Uniform-Price Auctions:

Update of the Treasury Experience

by 

Paul F. Malvey 

Christine M. Archibald 

Office Of Market Finance 

U.S. Treasury 

Washington, D.C. 20220 
Foreword 

While there has been a long-standing interest in the theory of uniform-price auctions, there 

had been very little empirical analysis when the Treasury inaugurated its experiment with regular 

uniform-price auctions of 2- and 5-year notes in September 1992. The October 1995 study and 

this update make valuable contributions to the body of empirical evidence. 

The conclusions in this update reinforce those reached in 1995. They provide empirical 

support for the theoretical proposition that auction participants will bid more aggressively in 

uniform-price auctions since successful bidders in uniform-price auctions pay only the price of the 

lowest accepted bid, rather than the actual price they bid, as in the multiple-price approach. Our 

experience also shows that uniform-price auctions produce a broader distribution of auction 

awards. These results have important policy implications. The findings indicate that uniformprice auctions can allow the Treasury to make improvements in the efficiency of market 

operations and reduce the costs of financing the Federal debt. These results are also important in 

another sense: they provide a clear example of how economic theory can make a significant and 

direct contribution to public policy. The Treasury is proud to have played a role in bridging the 

gap between theory and application. 

There are many people who contributed to this important effort, and while it is impossible 

to thank all the individuals involved, Secretary Rubin and I would like to personally commend the 

work of Deborah Danker, Darcy Bradbury, and Roger L. Anderson, who spearheaded these 

studies, as well as the staff of the Office of Market Finance, including Jill Ouseley, Paul Malvey, 

and Christine Archibald. Furthermore, we would like to thank Kerry Back, Sushil Bikhchandani, 

Jeremy Bulow, Carlo Cottarelli, Loretta Mester, Vincent Reinhart, and Suresh Sundaresan for 

their helpful insights and comments. 

Lawrence H. Summers

Deputy Secretary of the Treasury

October 26, 1998
Uniform-Price Auctions:

Update of the U.S. Treasury Experience 

Introduction 

One of the recommendations of the Joint Report on the Government Securities Market1 

was that the Treasury consider alternatives to the multiple-price auction technique for auctioning 

Treasury securities. After an extensive review of the issues, the Treasury announced on 

September 3, 1992, that it would conduct a uniform-price auction experiment for all auctions of 

2-year and 5-year notes. In October 1995, the Treasury published a study entitled, "Uniformprice Auctions: Evaluation of the Treasury Experience." (The “1995 Study”) This paper is an 

update of the major results presented in that study.2 It does not include an assessment of the 

performance of inflation-indexed securities, which Treasury began offering in January 1997 and 

are auctioned under a uniform-price format. 

The Treasury's stated purpose in conducting uniform-price auctions is to determine 

whether the uniform-price auction technique reduces the Treasury's financing costs compared 

with multiple-price auctions, by encouraging more aggressive bidding by participants, and 

whether it broadens participation and reduces concentration of securities on original issue. Thus, 

1 Joint Report on the Government Securities Market. Washington, D.C., Government Printing 

Office, 1992. 

2 Uniform-price Auctions: Evaluation of the Treasury Experience. Washington, D.C., U.S, 

Treasury, October, 1995.(Available on-line at <www.ustreas.gov/domfin/final.pdf>) 
2

both the original evaluation and this update have focused on the impact on revenues and the 

breadth of initial distribution of awards. 

The uniform-price technique differs in only one important way from the multiple-price 

auction technique that the Treasury has been using to issue notes and bonds since the 1970s.3 In 

the multiple-price format, competitive bids state the amount and yield desired and are ranked from 

the lowest to the highest yield. Awards are made at successively higher yields until the amount 

allotted for competitive tenders is fulfilled, with awards at the highest yield prorated. The process 

for the uniform-price auctions is identical except that, instead of awards being made at the 

individual yields stipulated by the bidders, all accepted bids are filled at the highest yield of 

accepted competitive tenders. 

Background 

The current state of auction theory involves many abstractions from the complexities of 

the real world.4 For example, auction theory is usually couched in terms of a single, indivisible, 

homogeneous good being sold at a one-time event (e.g., auctions for works of art), with each 

bidder submitting a single bid at the relevant time in the auction process, and behaving according 

to certain restrictive assumptions. Auctions for Treasury securities, however, are repeated on a 

periodic basis and are for multiple goods, for which bidders may submit a whole schedule of bids, 

some of which may be viewed as underwriting bids; there is an active, well-defined WI market in 

which participants can purchase the identical good (but at a known yield) at the time of an auction 

or before or after; and there is a well-defined group of bidders, which may or may not act 

according to the assumptions of auction theory, that participate in virtually all auctions. 

3 Treasury bills have been sold using multiple-price auctions since 1929. 

4 For recent surveys of auction theory, see McAfee and McMillan (1987) and Milgrom (1989). 

For surveys related specifically to Treasury auctions, see Mester (1988), Reinhart (1992), and 

Chari and Weber (1992). The following overview is based on these works. 
3

One of the basic results of auction theory is that under a certain set of assumptions the 

revenue to the seller will be greater with uniform-price auctions than with multiple-price auctions. 

The reasoning is that in multiple-price auctions successful bidders will pay the actual price they 

bid, whereas in uniform-price auctions, successful bidders pay only the price of the lowest 

accepted bid. Thus, by virtue of winning in a multiple-price auction, a successful bidder 

demonstrates that he is willing to pay a higher price than the market consensus. In that sense, 

winning is losing -- submitting a higher bid signals to other participants that one’s valuation 

exceeds that of others. There is a higher probability of a subsequent loss if the bidder were to 

attempt to sell the good in the after market. This is the “winner’s curse.” Its effect is to cause 

bidders to shade their bids below their true valuation of the goods. By contrast, in a uniformprice auction, all successful bidders pay the same price -- the lowest price accepted. Accordingly, 

bidders are less likely to shade their bids. 

It can be shown that relaxing the assumptions regarding bidder behavior will affect the 

predictions of auction theory regarding expected revenues under the two auction formats, 

resulting in other revenues rankings, or rankings that are indeterminate.5 

In light of the nonconformaties between auction theory and practice, Milton Friedman has 

put forth an informal analysis based on auction theory suggesting that the Treasury's traditional 

multiple-price auction technique costs the Treasury money and also favors the dealer community.6 

Friedman contends that switching to a uniform-price auction would reduce the cost of 

financing the debt. While the Treasury would give up the consumer surplus it receives as a 

discriminating monopolist, Friedman argues that the uniform-price format would more than offset 

this decline in revenue by increasing demand on two counts. First, as auction theory suggests, the 

5 See McAfee and McMillan (1987) or Mester (1988). 

6 Friedman originally proposed this idea in Friedman (1959). For a recent statement, see Friedman 

(1991). 
4

switch to a uniform-price format would lead to more aggressive bidding, because the fear of the 

winner's curse is reduced. 

Secondly, because uniform-price auctions are strategically simpler, they would reduce bid 

preparation costs and encourage more bidders to participate.7 The primary dealers would lose the 

extra rents they earn by the services they perform in the current system. That is, dealers are 

viewed as having a technical edge in the resources devoted to sophisticated financial analysis of 

the general factors moving the market, and in particular, the strength of demand for a given issue. 

A uniform-price format is perceived as leveling the playing field by reducing the importance of 

this specialized knowledge. According to Friedman, more bidders would be induced to bid 

directly in auctions because the fear of being awarded securities at too high a price is eliminated. 

The net impact of both factors, according to Friedman, would be to increase auction 

demand by enough to more than compensate for the revenues foregone by giving up 

discriminatory pricing. 

The Methodology 

In an effort to isolate the impact of auction technique, we compared the uniform-price 

auction performance of the 2-year and 5-year notes since September 1992 to the multiple-price 

performance of the same securities over the previous two years. Also, we compared the 

performance of the 2-year and 5-year notes under both auction formats to the multiple-price 

auctions of 3-year and 10-year notes over the whole period. 

7 Friedman's original argument regarding multiple-price auctions and the need for specialized 

knowledge also focused on the strong incentive for collusion among bidders. Reinhart (March 1992) 

and Chari and Weber (1992) also argue that uniform-price auctions will reduce market manipulation 

and the likelihood of a squeeze. 
5

In addition to auction technique, however, a constellation of other factors also affects 

auction results, such as the economic outlook, expectations for movements in absolute or relative 

interest rates, and any other factors affecting the portfolio decisions of dealers and investors. For 

example, the Treasury auction process has undergone regulatory and other changes that may also 

have had an impact on bidding strategies and trading practices of market participants. Also, the 

composition of the primary dealer community, as well as the large investor community, has 

changed over the years. The confluence of these and other factors produces significant auctionto-auction volatility in the data, making it difficult to isolate the impact of auction technique itself. 

For the 1995 Study, we divided the concentration data into two periods, the multiple-price 

auction period, January 1990 to August 1992, and the uniform-price period September 1992 to 

December 1994.8 In this update, we have added the period January 1995 to July 1998. 

The approach used to examine the effects of auction technique on concentration data was 

to compare concentrations of awards to the various groups and subgroups under the two auction 

techniques and to determine whether there was a statistically significant difference. 

The revenue data for the 1995 Study was also divided into two periods, which are slightly 

different from the periods used for the concentration analysis because of differences in data 

availability. The multiple-price period in this case includes data from June 1991 to August 1992, 

and the uniform-price period is from September 1992 to September 1995. We examined the 

effects of auction technique on revenues by comparing auction results in terms of bid yields in the 

auctions and yields in the contemporaneous when-issued (WI) market. We also examined trading 

patterns for the 2-year and 5-year notes on the mornings of auctions, around the time of auctions, 

8 We also broke each of these two periods into sub-periods. We divided the multiple-price period 

into the period before the Salomon Brothers improprieties were known (January 1990 to August 

1991) and the period afterwards (September 1991 to August 1992). The uniform-price period was 

originally further divided into periods of steady interest rates, rising interest rates, and falling interest 

rates. However, with only a couple of minor exceptions, there were no differences in results among 

these sub-periods. Data on auction bids, distribution of bids, and auction awards are U.S. Treasury 

data. 
6

and on the afternoons of auctions, both before and after the release of auction results, under the 

uniform-price and multiple-price techniques.9 We then examined whether any differences in 

performance are consistent with the purpose of conducting uniform-price auctions and whether 

the differences are consistent with the predictions of auction theory. 

The most direct way to determine the impact on revenue of auction technique is to 

compare auction prices under the alternate formats and determine if there is a statistically 

significant difference between the two. However, Treasury auctions are conducted in terms of 

yields, not prices. A direct comparison of auction yields is difficult because yields vary from 

auction to auction, giving rise to the need for a common reference point. Yields in the 

contemporaneous WI market provide such a common point of reference.10 

The contemporaneous WI yields are used as a benchmark against which to measure 

auction yields under the two formats because potential bidders for auctioned securities have a 

choice between purchasing securities at auctions or purchasing securities in the WI market 

anytime after the announcement of the securities to be auctioned. In particular, potential bidders 

face the choice between bidding in an auction or purchasing in the WI market in the time period 

from shortly before an auction up until the time of the auction.11 

The difference between auction yields and contemporaneous WI yields, or (Y

commonly referred to as the auction spread. A positive spread (or markup) means that the yield 

A - YWI), is 

9 Data on intraday market bid and ask yields and cumulative trading volume were obtained from 

GOVPX. 

10 Treasury auctions are usually held at 1:00 p.m. In some cases, such as when more than one 

security is auctioned on the same day, auctions have been held at other times. All data have been 

appropriately adjusted. 

11 Other issues regarding the relevance of the contemporaneous WI market, such as relative 

transaction sizes in auctions versus the WI market, yield movements around auction time, and market 

liquidity are addressed in the 1995 Study. 
7

in an auction is greater than the yield in the WI market at the time of an auction. Or, in terms of 

price, the price in an auction is lower than that in the WI market. 

To look at the distribution of awards we examined competitive awards at Treasury 

auctions. The competitive awards data is based on large competitive awards (based on bids of $1 

million or greater) to primary dealers, their customers, and direct bidders through the New York, 

Chicago, and San Francisco Federal Reserve banks and branches.12 We examined the 

concentrations of competitive awards, measured as percents of total private competitive awards, 

to the top five and top ten bidders and to respective bidder groups as a whole. We looked at four 

large bidder groups: primary dealers only for their own account; primary dealers plus their large 

customers; only large customers of primary dealers; and all large competitive bidders, whether 

primary dealers, other dealers, customers, or direct bidders. 

The Results 

As previously noted, the primary focus of the analysis is Treasury’s criteria for 

implementing the uniform-price auction technique: to determine whether it reduces financing 

costs, by encouraging more aggressive bidding, and whether it broadens bidder participation and 

distribution of awards on original issue. 

Distribution of Awards 

It is argued that uniform-price auctions will encourage more bidders to participate in 

competitive bidding by reducing the importance of specialized knowledge of market demand and 

the information costs associated with its collection. In October 1995, we found that the uniformprice technique did not expand the bidder base by bringing new groups of bidders, such as smaller 

12 Virtually all competitive bids and awards are made through these three banks and branches. 
8

bidders, directly into the competitive auction process. Within the large bidder groups, a 

reduction in the concentration of awards can be viewed as a corollary to increased distribution. 

In October 1995, we found no significant change in awards to the primary dealer 

community as a whole, but we found statistically significant evidence that the concentration of 

awards to the top primary dealers for their own accounts had been reduced. (See Chart 1.) The 

average shares of auction awards of 2-year and 5-year notes to the top five and top ten dealers 

declined, with the reductions ranging from about 5 percent to 15 percent. By contrast, the shares 

to the top dealers in 3-year and 10-year note multiple-price auctions either remained essentially 

the same or increased significantly. 

At the same time, the shares of awards to the top five, ten, and all large customers 

increased, with the total rising from about 17 percent to 25 percent for both the 2-year and 5-year 

notes, suggesting greater auction participation by large customers. (See Chart 2.) By contrast, 

the shares of awards to large customers for 3-year and 10-year multiple-price auctions over the 

same time periods did not change significantly. 

The reduced concentrations of awards to the top dealers reported in the 1995 Study may 

be attributed to two interrelated factors. The first is a widening in the overall distribution of 

auction bids under the uniform-price technique, as one might expect from auction theory. Under 

multiple-price auctions, there is a relatively tight distribution of large bids around the auction 

average because successful bidders pay the price actually bid. Under uniform-price auctions, 

however, the distribution of bids is much broader because there is no penalty for submitting bids 

well ahead of the market to ensure supply, unless such aggressive bids in the aggregate match or 

exceed the auctioned amount. 

The second factor is that the evidence suggests large dealers changed bidding strategies, in 

response to expected wider bid distributions, by splitting bids into more numerous smaller bids -­

some ahead of the market, some at the market, and some trailing off the market. 
9 

The combined effect of the broader distribution of bids and the greater incidence of bid 

splitting is that the bids of the larger, usually more aggressive dealers are increasingly interspersed 

with the more aggressive bids of other market participants (particularly large customers) who are 

trying to ensure supply in an auction. The net result is that at the margin the share of awards to 

the top groups of primary dealers has decreased. 

The recent data on the distribution of auction awards (January 1995 through July 1998) 

show similar results. Awards to the top five and top ten competitive bidders, whether primary 

dealers, dealers' large customers, or direct bidders, declined by significant amounts for the 2-and 

5-year notes during each part of the uniform-price period and for the period as a whole. (See 

Chart 3.) In most cases, the declines in concentration have remained relatively large over the 

whole period. For example, as originally reported, the share of awards to the top five competitive 

bidders for 2-year notes fell by about 10 percent, from about 45 percent to 35 percent, that for 5­

year notes fell by 17 percent, from about 53 percent to 36 percent, and the shares of both groups 

have remained around their lower levels since then. Meanwhile, the shares of awards to the top 

five, top ten, and all competitive bidders for 3-year and 10-year notes has remained essentially the 

same or increased. 

In addition, the data show there have continued to be statistically significant reductions 

over the entire uniform-price period in the shares of awards to the top primary dealers for their 

own accounts for the 2-year and 5-year notes. Over the same period, the shares of awards to the 

top five and top ten primary dealers of 3-year and 10-year notes remained essentially the same or 

increase. 

However, since 1995 there appears to have been an easing of the trend toward less 

concentration in the shares of awards to the top groups of primary dealers and to the top groups 

of large customers for both the 2-year and 5-year notes. For instance, although the shares of 

awards to the top dealers generally remain lower for the uniform-price period as a whole relative 

to the multiple-price period, the concentrations of awards to dealers have drifted upward. (See 
10

Chart 1.) Similarly, in the latest period, there has been some pullback in awards to large 

customers, so that their share of awards, although still higher, are no longer statistically different 

than under the multiple-price format. (See Chart 2.) The evidence suggests that some large 

customers may have returned to buying new supply from dealers rather than bidding in auctions 

through dealers. 

While the uniform-price technique continues to indicate reduced award concentrations to 

the top bidders, the recent trend toward slightly greater concentrations is a reflection of bids 

having become less dispersed. The tightening of bid distributions indicates a learning pattern on 

the part of primary dealers. As they have become increasingly experienced with the uniform-price 

technique, they have become more adept at gauging the relevant bidding ranges for the auctions.13 

Impacts on Revenue 

As described earlier, the most straightforward way to test whether the uniform-price 

auction technique reduces financing costs relative to the multiple-price technique, is to directly 

compare auction spreads, the difference between auction yields and contemporaneous WI yields, 

or (YA - YWI), under the two techniques. If the auction spread is significantly smaller under the 

uniform-price technique, then the premium to bidders is smaller, or alternatively, expected 

revenue to the Treasury is greater. 

Auction spreads are measured by comparing the announced auction yield results to the bid 

side of contemporaneous WI yields because dealers who need to cover short positions are far and 

away the primary participants in Treasury auctions, and short positions are established at the bid 

side of the WI market. 

13 This finding is supported by anecdotal evidence in conversations with primary dealers. 
11 

In the 1995 Study we examined the yields on accepted competitive bids in the 2-year and 

5-year note auctions held under the multiple-price auction format, from June 1991 through 

August 1992, and the uniform-price auction format, from September 1992 through September 

1995. The data showed that the average spreads of auction yield results over contemporaneous 

WI bid yields for 2-year and 5-year uniform-price auctions were smaller than those for multipleprice auctions, but the difference in yield spreads between the two auction techniques was not 

statistically significant. 

Chart 4 shows the average spreads between auction yield results and 1:00 p.m. WI bid 

yields for the multiple-price period, the whole uniform-price period, and also for two subperiods, 

that included in the 1995 Study and the data since then. As shown in the 1995 Study, the 

average auction spread for 2-year notes during the multiple-price period, 0.41 of a basis point, 

was cut by about half, to 0.22 of a basis point during the first part of the uniform-price period. 

For 5-year note auctions, the spread was reduced by about a third, from 0.33 to 0.20 of a basis 

point. The data since show the same results. By contrast, the spreads for the 3-year and 10-year 

note auctions, all held under the multiple-price format, increased during the latter period. 

Yet in spite of the proportionately large changes in the average auction spreads under the 

two auction techniques, we cannot say that there is a statistically significant difference between 

them for either the 2-year or 5-year note auctions. The primary reason for the lack of a 

statistically significant difference between auction spreads under the two formats is that under the 

uniform-price auction technique there is greater auction-to-auction volatility of the results with 

respect to the WI market. The greater volatility is partly a result of the broader and more volatile 

distributions of bids, and partly a result of the difference in the yield measure used to report 

auction results under the two techniques. In multiple-price auctions, an average yield concept is 

used, while in uniform-price auctions, the reported yield is not an average, but a marginal or stopout yield. An average of a relatively stable set of numbers is inherently less volatile than the 

endpoint of another set of numbers that exhibits more variability. Thus, uniform-price auctions 
12

may produce greater revenue on average, but present greater uncertainty regarding revenue at any 

given auction. 

Thus, a direct comparison of the average spreads under the two auction formats through 

September 1995 did not provide sufficient evidence to conclude that uniform-price auctions 

increased expected revenue to the Treasury relative to multiple-price auctions. However, by 

examining the average yield spreads for each technique separately, we did obtain significant 

results. That is, instead of comparing the spreads to each other, we examined whether auction 

results under the two techniques were significantly different from the yields in the 

contemporaneous WI market -- or whether the spreads themselves are significantly different from 

zero. The presence of statistically significant positive spreads between the auction results and the 

1:00 p.m. WI bid yields would represent expected premiums to successful competitive bidders, 

and expected revenue foregone by the Treasury. 

The results indicated that the average spreads between the auction average yields and the 

contemporaneous WI bid yields were positive and statistically different from zero for the 2-year 

and 5-year notes under the multiple-price format. For the 3-year and 10-year notes, the average 

spreads for the whole study period were also positive and statistically different from zero. 

By contrast, under the uniform-price format the average spreads for the 2-year and 5-year 

notes were not significantly different from zero. That is, the data showed that there was a 

statistically significant premium to successful bidders in multiple-price auctions, which implies that 

expected revenue to the Treasury is reduced, whereas there was no similar evidence of a 

significant premium to successful bidders under the uniform-price technique. This result is 

consistent with other evidence that there is a statistically significant premium for dealers bidding in 

multiple-price auctions.14 

14 See Simon (1994) and Nyborg and Sundaresan (1995). 
13 

Chart 4 also shows the data updated through May 1998. The addition of 64 more 2-year 

and 5-year note auctions, 32 of each, generates results consistent with those obtained previously. 

The average uniform-price auction spread for 2-year notes, at 0.20 of a basis point for the whole 

uniform-price period, still represents about a fifty percent reduction from the spread during the 

multiple-price period. Likewise, the average auction spread for 5-year notes, of 0.22 of a basis 

point, continues to reflect a drop of one-third from the multiple-price period. In addition, as 

measured by the standard errors, the volatility of auction-to-auction results for uniform-price 

auctions has been reduced in the latest period. 

The updated results continue to suggest, albeit not strongly, that expected revenue under 

the uniform-price technique is at least as great and probably greater than under the multiple-price 

technique. 

Volatility of auction-to-auction results 

The primary reason for the lack of statistical significance in the comparison of the yield 

results under the uniform-price technique to the contemporaneous WI yields is the auction-toauction volatility. Charts 5 through 9 show the behavior of the spreads of auction results to 1:00 

p.m. bid yields on an auction-to-auction basis for the 2-, 3-, 5-, 10- and 30-year securities. As 

charts 5 and 6 show, the behavior of the 2-year and 5-year spreads on an auction-to-auction basis 

under the two techniques is notably dissimilar. For the thirty multiple-price 2-year and 5-year 

note auctions from June 1991 to August 1992, the spreads between individual auction results and 

the 1:00 p.m. WI bid yields are almost uniformly non-negative (with the September 1991 2-year 

note auction being the only exception). For the forty multiple-price 3-year and 10-year note 

auctions (shown in Charts 7 and 8, respectively), in only three of the auctions have the average 

yields been below the 1:00 p.m. WI bid yields. 

Thus, the data show that under the multiple-price format there is a relatively stable and 

statistically significant average premium to successful competitive bidders. By contrast, under the 
14

uniform-price auction format, in more than half (70 out of 138) of the individual auctions from 

September 1992 to May 1998 the auction yields have been below the 1:00 p.m. WI bid yields, 

producing negative auction spreads. The import of this volatility for the purposes of this study is 

that, while on average uniform-price auctions may reduce financing costs, it is much less certain 

what the impact on revenue will be in any individual auction. 

Conclusions 

The Treasury's purpose in conducting uniform-price auctions is to determine whether the 

uniform-price auction technique reduces the Treasury's financing costs compared with multipleprice auctions, by encouraging more aggressive bidding by participants, and whether it broadens 

participation and reduces concentration of securities on original issue. Those are the criteria: the 

impact on revenues and the breadth of the initial distribution of awards. 

The main issue in empirically assessing the relative performance of the two auction 

techniques according to the criteria is actually two-fold: first, periodic Treasury auctions are only 

one of a vast array of very complex interdependent financial and economic events that occur every 

day. The auctions are not conducted ceteris paribus, as in a laboratory environment. The 

second, and corollary, factor is that, while the empirical results regarding breadth of distribution, 

or reduced concentration, are statistically significant, the results regarding the effects on revenues 

are weaker. In a direct comparison of the impact on revenues between the two techniques, the 

data show a small increase in revenues to the Treasury under the uniform-price technique, but the 

difference is not statistically significant.15 On this basis, we are unable to conclude that there is a 

difference in expected revenue. 

15 This is consistent with other findings. For example, see Heller and Lengwiler (1998). 
15 

However, by comparing the average auction yield spreads separately to the yields in the 

WI market, and testing whether each spread is statistically distinguishable from zero, we did 

obtain statistically significant results. The data show that the average yield spread is different 

from zero in multiple-price auctions, whereas there is no similar evidence for the uniform-price 

technique. On this basis, expected revenue under the uniform-price technique is marginally 

greater than under the multiple-price technique. 

The primary reason for the lack of a statistically significant difference between auction 

yields and WI yields under the uniform-price auction technique is greater auction-to-auction 

volatility of the results with respect to the WI market. The greater volatility is partly a result of 

the broader and more volatile distributions of bids, and partly a result of the difference in the yield 

measure used to report auction results under the two techniques. In multiple-price auctions, an 

average yield concept is used, while in uniform-price auctions, the reported yield is not an 

average, but a marginal or stop-out yield. An average of a relatively stable set of numbers is 

inherently less volatile than the endpoint of another set of numbers that exhibits more variability. 

Thus, uniform-price auctions may produce greater revenue on average, but they present 

greater uncertainty regarding revenue at any given auction. 
16

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AUCTION SPREADS Chart 5

AUCTION RESULTS - 1 PM WI BID YIELDS

2-YEAR NOTES

(June '91 through May '98)

Basis Points 

(2)

Averages and Std. Errors of Spreads 

Between Auction Yields & 1 pm WI Bid Yields 

6/91 - 8/92 9/92 - 5/98 

Avg. 

Std. Error 

0.41 b.p. 0.20 b.p. 

0.13 b.p. 0.15 b.p. 

(4)

6/91 10/91 2/92 6/92 10/92 2/93 6/93 10/93 2/94 6/94 10/94 2/95 6/95 10/95 2/96 6/96 10/96 2/97 6/97 10/97 2/98 

Auction Date 

Source: GOVPX, Inc. Department of the Treasury 

Office of Market Finance 

8 

6 

4 

2 

0 
AUCTION SPREADS Chart 6

AUCTION RESULTS - 1 PM WI BID YIELDS

5-YEAR NOTES

(June '91 through May '98)

Basis Points 

(2)

Averages and Std. Errors of Spreads 

Between Auction Yields & 1 pm WI Bid Yields 

6/91 - 8/92 9/92 - 5/98 

Avg. 

Std. Error 

0.33 b.p. 0.22 b.p. 

0.06 b.p. 0.21 b.p. 

(4)

6/91 10/91 2/92 6/92 10/92 2/93 6/93 10/93 2/94 6/94 10/94 2/95 6/95 10/95 2/96 6/96 10/96 2/97 6/97 10/97 2/98 

Auction Date 

Source: GOVPX, Inc. Department of the Treasury 

Office of Market Finance 

8 

6 

4 

2 

0 
AUCTION SPREADS Chart 7

AUCTION RESULTS - 1 PM WI BID YIELDS

3-YEAR NOTES

(August '91 through May '98)

Basis Points 

(2)

Averages and Std. Errors of Spreads 

Between Auction Yields & 1 pm WI Bid Yields 

8/91 - 8/92 9/92 - 5/98 

Avg. 

Std. Error 

0.50 b.p. 0.49 b.p. 

0.22 b.p. 0.09 b.p. 

(4)

8/91 2/92 8/92 2/93 8/93 2/94 8/94 2/95 8/95 2/96 8/96 2/97 8/97 2/98

Auction Date 

Source: GOVPX, Inc. Department of the Treasury 

Office of Market Finance 

8 

6 

4 

2 

0 
AUCTION SPREADS Chart 8

AUCTION RESULTS - 1 PM WI BID YIELDS

10-YEAR NOTES

(August '91 through May '98)

Basis Points 

(2)

Averages and Std. Errors of Spreads 

Between Auction Yields & 1 pm WI Bid 

Yields 

8/91 - 8/92 9/92 -5/98 

Avg. 

Std. Error 

0.56 b.p. 0.66 b.p. 

0.40 b.p. 0.14 b.p. 

(4)

8/91 2/92 8/92 2/93 8/93 2/94 8/94 2/95 8/95 2/96 7/96 10/96 2/97 8/97 2/98

Auction Date 

Source: GOVPX, Inc. Department of the Treasury 

Office of Market Finance 

8 

6 

4 

2 

0 
AUCTION SPREADS Chart 9 

AUCTION RESULTS - 1 PM WI BID YIELDS

30-YEAR BONDS

(August '91 through May '98)

Basis Points 

8 

6 

4 

2 

0 

(2) 

(4) 

8/91 2/92 8/92 2/93 8/93 8/94 8/95 8/96 2/97 11/97 

Averages and Std. Errors of Spreads 

Between Auction Yields & 1 pm WI Bid 

Yields 

8/91 - 8/92 9/92 -5/98 

Avg. 

Std. Error 

0.36 b.p. 0.46 b.p. 

0.19 b.p. 0.17 b.p. 

Auction Date 

Source: GOVPX, Inc. Department of the Treasury 

Office of Market Finance 

30