Bidder Participation and Information in Currency Auctions
  • 1 0000000404811396https://isni.org/isni/0000000404811396International Monetary Fund
  • | 2 0000000404811396https://isni.org/isni/0000000404811396International Monetary Fund

Contributor Notes

Author(s) E-Mail Address: ausubel@econ.umd.edu; rromeu@imf.org

This paper studies the participation and performance of sophisticated versus unsophisticated auction participants in an environment with numerous bidders, uncertainty, and asymmetric information. We examine multi-unit, pay-as-bid, currency auctions conducted by the Central Bank of Venezuela. We find that sophisticated bidders outperform their less sophisticated rivals during periods of high volatility, apparently as a result of their superior informationgathering ability. The result is consistent across both quantity (sophisticated bidders win more market share) and price (sophisticated bidders pay lower premiums). The result is consistent with the view that a pay-as-bid auction format may be detrimental to participation by less-informed bidders.

Abstract

This paper studies the participation and performance of sophisticated versus unsophisticated auction participants in an environment with numerous bidders, uncertainty, and asymmetric information. We examine multi-unit, pay-as-bid, currency auctions conducted by the Central Bank of Venezuela. We find that sophisticated bidders outperform their less sophisticated rivals during periods of high volatility, apparently as a result of their superior informationgathering ability. The result is consistent across both quantity (sophisticated bidders win more market share) and price (sophisticated bidders pay lower premiums). The result is consistent with the view that a pay-as-bid auction format may be detrimental to participation by less-informed bidders.

I. Introduction

Perhaps the most often studied issue in the economics literature on multi-unit auctions is the performance of the traditional pay-as-bid auction versus more recent alternatives. Empirical studies have generally contrasted the pay-as-bid auction (in which winning bidders pay the amounts of their winning bids) with the uniform-price auction (in which winning bidders pay a single clearing price for every unit that they win).2 Theoretical studies have examined the properties of equilibria in the pay-as-bid and uniform-price auctions3 as well as proposing new approaches to auctioning multiple units.4

The earliest critique of the pay-as-bid auction format is due to Milton Friedman. In testimony before the Joint Economic Committee of the US Congress in 1959, he argued: “If you pay the price that you bid, then it really makes a great deal of difference that you should bid very close to the final price at which the auction is going to be settled. The only way to assure that you do so is to get together with other people and arrange your bids.” (Friedman, 1959) In later years, he supplemented his critique by arguing that the pay-as-bid format then used by the US Treasury “reduces participation, changes the demand schedule as it appears to the Treasury, probably raises the costs for the Treasury, and is inferior to an alternative method of bidding under which all purchasers would pay the same price.” (Friedman, 1964, p. 513.) By contrast, in a uniform-price auction, “no one is deterred from bidding by fear of being stuck with an excessively high price. You do not have to be a specialist.” (Friedman, 1991.)

In the current paper, we reexamine Friedman’s critique, empirically, within the context of a series of recent currency auctions conducted by the Central Bank of Venezuela. Our premise is that, if asymmetric information is a problem for bidders in a pay-as-bid auction, this problem worsens in times of greater volatility and uncertainty. Thus, if limited participation by less-informed bidders is a problem generally, then it should be a bigger problem at times when their informational disadvantage is more consequential.

The dataset utilized here has a number of advantages for assessing Friedman’s argument, including the ability to track sophistication levels and bidder behavior outside the auctions. Individual bids are known for all participants in all of the auctions. Notably, the failure to bid in a particular auction is also observed. It is possible to track the bidders from one auction to the next, and to match the bidders’ bids with bidder-specific variables that may influence the bidding. The auctions occurred during a time period in which the relevant currency market was subject to varying levels of incomplete information, and there exist some proxies for the degree of incomplete information. And the auctions occurred at a very high frequency (three times per day), meaning that the changes in volatility and uncertainty were likely to be the most important changes affecting the bidders during the sample period.

The notion of “more sophisticated” or “better informed” is operationalized empirically in this paper by looking at the size of the bidders’ retail businesses: larger is equated with more sophisticated. As it turns out, more sophisticated bidders by this measure do outperform their less sophisticated colleagues, particularly during high volatility periods. This result appears in the currency auctions studied here—an environment with numerous bidders, uncertainty, and asymmetric information. Driving this information asymmetry is probably two factors. First, the relevant private information in this market is probably the order flow of customers, and the bidders with larger retail businesses are in a position to aggregate the order flow of a larger set of customers. Second, the larger bidders have the economic incentive to acquire better information-gathering and information-processing technology related to the currency markets than other bidders, meaning that they should be expected to invest in becoming more sophisticated in an informational sense.

The Venezuelan authorities turned to currency auctions to efficiently allocate foreign currency reserves when they exited a crawling peg exchange rate regime. Under this regime, authorities guaranteed a price at which they buy or sell any amount of foreign currency. Once the price of foreign exchange was determined in an auction, its results changed the value of balance sheets and portfolios; hence there was broad interest in the auctions. Information asymmetries in currency auctions originate from internal signals of economic aggregates that market participants, such as banks, create to help predict the short-run demand for foreign exchange. These signals are based on private information (such as customer order flow for dollars) that is available at very high frequencies, and they are used to form bids in the auctions.5 Our results show how more sophisticated auction participants use these signals to outperform less sophisticated bidders, especially during periods of high uncertainty.

Our analysis departs from most previous empirical studies of auctions in two ways. First, bidder participation is treated endogenously, rather than as an exogenous statistic to be correlated with other results. In our analysis, the number of participants in a given auction is not merely a random draw. Rather, a bidder’s decision to enter the auction is an integral part of her strategy space. That is, based upon her needs for currency and her private information, a bidder decides the prices and quantities to bid. We include, however, the possibility that the bidder may optimally not bid at all (or, equivalently, may bid for a zero quantity). Previous work has sometimes modeled endogenous entry into an auction using some entry cost. However, such an approach is not designed to address the issue of bidders exiting because of uncertainty or adverse market conditions, which is explicitly treated here. That this issue typically has been sidelined in the literature is understandable, considering the data requirements necessary to capture the behavior of market participants choosing not to enter the auction. The richness of our dataset enables us to examine this issue, however, our analysis is also robust to critiques regarding this issue. Specifically, one concern is that predicting participation in the auction also can predict bidding behavior. Our results are robust to this critique in that conditional on participation, we continue to find that more sophisticated banks outperform their less sophisticated colleagues.

Second, our study centers on who are the winners, the quantities that they win, and the prices that they pay. That is, we investigate what separates the winners from the losers during volatile times. Our answer is the sophistication of the bidder. While previous work has focused extensively on detecting a winner’s curse in the aggregate outcome, we focus more specifically on finding the effect of market volatility and private information on individual bidder behavior and the disaggregated outcomes.

The next section gives institutional background. It is followed by Section III, which gives the methodology used. Descriptive statistics are presented in Section IV. Section V presents estimation results, and Section VI concludes.

II. Some Institutional Details

The data utilized come from thrice daily currency auctions held by the Venezuelan Central Bank (VCB). These auctions were instituted when, on February 15, 2002, Venezuela abandoned its fixed peg exchange rate (it stopped supporting a fixed dollar price at any quantity demanded, and instead provided a fixed daily quantity of dollars at the pay-as-bid auction price). Venezuela is one of the the top five oil exporters in the world, with a state-controlled oil industry that comprises about 20-25 percent of GDP. The daily dollar revenue generated by the national oil company’s exports is surrendered to the VCB. This surrender requirement guarantees that the currency auctions play a prominent role in the provision of dollars to the private sector. In Venezuela, market participants demand dollars to spend on imports and for international asset diversification.

During the period in which the data were collected, the VCB held currency auctions each working day at 9:30 am (called auction 101), 11:00 am (called auction 102), and 1:30 pm (called auction 103). The amount to be sold in each of the three auctions was the same and was known in advance by the bidders. At the beginning of the sample, this amount was $20 million per auction (for a daily total of $60 million), which was reduced within three weeks to $15 million per auction (for a daily total of $45 million). Each participant was permitted a maximum of three bids which had to be at least $50 thousand each, and the sum of all three could be no more than 15 percent of the total to be sold in the auction (implying a maximum bid of $2.25 million per bidder in an auction, for most of the sample period). The auctions were conducted as simple pay-as-bid auctions: the bids were aggregated, the clearing price was determined, and winners (bids of at least the clearing price) paid the amounts of their bids. After each auction, the VCB published the maximum winning bid, the minimum winning bid (i.e., the clearing price), and the weighted average winning bid; and each participant was privately informed of her winnings.

At the time, the participants in the currency auctions were a diverse group of banks and exchange houses that collectively intermediated dollars in Venezuela. To service their clients’ demand for dollars, they could purchase dollars at auctions, purchase dollars at the retail level from clients willing to sell, or attempt to obtain dollars from the interbank market. The latter was not as reliable an option as in the typical currency or debt market, because the Venezuelan authorities heavily regulated and taxed interbank trading and asset movements.

III. Methodology

This section outlines the empirical approach used to analyze bidding performance in auctions. This approach centers around examining if more sophisticated bidders are able to outperform their less sophisticated colleagues in times of high uncertainty. In pursuing this end, one concern is finding an accurate measure of bidding performance. In particular, previous studies have suggested that the number of bidders declines during times of uncertainty or increased volatility.6 Given this correlation, the researcher’s measurements of bidding and winning performance would reflect a different pool of bidders during volatile versus tranquil periods. If auction participants were randomly selected, observing a subset would not bias the estimations. However, it is difficult to argue that market participants bidding in the auctions are a random sample of the potential participants; more likely, there is selection bias. Hence, a naïve analysis of auction performance is subject to the critique of Heckman (1979) and, as a consequence, the approach of that study is used here.

The estimation difficulties originating from self-selection can be overcome if variables that predict participation (but not auction performance) are identified. In the case of currency auctions, such variables can be found in the microeconomics of exchange rates. This literature typically models the optimal holdings of currency market participants as driven by two effects: inventory effects and information effects.7 Inventory effects refer to a currency dealer’s need to replenish her inventory when it is running low, and to reduce her currency inventory when it runs higher than the optimal level. Information effects refer to a dealer’s ability to update her estimates of variables relevant to exchange rates through her business with clients. Put crudely, by observing whether customers initiate more purchases or sales, the currency dealer can aggregate information that is dispersed across agents in the economy. The information being aggregated reflects people’s expectations, risk aversion, demand for money – all variables relevant for determining the exchange rate, but unavailable at high frequencies. It is assumed here that the public’s purchases of foreign currency are driven, at least in part, by variables such as their risk aversion and expectations of future inflation. Hence, the dealer who observes the most customer purchases learns the most information in real time about the aggregate state of the economy. This information serves as a basis for speculation and portfolio rebalancing and would drive a dealer to participate in the auction.

Accordingly, the probability that a bank will show up to the auction is modeled as a simple Probit using three variables dictated by microstructure exchange rate models. These are: a bank’s need to replenish its inventory of dollars and corporate and private order flow. The inventory component of the estimation attempts to capture the liquidity needs of a bank, and is estimated here using the deviation from the optimal inventory (called “invdev”), as well as a squared deviation, and a lag of each. These are a better fit for Venezuela because of the heterogeneity of banks in the sample. Order flow is decomposed into corporate and private order flow because of the different informational value this decomposition could bring to the estimation. The variables used are sales to corporate clients (called “q_j”), and the daily dollar sales to private individuals (called “q_n”). Identification is achieved because the inventory terms are the instruments used to predict auction participation, but they are not used in the performance equation below since they are not useful in forming bidding strategies.

Prob{ Auctiont}=c+α1invdevt+α2invdevt1+α3invdev2t+α4invdev2t1+α5q_jt+α3q_nt+et1  (1)

Having controlled for the self-selectivity, auction performance is then modeled as depending on the bank’s level of sophistication, the level of uncertainty in the market, and an interaction, and squared interaction terms. As for inventory estimation, the non-linearity in the interaction terms is a better fit for Venezuela because of the heterogeneity in bank sophistication. Order flow is included in the performance equation so as to control for information received by sales to retail clients which would contribute to the superiority of banks’ bidding strategy, but not necessarily depend on banks’ sophistication level.8 Hence, the effect of bank sophistication on auction performance is captured independently of the information from the daily order flow. The resulting estimation equation is:

(Bidder Performance)t=c+β1St+β2Ut+β3(StUt)+β4(StUt)2+auc2t+auc3t+α5q_j+tα3q_n+tet2  (2)

Equation (2) gives the estimating equation for bidder performance. St represents a measure of bank sophistication. Ut represents a measure of market-wide uncertainty on the day of the auction. The interaction terms are represented as products of S and U, and dummies for the second and third auctions of the day are represented by auc2 and auc3. The coefficients on q_jt and q_nt capture order flow information that could be used by the banks to form bids. Heckman’s correction for the latent selectivity from equation (1) is incorporated and clustering the observations around banks and using Huber/White estimates of the standard errors control for general forms of serial correlation and heteroskedasticity.9 The estimated marginal effect of sophisticated banks’ performance during volatile periods is calculated as: β^3+2β^4(S¯U¯). Note that the sophistication and uncertainty regressors are excluded from the selectivity equation, and hence, the marginal effect does not need to take into account a change in the probability of observing a bank.10

IV. Descriptive Statistics

The data used in this study provide a relatively complete depiction of the process of foreign currency intermediation in Venezuela for the period February 18 to June 7 of 2002. There are 42 unique participants in the 231 auctions that occurred in the 77 business days in the sample. Altogether, there are 5584 unique bidding strategies observed, where an auction participant wins some non-zero quantity in an auction 3437 times. Beyond observing the individual banks’ bids and winnings in the auction, one is able to observe their behavior in the interbank and retail currency markets. In particular, each bank (along with approximately 30 other exchange houses that do not participate in the currency auctions) report their daily sales and purchases of dollars to retail clients and most also report inventory.

A. Bidding Performance Measures

Two market-share-based bidding performance measures are used (see Table 1 on page 22 to reference variable definitions). The first, called “wbank,” is given by a bank’s total winnings at an auction divided by the total amount auctioned off. The second market–share-based bidding performance measure, called “wbid,” is given by a bank’s total bid at an auction divided by the amount auctioned off. Two cost-performance-based variables are also used to measure bidding performance. The first, called “clpr,” represents the premium a bank pays and is the signed, squared deviation of each bank’s weighted mean winning bid from the auction’s weighted mean winning bid. The second is called “prem,” and represents the difference between a bank’s weighted average price paid for winnings and the clearing price in the auction.

Table 1.

Variable Definitions

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Notes: Table 1 gives definitions for the estimation variables.

Figure 1 on page 18 depicts average bidding behavior in the three intraday auctions. The figure is subdivided into three panels, one for each of the three daily auctions (hence depicting intraday seasonality). Each panel depicts bidding behavior at standard bid sizes (multiples of 50,000 U.S. dollars). The top panel shows the average cover ratios for each bid size (amount won at that bid size over total amount auctioned off across all standard bid sizes), and it indicates that the majority of the dollars auctioned off go to bids in the 500,000 to 1 million U.S. dollar range. Note, however, that the average cover ratio of the largest bid size, 2.25 million U.S. dollars, also spikes, with the most disproportionate spike coming in the third auction.

Figure 1.
Figure 1.

Bidding Behavior by Bid Size and Intraday Auction

Citation: IMF Working Papers 2005, 157; 10.5089/9781451861761.001.A001

Notes: Figure 1 shows bidding behavior across the three daily auctions is depicted in order from left to right. The top panel shows the cover ratio across bid sizes; the second shows the average winning price, with the diameter of the bubbles scaled by the frequency of winnings in that bid price category. The third panel shows the variance of winning bids across bid sizes.

The middle panel shows the average winning bid price for each bid size across the auctions. The diameter of the bubbles is scaled by the frequency or proportion of bids that appear in that category – the more bids appear in the bubble, the bigger it is. Here one observes more winning bidders concentrating on medium size bids, and paying a higher average price as the bid size increases. The largest bid size group, however, again bucks the trend by paying a lower average price for its winnings across all three intraday auctions. That is, there is a group (of approximately the same percentage of total bidders across all three auctions) that obtains a disproportionate fraction of the dollars auctioned off at lower unit prices.

The lower panel shows the variance of prices in all three auctions by bid size. Here, the prices tend have similar volatility across bid sizes in the first auction, and show differences in the second and third auctions of the day, with no apparent pattern across standard bid sizes.

B. Bank Sophistication Measures

Five different measures of bank sophistication are used to capture any possible information advantages that may be present in the data. Two of the measures are based on an average of bank behavior throughout the sample. These aggregate measures are called “banksize” and “bksize”. The measure “banksize” captures the average sales of dollars to retail clients. The measure “bksize” captures both sales to retail clients and purchases from retail clients. Both measures are constructed as the average for each bank divided by the sum of the averages for all banks (see Table 1 on page 22 for variable definitions). These measures capture potential differences suggested by market practitioners who argue that sales of dollars to retail clients are relatively more important in Venezuela due to the large government revenue in dollars from oil sales that is intermediated by the banking sector. These two measures are unchanging throughout the sample and categorize at once the sophistication level of a bank. The reasoning behind using retail-sales-based measures of sophistication is that economic information relevant for price discovery is dispersed across economic agents (for example, money demand and risk preferences). Banks with higher sales will interact with more agents, and they will have more information regarding these agents’ private information about the value of the dollar. Their information advantage derives from their superior knowledge of market conditions, and of the resulting auction equilibrium prices.

Figure 2 on page 19 compares these measures of bank sophistication for all banks and exchange houses in Venezuela (the universe of potential auction participants). The figure is divided into four panels: the two left panels graph banksize, and the two right panels graph bksize. The upper graphs confine themselves to banks and exchange houses with more than 1 percent of sales, whereas the lower panels show these measures for all banks and exchange houses. The lower panels show inverted abscissa scales and the right panels show inverted ordinate scales. The graphs show large differences in the banks’ relative market shares. Of 72 banks and exchange houses in the market, fewer than 20 control 99 percent of the sales, with the six largest controlling over 50 percent of the market (note the similarity to the U.S. Treasury auction market). In the bottom panel we can see the fifty or so banks and exchange houses not depicted in the top panel being dwarfed by the others’ market size.

Figure 2.
Figure 2.

Bank Sophistication Measures

Citation: IMF Working Papers 2005, 157; 10.5089/9781451861761.001.A001

Notes: The top two panels of Figure 2 depict market share measures for banks that average at least 1 percent of daily sales. The lower two panels depict the entire market (with inverted abscissa scales). The left two panels depict banksize, the measure of average sales to retail clients, and the right panel captures bksize, the measure of sales and purchases to retail clients.

These bank sophistication measures are complimented by performance measures based on daily market share, called “bsize.” Using the previous day’s market share (called lagged bsize, or “lbsize”) and a moving average of the prior five business days (which is called “bsizema5”), one can observe potential dynamics in the sophistication of banks throughout the sample. These measures are intended to capture any possible changing market power within the sample period.

C. Measures of Uncertainty

Measures of uncertainty are used to gauge the effectiveness of a sophisticated bidding strategy at times when the market equilibrium is not easily discernable. The evidence presented here is based on nine measures of uncertainty. Three of these are external to the market and are used as exogenous measures of uncertainty. The other six are based on observed market volatility, or de facto uncertainty present in the market at the time of bidding.

External Uncertainty Measures

The three external measures of uncertainty are based on three assets that trade concurrently with the foreign exchange market. The first is the forward premium on the three-month currency forward for the Bolivar. The second is the Venezuelan component of JP Morgan’s Emerging Market Bond Index, which characterizes country risk for Venezuela. The third is a parallel exchange rate implicitly given by the concurrent sales of equity shares of Venezuela’s well-known media company, Compañía Anónima Nacional de Teléfonos de Venezuela (CANTV) on the New York Stock Exchange (as an ADR) and on the Caracas Stock Exchange. Since the same asset is sold in both markets in different currencies, their prices implicitly define exchange-rate parity. During periods of exchange controls, this last measure has become a widely observed indicator of parallel market exchange rates.

Figure 3 on page 20 graphs these three measures of volatility. The upper left shows the forward premium, which consistently shows the same periods of uncertainty. The top right panel graphs the Emerging Market Bond Index uncertainty measure (called “embi”) for each day of the period. One can observe the volatility increase in the beginning of the sample, and later around mid-April, due to an increase in the macro-political uncertainty. The bottom panels compare the market exchange rate with the implicit CANTV exchange rate (called “cantvxr”). On the bottom left is the level and the estimated standard deviation, and on the bottom right panel is the CANTV exchange rate graphed against the market rate. As the points veer off the 45 degree diagonal, the equity markets are taking a different view of the exchange rate than the currency markets.

Figure 3.
Figure 3.

External Indicators of Market Volatility

Citation: IMF Working Papers 2005, 157; 10.5089/9781451861761.001.A001

Notes: Figure 3 shows the external indicators of currency market volatility. The upper left panel depicts the premium on a three month currency forward contract. The upper right panel depicts the Venezuelan component of the Emerging Market Bond Index. The lower left panel depicts the five-day standard deviation of the CANTV exchange rate. This exchange rate is plotted against the market rate in the lower right panel.

Observed Market Uncertainty Measures

Beyond the uncertainty reflected in other markets, one can also observe uncertainty in the currency market itself. Periods of uncertainty in the market are tracked using six variables. Three of these variables measure the volatility of the winning bids, while the other three measure the volatility of all bids.

Uncertainty Measures Based on Winning Bidders

The uncertainty measures that focus just on winning bidders are three. First, “spread” captures the difference between the highest and lowest winning bids in the pay-as-bid auction. This statistic is ex-post common knowledge because the Central Bank published both the highest and lowest winning bid after each auction. The second measure, “sprd,” is the difference between the highest and lowest weighted winning bids at an auction. Sprd is analogous to spread, but uses weighted bids. The third measure, “sd,” is the standard deviation of all weighted winning bids.

Uncertainty Measures Based on All Submitted Bids

The second group of variables examines the uncertainty present in the auctions via all bidders’ demand schedules. The three measures used are: “asprd,” which measures the difference between the highest and lowest weighted submitted bid; “asd” measures the standard deviation of all banks’ submitted weighted bids in the auctions; “amdev” measures the average absolute deviation from the mean of all submitted weighted bids in the auction. Asd and amdev differ in that asd weighs outliers more. Figure 4 (page 21) shows a matrix of scatter plots of the volatility measures across the sample. The names of the variables depicted in the rows/columns are labeled along the diagonal of the matrix. The external measures of volatility tend to stray from the diagonal of each graph, indicating that they are picking up different measures of vitality than the internal measures.

Figure 4.
Figure 4.

External and Currency Market Volatility Indicators

Citation: IMF Working Papers 2005, 157; 10.5089/9781451861761.001.A001

Notes: Figure 4 contrasts the external volatility indicators with the different measures of observed currency market volatility. The latter group is composed of six measures. The first three are drawn only for winning bids. These are: spread, sprd, and sd (definitions given along the diagonal). The last three measures are taken over all submitted bids: asprd, asd, amdev.

V. Results

The results presented in this section point to a consistent pattern in which banks falling within the various taxonomies intended to capture sophistication show higher winnings and pay lower price for these winnings during volatile times relative to their unsophisticated competitors in the pay-your-bid auctions. Moreover, these results obtain while controlling for sophistication and market uncertainty independently, as well as for idiosyncratic information from microstructure effects in the retail market. Estimations using the variety of measures described in Section IV are presented for performance based on market share in Table 3 through Table 11 (pp. 24 – 32), and for performance based on prices in Table 12 through Table 20 (pp. 33 – 41). The first set of tables considers whether sophisticated banks capture a larger share of the market than their unsophisticated colleagues, whereas the second set considers whether sophisticated banks pay more for their winnings than their less sophisticated colleagues.

Table 2.

Descriptive Statistics

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Selection equation variables.

Notes: This table shows descriptive statistics for the estimation variables for the period February 18 to June 7, 2002. While there are 42 unique banks and exchange houses participating in the auctions, there are over 70 banks and exchange houses participating in retail dollar market (hence the differences in the number of observations from one market’s variables to the other).
Table 3.

Assessing Quantity-Based Performance Using Spread for Volatility

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Notes: The upper panel in Table 3 shows estimation with selectivity, and the lower panel shows estimation with OLS. For each estimation, the left panel shows estimates using wbank (as the left-hand-side variable) -- bank winnings as a percentage of the total amount auctioned off, and the right panel shows estimates using wbid -- bank bidding as a percentage of the total amount auctioned off. The uncertainty and sophistication measures are reported across the top of the table, and the results are reported in the row labeled “U” and “S” respectively. “S,” bank sophistication based on market share, is given by: banksize (average retail sales), bksize (average retail sales and purchases), lbsize (previous days retail customer sales), bsizema5 (five-day moving average of retail sales). The rows labeled “S*U” and “S*U^2” report the interaction and squared interaction terms, respectively, and “auc2” and “auc3” report indicator variables for the second and third auctions of the day. The selection equation uses the deviation from the average inventory over the past five days, the order flow from corporate and non-corporate customers. Statistics are reported in the bottom panel.
Table 4.

Assessing Quantity-Based Performance Using Sprd for Volatility

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Notes: See notes on Table 3, page 24.
Table 5.

Assessing Quantity-Based Performance Using Sd for Volatility

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Notes: See notes on Table 3, page 24.
Table 6.

Assessing Quantity-Based Performance Using Asprd for Volatility

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Notes: See notes on Table 3, page 24.
Table 7.

Assessing Quantity-Based Performance Using Asd for Volatility

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Notes: See notes on Table 3, page 24.
Table 8.

Assessing Quantity-Based Performance Using Amdev for Volatility

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Notes: See notes on Table 3, page 24.
Table 9.

Assessing Quantity-Based Performance Using Cantvsd for Volatility

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Notes: See notes on Table 3, page 24.
Table 10.

Assessing Quantity-Based Performance Using VBN3MCurncy for Volatility

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Notes: See notes on Table 3, page 24.
Table 11.

Assessing Quantity-Based Performance Using EMBI for Volatility

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Notes: See notes on Table 3, page 24.