and hence the quote spread for the market maker would be reduced. Observing the volatility of return during the post- decimalization period, the annual volatility (σ)7 of DIA and QQQ were both on the rise, indicating that the increase in trading volume caused the price risk of ETFs to rise. And for the average square root of time between trades( )t ,8 that of DIA was 0.87 minutes during pre-decimalization,
7 Daily return volatility rate is converted to annual return volatility rate using 252 .
8 As volatility rate is estimated on yearly basis, hence the time between two transactions within a day must be converted on yearly basis for evaluation. Therefore, the unit between two transactions is the
dropping to 0.69 minutes during post-decimalization, whereas that of QQQ dropped from 0.34 minutes to 0.31 minutes, indicating that decimalization shortens the market maker’s period of inventory holding.
Table 1
Summary Statistics for Diamond
The EWES, and VWES are the equal-weighted average of the effective spreads, and volume- weighted effective spread, respectively; S, InvTV and σ are the share price, the inverse of trading volume, and the intraday price volatility estimated by the Garman and Klass (1980) method, respectively; t is the average of the square root of the number of minutes between trades; IHP is the inventory holding premium computed by the equation
[2 (0.5 )]
IHPS N t , where S is the average trading price. The sample period before decimal pricing is June 15, 2000–January 26, 2001, and the post-decimal sample period is January 29, 2001–September 10, 2001.
Variable Pre-decimal Post-decimal Difference
(2)-(1)
Change Means(1) Median Means(2) Median in %
S 107.183 106.932 105.037 105.49 -2.146 -- -2.00%
TV 1,092,397 903,100 2,275,647 1,862,500 1183250 -- 108.32%
σ 0.14680 0.13172 0.15874 0.14652 0.01194 -- 8.13%
t 0.87419 0.85502 0.68651 0.68022 -0.18768 -- -21.47%
Spread
VWES 6.3066E-03 1.1119E-03 3.7535E-03 1.0924E-03 -2.55E-03
-40.48%
(1.34) EWES 1.4921E-04 0.9396E-04 1.0295E-04 0.6936E-04 -0.46E-04
-31.00%
(2.88) ***
Component
InvTV 1.4042E-06 1.1076E-06 0.6164E-06 0.5369E-06 -0.79E-06
-56.10%
(-9.31) ***
IHP 9.8637E-04 9.3724E-04 8.3112E-04 7.8869E-04 -1.55E-04
-15.74%
(-4.75) ***
Note: T statistics in parentheses; ***, **, and * indicate significance at the 1%, 5%, and 10% levels, respectively.
number of minutes and should be divided by 390 (total number of minutes in a transactional day) and divided by 252 (number of transactional day in a year).
Table 2
Summary Statistics for Cube (QQQ)
The EWES, and VWES are the equal-weighted average of the effective spread, and volume-weighted effective spread, respectively; S, InvTV and σ are the share price, the inverse of trading volume, and the intraday price volatility estimated by the Garman and Klass (1980) method, respectively; t is the average of the square root of the number of minutes between trades; IHP is the inventory holding premium computed by the equation IHPS[2 (0.5N t)], where S is the average trading price. The sample period before decimal pricing is June 15, 2000–January 26, 2001, and the post-decimal sample period is January 29, 2001–September 10, 2001.
Variable Pre-decimal Post-decimal Difference
(2)-(1)
Change Means(1) Median Means(2) Median in %
S 82.3589 86.0426 45.0484 43.5492 -37.3105 -- -45.30%
TV 23,589,227 20,552,050 31,746,576 29,937,000 8157349 -- 34.58%
σ 0.42052 0.37787 0.50602 0.39579 0.0855 -- 20.33%
t 0.34069 0.33682 0.30392 0.30188 -0.03677 -- -10.79%
Spread
VWES 4.5202E-03 1.6076E-03 1.7827E-03 0.9015E-03 -2.74E-03
-60.56%
(-2.83) ***
EWES 3.3811E-05 2.8037E-05 1.2804E-05 0.9297E-05 -2.10E-05
-62.13%
(-8.13) ***
Component
InvTV 5.3786E-08 4.8657E-08 3.6297E-08 3.3404E-08 -1.75E-08
-32.52%
(-6.75) ***
IHP 8.8707E-04 8.3441E-04 5.4085E-04 4.0614E-04 -3.46E-04
-39.03%
(-3.51) ***
Note: T statistics in parentheses; ***, **, and * indicate significance at the 1%, 5%, and 10% levels, respectively.
Compared to the estimates of individual stock spreads in the existing literature, the quoted spreads of ETFs, which have a diversification advantage, are smaller than those of their individual stock components.
Next, observing the change in spread reveals that the post-decimalization spread proxy variables are all smaller than the pre-decimalization estimates. Furthermore, the difference between pre- and post- decimalization is statistically significant. This result is consistent with those of Harris (1994), Ahn et al. (1996), Bollen and Whaley (1998), and Bessembinder (2000), indicating that the spreads of ETFs that possessed a diversification advantage were small and that decimalization had the effect of lowering the spreads quoted by market makers. Observing the percentage-wise difference between pre-decimalization and post- decimalization spreads, the QQQ with high trading volume has a larger reduction magnitude, reaching 62.13% on EWES. It can be observed that estimators of all spreads are higher than the median regardless of their pre- or post-decimalization provenance, indicating that the distribution of spread is skewed left and implying that the bid–ask spread is higher.
Regarding the spread component, the variable InvTV of DIA and QQQ are all significantly lowered due to increased trading volume after decimalization, indicating that the average unit order processing cost declined under decimalization. The average expected IHP of DIA and QQQ are also lower and the average differences of both are negative and statistically significant, where DIA declines from the 0.0009863 pre- decimalization to 0.0008311 post-decimalization, and QQQ drops from 0.000887 to 0.0005408, indicating that decimalization has reduced the inventory costs of market makers holding ETFs.
1. At-the-money Call as IHP
Table 3 presented the results of the structural model of DIA and QQQ, which used the bid–ask spreads as dependent variables, and the spread components as independent variables. In the table, we employ two types of bid–ask spreads, EWES and VWES, and compare the results of the pre- and post-decimalization samples. Using EWES and VWES as spread proxies and observing the regression coefficient α1 of the inverse of trading volumes, we find that except for VWES during pre-decimalization were not statistically significant, all coefficients are theoretically positive and statistically significant, and pre-decimalization are all smaller than post- decimalization, indicating the degree of influence of order processing costs on the bid–ask spread rose for DIA after decimalization. But QQQ was not consistent with the results of DIA and with theory.
In the test of IHP regression coefficients, we discovered that, except for insignificant coefficients, the pre- and post-decimalization coefficient values α2 were all positive and statistically significant, indicating that the
IHP and bid–ask spread are positively related, i.e., the higher the IHP, the larger the bid–ask spread, consistent with the theoretical symbol in general.
Comparing pre- and post-decimalization periods, except for VWES in the DIA sample, the IHP coefficients all show a decline after decimalization and are statistically significant, indicating that by increasing a unit of IHP, spread increment magnitude declines after decimalization.
Table 3
Structural Model of Spread
MODEL: SPRDi t, 01InvTVt2IHPtt
SPRD is the spread measured by EWES and VWES, respectively. And EWES and VWES are the equal-weighted effective bid–ask spread, and value-weighted effective bid–ask spread, respectively; InvTV is the inverse of trading volume; IHP is the inventory holding premium computed by the equation IHPS[2 (0.5N t)], where S and t are the average trading price and the average of the square root of the number of minutes between trades; α and ε are the regression coefficient and error term, respectively; pre represents the sample before decimal pricing, the period June 15, 2000–
January 26, 2001; and post, on the other hand, represents the sample after decimal pricing, the period January 29, 2001–September 10, 2001.
SPRDi Sample Period
Coefficient estimates
R2
α0 α1 α2
EWES
DIA-pre -0.00014 37.08 0.2427
(-3.00) *** (3.01) *** (6.13) *** 0.21
DIA-post -0.00001 57.24 0.0984
(-0.42) (2.39) ** (2.99) *** 0.08
QQQ-pre -0.00002 220.06 0.0450
(-1.81) * (2.65) *** (5.78) *** 0.18 QQQ-post 0.00002 -107.67 -0.0002
0.01 (5.85) *** (-1.52) (-0.22)
VWES
DIA-pre 0.00691 -1251.55 1.1674
0.004 (0.97) (-0.67) (0.20)
DIA-post -0.00431 3333.51 7.2356
0.07 (-1.71) * (1.87) * (2.94) ***
QQQ-pre -0.00012 -21948 6.5645
0.05 (-0.03) (-0.65) (2.08) **
QQQ-post 0.00295 -33091 0.0294
0.01 (2.78) *** (-1.26) (0.09)
Note: T statistics in parentheses; ***, **, and * indicate significance at the 1%, 5%, and 10% levels, respectively.
2. COLLAR as IHP
Imagine a market maker who has no inventory to accommodate a customer’s buy order at its ask price; the expected value of IHP could then be regarded as a call. But IHP estimated with the at-the-money call is very likely to be overvalued because a valuable call will be purchased away, a
condition that the market maker long a call and sell an out-of-the-money put at the same time. Therefore, IHP will be a COLLAR, and it will be the gap between an at-the-money call and an out-of-the-money put. To observe the explanatory ability of COLLAR value estimated by at-the-money call deduct out-of-the-money put for IHP, we simulated the exercise price using two degrees of out-of-the-money magnitude, 0.01% and 0.02% away from spot price, so as to carry out the structural model of bid–ask spread.
Tables 4 and 5 present the results of running a spread structural model of DIA and QQQ by COLLAR as IHP proxy variables. We discovered that the larger the degree of the out-of-the-money put, the smaller is the coefficient value α2 and the model appropriateness becomes worse;
therefore the R2 value becomes smaller, indicating that a put with higher out-of-the-money degree will have a smaller influence on the market maker’s quote spread. Except for values of VWES in the DIA sample, the values of α2 were all statistically significant and showed a tendency to decline after decimalization.
Comparing the average estimated IHP value estimated by the at-the- money call with that estimated by COLLAR and their coefficients from the structural model, we find that the difference between them is small. At the same time, the empirical results when both use EWES as spread proxies were similar. Turning to QQQ results, though coefficient α2 for COLLAR and the at-the-money call is consistent, α1 is different. So we use 2.5 times standard deviation as a picking range, and delete those spreads and IHP out of this range to rerun the structural model in order to do a robust check.
Since this 2.5 times multiple standard deviation range would make spreads using VWES as proxy have much more extreme values and cause the sample size become too small, we run the robustness check only for EWES.
Table 4
Structural Model of Spread Using Collar as IHP: DIA MODEL: SPRDi t, 01InvTVt 2COLLARtt
SPRD is the spread measured by EWES and VWES, respectively. And EWES and VWES are the equal-weighted effective bid–ask spread, and value-weighted effective bid–ask spread, respectively; InvTV is the inverse of trading volume; COLLAR is an option-type measure of IHP which is modeled as the difference between an at-the- money call and an out-of-the-money put. Here we set the exercise prices of the put at 0.01% and 0.02% away from the current security price, respectively. α and ε are the regression coefficient and error term, respectively; pre represents the sample before decimal pricing, the period June 15, 2000–January 26, 2001; and post, on the other hand, represents the sample after decimal pricing, the period January 29, 2001–
September 10, 2001.
SPRDi ％ Sample
period
Coefficient estimates
R2
α0 α1 α2
EWES
0.01%
DIA-pre -0.00015 36.92 0.2494
0.21 (-3.03) *** (2.99) *** (6.03) ***
DIA-post -0.00002 57.56 0.1052
0.08 (-0.57) (2.41) ** (3.10) ***
0.02%
DIA-pre -0.00014 37.08 0.2428
0.21 (-3.00) *** (3.01) *** (6.13) ***
DIA-post -0.00001 57.24 0.0985
0.08 (-0.42) (2.39) ** (2.99) ***
VWES
0.01%
DIA-pre 0.00667 -1240.36 1.3987
0.004 (0.91) (-0.67) (0.22)
DIA-post -0.00432 3317.13 7.2727
0.06 (-1.68) * (1.85) * (2.87) ***
0.02%
DIA-pre 0.00691 -1251.34 1.1715
0.004 (0.97) (-0.67) (0.20)
DIA-post -0.00431 3333.35 7.2361
0.07 (-1.71) * (1.87) * (2.94) ***
Note: T statistics in parentheses; ***, **, and * indicate significance at the 1%, 5%, and 10%
levels, respectively.
Table 5
Structural Model of Spread Using Collar as IHP: QQQ MODEL: SPRDi t, 01InvTVt2COLLARt t
SPRD is the spread measured by EWES and VWES, respectively. And EWES and VWES are the equal-weighted effective bid–ask spread, and value-weighted effective bid–ask spread, respectively; InvTV is the inverse of trading volume; COLLAR is an option-type measure of IHP which is modeled as the difference between an at-the-money call and an out-of-the- money put. Here we set the exercise prices of the put at 0.01% and 0.02%
away from the current security price, respectively. α and ε are the regression coefficient and error term, respectively; pre represents the sample before decimal pricing, the period June 15, 2000–January 26, 2001; and post, on the other hand, represents the sample after decimal pricing, the period January 29, 2001–September 10, 2001.
SPRDi ％ Sample
period
Coefficient estimates
R2
α0 α1 α2
EWES
0.01%
QQQ-pre -0.00002 224.73 0.0484
0.18 (-2.01) ** (2.70) *** (5.77) ***
QQQ-post 0.00001 -59.34 0.0059
0.03 (3.24) *** (-0.80) (1.72) *
0.02%
QQQ-pre -0.00002 220.25 0.0451
0.18 (-1.81) * (2.66) *** (5.78) ***
QQQ-post 0.00001 -86.26 0.0023
0.02 (4.45) *** (-1.18) (0.95)
VWES
0.01%
QQQ-pre 0.00025 -24346 6.3404
0.04 (0.06) (-0.72) (1.87) *
QQQ-post 0.00227 -26039 0.9476
0.01 (-1.68) (1.85) (2.87)
0.02%
QQQ-pre -0.00011 -22002 6.5559
0.05 (-0.03) (-0.66) (2.08) **
QQQ-post 0.00265 -29919 0.4153
0.01 (2.15) ** (-1.10) (0.46)
Note: T statistics in parentheses; ***, **, and * indicate significance at the 1%, 5%, and 10%
levels, respectively.
From Table 6, it is evident that the influence of order processing costs over spreads is enhanced after decimalization, whereas that of IHP is diminished, which are strongly implied by the regression coefficients.
Furthermore, observing the intercept values of the structural model in the robustness check, we find that these values are all reduced after decimalization and are smaller than the minimum one penny quote unit.
However, except for one insignificant coefficient, all other significant coefficients are close to zero.
Table 6
Robustness Test of Structural Model on Collar and EWES MODEL: EWESi t, 01InvTVt2COLLARt t
EWES is the equal-weighted effective bid–ask spread; InvTV is the inverse of trading volume; COLLAR is an option-type measure of IHP which is modeled as the difference between an at-the-money call and an out-of-the-money put.
Here we set the exercise prices of the put at 0.01% and 0.02% away from the current security price, respectively. α and ε are the regression coefficient and error term, respectively; pre represents the sample before decimal pricing, the period June 15, 2000–January 26, 2001; and post, on the other hand, represents the sample after decimal pricing, the period January 29, 2001–
September 10, 2001. Using 2.5 standard deviations from EWES and COLLAR as a cut-off, we remove samples outlying 2.5 standard deviations.
Sample ％ Sample Period
Coefficient estimates R2
α0 α1 α2
DIA
0.01%
Pre 2.15E-04 37.19 0.3192
0.29 (1.53) * (3.01) *** (7.13) ***
Post 1.98E-04 59.81 0.0912
0.15 (0.89) (2.99) *** (5.12) ***
0.02%
Pre 2.09E-04 37.85 0.3007
0.30 (3.00) *** (3.29) *** (7.01) ***
Post 2.01E-04 56.85 0.0891
0.16 (0.95) (2.49) ** (5.02) ***
QQQ
0.01%
Pre 0.89E-04 189.73 0.0618
0.20 (1.01) (2.25) ** (6.07) ***
Post 0.98E-04 191.54 0.0069
0.11 (1.84) * (1.89) * (2.42) **
0.02%
Pre 0.88E-04 190.01 0.0559
0.25 (1.82) * (2.11) ** (5.95) ***
Post 0.99E-04 191.61 0.0038
0.10 (1.95) * (1.78) * (2.15) **
Note: T statistics in parentheses; ***, **, and * indicate significance at the 1%, 5%, and 10% levels, respectively.
3. STRADDLE as Adverse Selection Cost
Copeland and Galai (1983) modeled the adverse selection costs in the bid–ask spread component as STRADDLE. Therefore, in order to observe the variation of adverse selection costs between buyers’ and sellers’
markets, we employed three scenarios, including the first decile (Q1), median (Q2), and the third decile (Q3) to simulate spot price, where median is the bid and ask price midpoint, the call exercise price is the ask price, and the exercise price of the put is the bid price. Table 7 presents the results of the effects of STRADDLE and order processing costs on EWES.
Table 7 shows that all coefficient values α2 are positive in the DIA sample. Though the sign of α2 is not consistent for the QQQ sample, it remains evident that entire coefficients are significantly lowered, implying that the effect of adverse selection on spread decreases after decimalization.
In addition, observing that the market consists of buyers (spot price = Q1) as well as sellers (spot price = Q3), we find that the influence of adverse selection on spreads would be strongest when the spot price is set at the median; that is, the effects of adverse selection on spreads would decline if the spot price varied to either side. Table 8 presents the results of the effects of STRADDLE and order processing cost on VWES, which are similar to the former results for VWES; that is, there is some inconsistency.
