Initial Draft: 2002.11.11
Current Draft: 2003.04.03
Auction Participation and Market Uncertainty:
Evidence from Canadian Treasury Auctions
Dennis Lu Ö
Competition Bureau
Industry Canada
Jing Yang Ö
Financial Markets Department
Bank of Canada
Ö
This draft contains preliminary results and should not be quoted without permission of the authors. The views
expressed in this paper are those of the authors and does not necessarily reflect those of the Bank of Canada, the
Commissioner of the Competition Bureau, the Competition Bureau, and Industry Canada. The authors thank Guofu
Tan and Dave Bolder and Scott Hendry for their helpful comments and suggestions. All remaining errors are our
own. We thank Philippe Muller for his help in obtaining the data. We also thank Mark Pellerin, Paul ShakoDjunda, Grahame Johnson and George Nowlan for sharing their institutional knowledge with us.
Please address correspondence either to Dennis Lu, 50 Victoria Street, Gatineau, Quebec, K1A 0C9, call
819.956.2907, fax 819.953.6400, or email lu.dennis@ic.gc.ca or to Jing Yang, Bank of Canada, Ottawa, Ontario,
K1A 0G9, call 613.782.7893, fax 613.782.7136, or email JYang@bank-banque-canada.ca.
Auction Participation and Market Uncertainty:
Evidence from Canadian Treasury Auctions
Abstract
Using data from over 800 Canadian Treasury auctions on bonds and treasury bills from 1994 to
2001, we first investigate how the profits and auction concentration are affected by the level of
participation measured by the number of bidders and bids. We find that the bidders’ profits are decreasing
in the number of bidders while concentration is increasing in the number of bidders. We attribute the
latter to the increase in the bid quantity when the number of bidders increases. Moreover, we also find
that despite a similar impact on overall profits, the number of bids has a negative effect on auction
concentration. Secondly, we study how bidders change their bidding strategies in response to increased
market uncertainty and competition. We document empirical evidence in support of a Winner’s Curse and
Champion’s Plague in Canadian Treasury auctions. In fact, the bidders shift down their demand curves to
respond to increased market uncertainty. When faced with lessened competition, bidders are found to
lower bid prices and increase bid-to cover ratio. We also investigate the impact of an extreme even such
as
September,
11,
2001
on
Canadian
treasury
auctions.
1. Introduction
In this paper, we analyze the performance of treasury auctions using a data set
obtained from the Bank of Canada for over 800 auctions held from 1994 to 2001. We are
mainly interested in how these auctions perform and how the bidders adjust their
behaviour in response to the change in the number of participants and the uncertainty in
markets.
The effects of participation on auctions should be of interest to policy makers
owing to the possibility of consolidation in the Canadian financial markets.1
Since most
of the major players in these markets, especially the banks, are also auction participants,
any mergers by these players will likely affect the auctions. If the effects of participation
are significant, then the Bank and other policy makers may need to make institutional
changes to the auctions. This paper then provides a starting point for a study into making
such changes. It documents the features of the Bank’s auctions and provides evidence on
how participation and uncertainty affect these auctions.
Our analysis begins by examining the effect of the number of bidders on the
Bank’s auctions. In particular, we study the relationship between the participation
variables and the auction performance variables such as profits of bidders and
concentration of the winning bids. While theories on multi-unit auctions is relatively
scarce, theories on single unit auctions suggest ambiguous results for the effect of the
number of participants on bid price and bidders’ profits. In response to uncertainty,
current theories suggest that bidders may lower and disperse their bids in order to avoid
over-bidding.
Our results show a inverse relationship between profits and the number of bidders.
The discount, the difference between market yield and bid yield, is also found to be
negatively related to the number of bidders.
Taking the two together, we find that with
1
In 1998, four out of the five major Canadian banks attempted to merge but the Canadian government
blocked both mergers due to regulatory concerns. See Bolton and Kennish (2000) for more details.
1
more competition, participants bid at higher prices thereby lowering their profit. In a
multi-unit auction, a bidder may adjust the degree to which he spreads out his bids in
response to variation in auction participation and market uncertainty. We find that the
bidders increase bid dispersion and reduce bid quantity when faced with greater number
of bidders in Canadian treasury auctions.
Besides the number of bidders, we also use the number of bids as a proxy for the
level of auction participation. We find that the effects of the number of bids on bid price,
bid quantity and intra-bidder dispersion are very similar to that of the number of bidders.
A bidder is found to increase his bid price, bids dispersion and to reduce his bid quantity
when the number of bids increases. For auction concentration, we find the auction
allocation for top five winning bids is decreasing when the number of bids increases.
We also document how bidders in Canada adjust their bidding strategies in
response to an increase in market uncertainty. Bidders are found to reduce their bid prices
and increase bids dispersion in response to an increase in uncertainty. We also find that
market volatility is positively related to the profits of the winning bids but negatively
related to the concentration of the winning bids. This is likely to be a result of the change
in bidding strategies.
At the same time, concentration is reduced as the bidders are
dispersing their bids. With more competition, the winning bids capture less profit while
with more uncertainty, the winning bids capture more.
Lastly, to illustrate how extreme uncertainty may affect bid shading; we examine
the auctions right after the unexpected events of September 11, 2001.
For some
securities, we found that both bid discount and bids dispersion from these auctions were
relatively higher than the average values from the auctions over the entire sample.
The paper is organized as follows. Section 2 provides a short survey of the
literature related to treasury auctions. Section 3 discusses some institutional details about
the Bank of Canada's auction. Section 4 describes the raw data and how the data set was
constructed. Section 5 provides our empirical results regarding how the number of
2
participants and uncertainty affect the auctions. Section 6 concludes the paper with some
remarks. All tables are in the appendix.
2. Literature Review
The paper studies the effects of participation and uncertainty on the Bank of
Canada’s treasury auctions.2 In the literature, there are two general types of auctions,
private value and common value auctions. The difference between the two auction types
is fundamental in the theoretical literature on auctions, and has important implications for
bidding strategies. To relate the two types of auctions with our study, we distinguish the
two types on the basis of the predicted relationship between bid prices and the number of
competing participants. In turn, we can link bid prices to bidders’ profits and bidding
strategies. In this section, we draw out some empirical predictions of variations in the
number of bidders and market uncertainty for bidding behavior and auction performance.
Under a private value
auction, bidders’ valuation is based on personal
3
preferences . Differences in valuations are caused by idiosyncratic features in the bidders
themselves. In common value auctions, the auctioned good typically has an objective,
though unknown value (for example, the future resale price). In this case, the differences
in valuations are caused by differential estimates of the true value of the good by the
different bidders.
The implications of asymmetric information are very different for private value
and common value auctions. In a private value auction, a bidder’s belief would not be
affected by the other bidder’s private information. By contrast, in a common value
auction, a winning bidder would update his estimate upon learning the other bidders’
signals and realize that he most likely over-estimated the value of the object, this is called
2
Empirical studies on treasury bills auction tend to focus on how bidders may bid rates higher
than market rates because of risk associated with uncertainty. Examples include Cammack (1991)
and Nyborg, Rydqvist, Sundaresan (2002).
3
See Vickery (1961).
3
“winner’s curse”4. A rational bidder would reduce his bid price taking into account the
winner’s curse. Ausubel (1997) explains how the winner's curse may be compounded in
multi-unit auctions. In multi-unit auctions, the auctioned assets can be shared among
several buyers. A bidder then forms his conditional expectation based on the number of
units he won.
When buyers’ valuations are interdependent, the more a buyer wins the
worse news for him. Ausubel terms this phenomena as the “champion's plague”. A
rational bidder can shift down his demand schedule by reducing quantity at a given price
to account for this champion's plague.
As for the implication of changes in the number of bidders, private value and
common value auction theories provide different predictions. In a private auction, a
bidder’s estimate does not depend on his opponents’ information, so the number of
bidders should not affect his expected value of the object. However, the buyer may
change the bidding aggressiveness depending on the auction format. In a second price
auction, where the winner pays at the second highest bid, theory predicts that the optimal
bidding strategy for a buyer is to bid at his expected value of the object which is
independent from the number of participants. On the contrary, in a first price auction,
where the winner pays at his own bid price, auction theories predict that the optimal bid
price increases when the number of bidders increases. Since an increase in competition,
reduces the likelihood for a participant to win, each buyer should bid closer to his
expected value. Therefore, one possible outcome in a private value auction is that the bid
prices increase as the number of bidders increases.5 However, an opposite outcome in a
private value auction may also be possible when a private auction contains a commonvalue component. Pinkse and Tan (2001) demonstrate that this common-value component
may cause a buyer to lower his bid price when the number of bidders increases. They
refer to this effect as affiliation effect.6
4
Wilson (1977) and Milgrom and Webber (1982) were among the first to study this phenomena due to the
difference between the unconditional and conditional expectations of the goods being sold.
5
See Waehrer and Perry (2003).
6
Pinkse and Tan (2001) explain this effect in detail.
4
In a common value auction, winning the auction reveals to the winner that he may
have over-estimated the value of the auctioned object. Adding more bidders simply
aggravates this winner’s curse since out-bidding a large group of bidders may imply an
even greater overestimation of the object’s value.
A rational bidder adjusts his
expectation of the value of winning and therefore shades his bid accordingly. In short,
pure common value auction theory predicts an inverse relationship between bid prices
and the number of bidders. For examples, see Harstad (1990), Matthews (1994), Levin
and Smith (1994), Bulow and Klemperer (1999).
The question of whether treasury auctions are pure common value or private value
auctions is still undecided. The argument for common value auction is that primary
dealers buy in the auction mainly to resell in the secondary market. The existence of the
after-auction secondary market trading tends to imply the value of the auctioned security
is affected by the other bidders’ signals, which suggests a common value component in a
treasury auction. With a common value auction with no reserved price but allowing for a
perfectly competitive market, Bikhchandani and Huang (1989) were the first to model a
treasury auction in which the existence of a secondary market may induce higher bids in
order to obtain better prices from the resale buyers.
On the other hand, the existence of when-issued forward trading before the
auction implies that bidders are conditioning their bidding strategies on their own
idiosyncratic forward positions. To some extend, bidders may view a treasury auction as
a private value auction as they enter the auction with heterogeneous inventory positions
and bid accordingly. This implies that the results from an auction proceeded by forward
trading may significantly differ from the predictions of models where there is no such a
market. Viswanathan and Wang (2000) are among the first to build a model that
considers the Treasury auction process (multi-unit auction) along with pre-auction
heterogeneous
inventories
an
after-auction
trading.
They
demonstrate
that,
with
heterogeneous inventory across bidders (private value), after-auction trading creates a
common-value component for the auctioned security since the other bidders’ signal
affects the after-auction trading price. Furthermore, the existence of when-issued trading
seems to have the opposite effect on buyers’ bidding strategies. The common value effect
5
(refered to as affiliation effect in Pinkse and Tan, 2001) suggests bidders bid more
cautiously to offset the winner’s curse; while a risk-reduction effect—any quantity
received in the auction is partially hedged in the when-issued market—might induce
more aggressive bidding in the auction. Overall, in terms of the impact of changes in the
number of bidders on bid prices, the model suggests an ambiguous result.
To the best of our knowledge, there is no study on how mergers among bidders
may affect multi-unit auctions but there is a small theoretical literature dealing with the
effects of mergers among the bidders on auctions. Mares and Shor (2003), using a singleunit, common value auction framework, show that a merger among bidders has two
countervailing effects: a competition effect and an informational effect. On the one hand,
the merger reduces the number of active bidders and, in turn, competition. This lessened
competition may reduce the price paid at auction. On the other hand, the pooling of
information within bidders increases the precision of estimates of the value of auctioned
object, which may lead to more aggressive bidding. They demonstrate that more
aggressive bidding does not offset the downward price pressures of diminished
competition. Other studies on the effect of mergers include Brannman and Froeb (1997),
Waehrer (1997), Froeb, Tschantz, and Crooke (1998), Dalkir, Logan, and Masson (2000).
However, these papers are typically motivated by examples dealing with a buyer holding
an auction among sellers.
Empirical studies on treasury bill auctions tend to focus on how bidders may bid
rates higher than market rates because of risk associated with uncertainty.
example, Cammack, 1991 and Nyborg, Rydqvist, Sundaresan, 2002).
(See, for
More recently,
Keloharju, Nyborg and Rydqvist (2002) observe that bidders in the Finnish Treasury
auctions have not significantly changed their demand schedules due to increase
competition.
They hypothesize that the bidders may have monopolistic power in order to
explain their findings.
3. The Bank of Canada's Auction
In this section, we summarize the institutional features of the Bank of Canada
auctions for Treasury bills and bonds. Treasury bills are short-term securities with
6
maturity within 12 months while bonds are long-term securities that mature between 2 to
30 years in the future. The Bank of Canada holds auction on 3, 6 and12 month treasury
bills once every two weeks and 2, 5, 10 and 30 year nominal bonds once every quarter. In
all auctions, the participants are informed one week in advance as to the types and the
quantities of securities to be auctioned.
The Canadian treasury auctions are multiple-unit, discriminatory, and sealed-price
auctions. The bidders can submit multiple bids for multiple units. Auction participants
submit tenders electronically before the specified time deadline. Tenders can be either a
competitive bid or a non- competitive bid . A competitive bid constitutes a yield-quantity
pair while a non-competitive bid comprises of only a quantity. For example, a
competitive bid is to buy $10 million at 5%; a non-competitive bid consists only of the
amount, $3 million. Each bidder is allowed only one non-competitive bid with a limit of
$3 million.
There are two types of bidders: government securities distributors and customers.
Customers cannot bid directly in the auction while government securities distributors bid
on their own behalf, subject to auction limits, as well as submitting bids for its customers.
The bids for customers must be listed separately and have their own auction limits. Some
of the distributors are designated as primary dealers whose participation in both the
primary and secondary markets for the Government of Canada securities must be above a
certain threshold level. The Bank of Canada can participate in the auction by submitting
non-competitive bids; the upper limit on a non-competitive bid does not apply to the
Bank. However, the Bank will in advance announce the quantity it will bid in an auction.
Different auction constraints apply to different types of participants. All
participants are subject to the maximum bidding limit: one third of the issue amount in a
Treasury bill auction and one fifth in a bond auction. Primary dealers, a subset of
government securities distributors, are also subject to constraints in the form of minimum
bid price and quantity. The minimum bid quantity for a primary dealer is determined
based on a primary and secondary market participation. Each distributor also has a
customer submission limit or how much each customer can bid through the dealer.
7
Finally, there is an aggregate limit for the amount that a distributor and its customers can
bid. Each distributor's bidding limit is then determined via its own limit, its customer’s
submission limits, and the aggregate limit.
When the auction closes, the Bank distributes the auction units to bidders. Noncompetitive bids are allotted in full, prior to competitive bids, at a common price using a
quantity weighted average of all wining yields. Afterwards, the competitive bids are filled
starting with the lowest yield and continuing up until the Bank of Canada reaches the
cutoff yield. The cutoff yield is the lowest yield where the sum of noncompetitive and
competitive bid quantities is greater than or equal to the issuing amount. If the total
quantity demanded at the cutoff yield is greater than the auction quantity, the bid quantity
at the cutoff yield is only partially allotted. If there is more than one bidder at the cutoff
yield, the remaining amount is shared among the bidders weighted according to the
amount of their bids.
3.1. An Example
Table 1 provides some descriptive statistics from one particular auction. The issue
amount was $2,500 million and was fully allotted. There were 12 bidders with 36 bids.
The highest bid yield is 5.3% and the lowest bid yield is 5.148%. The second and third
columns list the yield-amount bids.
In the first entry, LJB's bid of $3 million is a non-competitive bid, as it has not a
yield amount. Being a non-competitive bid, it is filled first or allocated its full bid amount
ahead of all competitive bids. By having the lowest bid yield of 5.148%, bidder FKA's
competitive bid amount of $25 million is filled next.
Each subsequent bidder is filled until the bid yield reaches 5.2%, which is then the
cutoff yield. At this yield, only $655.5 million out of the issue amount have not been
allotted. Furthermore, there are 6 bids at 5.2% with a total bid amount of $720 million.
Since bidder AXG's bid amount was $100 million, the bidder is then allotted (100/720) x
$655.5 = $91.042 million.
8
The average yield is then calculated as follows: average yield = average yield x (3
/ 2,500) + 5.148% x (25 / 2,500) + 5.165% x (50 / 2,500) + …+5.2% x (655.5 /2,500).
For this auction, the average yield is calculated to be 5.189805%.
4. Data
The data set contains the actual demand schedules of the bidders as well as the
auction awards to each winning bidder for over 800 Bank of Canada auctions. The
bidders may either be a government securities distributor or a customer. As a reference
point, we try to use the same variables as in Nyborg, Rydqvist, and Sundaresan (2002).
For each auction of a particular type of security, there are two types of the auction
variables: bidding variables and auction performance variables.
4.1. Bidding variables
For bidding variables, we have the following for each auction and the
participating bidders: bidding discount, quantity, and intra-bidder dispersion.
Given
auction i, let (a ij (b) , yij (b) ) be a amount-yield pair in bid number b submitted by bidder
j. For the same auction, let n ij be the number of bids submitted by bidder j. In auction i,
bidders j’s average bid amount is then
∑
=
n ij
aij
b =1
a ij (b)
nij
,
(1)
while bidder j’s average bid yield is
yij =
1
n ij
yij (b) .
∑
nij b=1
(2)
9
The discount variable δ ij is calculated as the difference between each bidder’s
quantity-weighted average bid yield and the market yield at the end of the day,
 nij

δ ij =  ∑ yij (b) wij (b)  − Yi
 b=1

(3)
where Yi is the market yield at the end of the auction day and weight wij (b) is the
fraction of bid b in the total quantity bid by j in auction I, ie. wij (b) =
aij (b)
∑b=1 aij (b)
nij
.
The quantity variable qij is measured as the ratio of each bidder's average bid
amount to the auction issue amount,
q ij
∑
=
nij
b =1
a ij (b )
Qi
,
(4)
where Qi is the issue amount for the auction.
The dispersion variable is calculated as the quantity-weighted standard deviation
of bidder j’s bid yield in auction i.
σ ij =
1
nij
(∑
nij
b =1
)
( yij (b) − yij ) 2 wij (b) .
4.2. Auction Performance Variables
10
(5)
To measure the performance of each auction, the performance variables are
calculated for each auction rather than for each bidder. These performance variables are
profit and concentration.
For auction i, let N i be the number of bidders per auction. First, we need to define
another weight wˆ ij ( b) as
wˆ ij (b) =
aˆ ij (b)
(6)
∑k =1 aˆ ij ( k )
nˆij
where aˆij (b) and yˆ ij (b) are the allocated quantity and the winning competitive bid yield
for bid b of bidder j. The profit variable is determined as the difference between the
average of all bidders’ quantity-weighted winning bid yield and the market yield at the
end of the day. It is defined as,
Ni
πi = ∑
j =1
(∑
nij
b =1
)
yˆ ij (b)wˆ ij (b) − Yi .
(7)
where N i is total number of bidders in auction i. Note that the weights for the
performance variables are constructed using the winning bid quantities, as opposed to all
the submitted bid quantities which are used to
construct the weights in the bidding
variables.
The concentration variable is defined as the ratio of top five winning bid
quantities to the total allocation for all competitive winning bids.
Note that we do not
include the allocation for non-competitive bids.
 ∑ nij aij (b)ϕ ij ( b) 
,
φ i = ∑  b =1


A
j =1
i


Ni
(8)
∆
1 : b ∈ D
where ϕ ij (b) = 
and D = { set of top 5 wining bids}.
0 : b ∉ D
11
where ϕ ij (b) takes value of one if bid b is one of the top five winning bids, and zero
otherwise. Ai is the allocation for all competitive winning bids in auction i.
4.3. Market Uncertainty
To measure uncertainty, we estimate auction day volatility using an ARCH (2)
process for bond returns. This is a measure for the precision of bidders' signals. Let Pt be
the bond price. Assume that the bond return follows a random walk with drift given by
Pt − Pt −1
=θ +εt
Pt −1
We pool the cross section and time series data for Treasury bills with three
months, six months and one year to maturity and four bench mark bonds with two, five,
ten and thirty years to maturity between 1994-2001. We calculate DURt as the durations
for all the benchmark bonds to control for the convexity of the yield curve. Our
uncertainty measure is the volatility of the error term in equation above is defined as
ε t2 = β 0 + β 1ε t2−1 + β 2 ε t2−2 + β 3 DUR t + et
5. Empirical Findings
In this section, we investigate how the Bank of Canada’s auctions are affected by
participation as well as uncertainty.
We use the number of bidders and the number of
bids to measure auction participation and the conditional volatility of bond returns to
measure market uncertainty.
Since the number of bidders and the number of bids are
correlated, we run ten separate regressions with pooled cross section data on bid discount,
dispersion, quantity, profit and concentration:
Z = α1Voli + α 2 Sizei + α 3 Bidders i + α D + µ t
or
Z = α1Voli + α 2 Sizei + α 3 Bids i + α D + µ t
12
where Z = [δ i , σ i , qi , π i , φi ] or equivalently, the variables: discount, dispersion , quantity,
profit, and concentration.
The other variables are defined as follows: Vol
is the
conditional volatility, Size is the size of each auction, Bidders is the number of bidder,
and Bids is the number of bids. To capture the fixed effect from securities across different
maturities, we include six dummy variables, which are denoted in the matrix,
D = [ D3 M , D6 M , D1Y , D 2Y , D5Y , D10Y , D30Y ] with the corresponding vector of coefficients,
α . For example, the dummy variable, D3 M , takes value of one if the security is the 3-
month treasury bill and zero otherwise.
5.1. Summary Statistics
In calculating the summary statistics, we compute the average discount, quantity
and dispersion as follows: δ i =
∑
Nj
j =1
Nj
δ ij
,qi =
∑
Nj
j =1
Nj
qij
,σ i
∑
=
Nj
σ ij
j =1
Nj
. The results are
listed in Tables 2 and 3.
Taking the monthly average of all auctions, Figure 1 shows that the number of
bidders and bids has been declining over time.
Linear trends are added to illustrate the
decline in both variables. The average number of bidders for each auction is 18.379 with
a minimum of 9 bidders and a maximum of 26. The average number of bids is 63.422
with a minimum of 30 and maximum of 117. On average, each bidders making 3.45 bids
in each auction.
concentration.
Figure 2 describes the monthly average of all auctions for profits and
Using a Dickey-Fuller test with a 5% critical value, the series for profits
is found to be stationary when include a time trend, while the series for concentration is
found to be non-stationary. The averages are 0.0163 for profits and 0.6686 for
concentration.
As for volatility and size, the monthly average of all auctions is shown in Figures
3 and 4. The series for volatility is stationary while the series for size is non-stationary at
a 5% significant level. Note the spike around September 11, 2001 for the volatility series
13
in Figure 3. Average volatility is 0.000153 with a standard deviation of 0.000041, while
the average size is 1858.7 ($ million) with a standard deviation of 716.04.
As for the
rest of the variables, the average values are: 0.040 for discount, 0.00514 for dispersion,
and 0.038131 for quantity.
5.2. Impact of auction participation
Our empirical results on the first group of regressions with the number of bids are
listed in Table 4. The coefficients for bidders are significant in all the regressions. Since
the number of bidders is used as a proxy for the competition level, we have the expected
result:
the bidding discount and winning profit decrease in the number of bidders, or the
level of competition. The results imply that for every additional bidder entering the
auctions, the average profits of the bidders are reduced by 2.8 basis points. Competition
among bidders reduces the rent that the winning bidders can extract from the auction.
Mares and Shor (2003) demonstrate that mergers among bidders leads to less
aggressive bidding. In the regression of discount, the number of bidders has a negative
impact on bid shading. With fewer bidders, bidders increase their bid shading and bid
more cautiously. In the regression on bid quantity, the negative coefficient shows that, in
response to lessened competition, bidders increase the quantity demanded. Taking the
two effects together, when faced with reduced number of participants, bidders tender a
lower price or larger quantities7 .
The effects of the number of bids on bidding are very similar to that of the
number of bidders. Table 5 shows that the coefficients for bids are all significant in the
regressions except for the regression with profit. The decision on being a bidder depends
on how much profit is made in the auction, not the number of bids. Like the coefficient
for bidders, the coefficient for bids is positively related to bid dispersion and negatively
7
Note that change in the number of bidders and a merger are not necessarily the same. This research does
not measure the informational effect that occurs with a merger. After merge, the merged bidder shares a
14
related to the bid shading and quantities. As expected, the number of bids has a
significant and negative effect on concentration.
5.3. Impact of market uncertainty and size
The coefficients for volatility are significant at the 5% level in Table 4 for the
regressions with discount, dispersion, and award concentration as dependent variables.
Furthermore, volatility is significant at the 10% level for the quantity regression but not
significant for the profit regression.
From the regressions for discount and dispersion, we
find positive coefficients for volatility which indicate that the difference between bid
yields and market yields increases with market volatility. This result is consistent with
Cammack (1991), Bikhchandani and Huang (1991), Nyborg, Rydqvist, Sundaresan
(2002), Keloharju, Nyborg, and Rydqvist (2002), and others. The results for bidding
dispersion, consistent with Sundaresan (1994), show that bid dispersion is negatively
related to the auction size and positively related to market volatility. In the regression for
quantity, the coefficient for volatility is negative, as found by Nyborg, Rydqvist, and
Sundaresan (2002).
This result supports the “champion’s plague” hypothesis which
predicts that a bidder may want to reduce his bidding quantity in response to an increase
in uncertainty.
From both Table 4 and Table 5, the coefficients for size are all significant at the
5% level, except for the coefficient for dispersion regression with the number of bids as
an independent variable.
Furthermore, all the coefficients move in the same direction
whether the regression uses the number of bidders or the number of bids as an
independent variable.
In the regressions for discount, auction size is positively related to the discount,
which suggests that the larger the auction size the lower bid prices. Moreover, an increase
in the auction size results in higher profits and lower concentration.
With larger auction
joint information set; this informational advantage may lead higher bid price. Our research has only
captured the competition effect caused by a reduction in the number of bidders.
15
size, the bidders can extract higher rents but, at same time, win smaller portions of each
auction.
5.4. Fixed Effects: Different Securities
There are seven types of securities in our samples:
3-month, 6-month, 1-year
treasury bills, and 2-year, 5-year, 10-year, and 30-year bonds. We construct dummies to
capture the fixed effects from the seven different securities. With no intercept, the
dummy variable coefficients reflect the average bid shading, bid dispersion, quantity,
profit, and award concentration for each individual securities, taking account the size of
the auction, the volatility of the secondary markets, and the number of bidders or bids.
First of all, the dummy variables are significant in most of the regressions in
Table 4 and Table 5.
For brevity, we only discuss the results in Table 4 since the results
in Table 5 are quite similar.
Expected profits in yields diverge greatly across the different securities. The 2year bond auctions have the highest average profit of 9.107%. Yet, at the two ends of the
yield curve, the average profits are both negative for 30-day treasury bills and 30-year
bonds. We postulate that the results may be due to the different features on the secondary
markets for these securities.
The average award concentrations appear to be similar
across different securities with a slightly greater concentration in treasury bills auctions
than in bonds auctions.
The coefficients for discounts are mostly positive, regardless of the type of
security. Among them, the 2-year bond auctions seem to have the largest discounts,
roughly seven times the discount for the 1-year treasury bill auctions. In the quantity
regression, all the treasury bills and bonds have similar expected bidding quantities after
controlling for the auction size effect.
16
5.5. Extreme Uncertainty: September 11, 2001
From the market volatility data in Figure 5, we clearly observe a spike around
September 11, 2001. Following that date, the Bank of Canada held three treasury bill
auctions: 3-month, 6-month, 1-year. To compare how the bidders react to extreme
uncertainty, we use a t-test to compare how the average discounts and the average
dispersion differ from the auctions after September 11 and from the auctions in the rest of
the sample.
From Table 6, only the values for the auction from the 3-month auction were
both significant. The average discount and dispersion increased in this auction relative to
all other auctions.
With such an unexpected event, our earlier results on the effects of
uncertainty on bidding behavior are supported, albeit only for 3-month treasury bills.
6. Conclusion and further research
Using data from over 800 Canadian Treasury auctions on bonds and treasury bills
from 1994 to 2001, we find that bidders’ profits are decreasing in the number of bidders
while the concentration increases with the number of bidders. Moreover, we also find that
despite a similar impact on overall profit, the number of bids has a negative effect on
auction concentration. We do not yet have satisfactory models of auctions to help explain
this difference. We document empirical evidence in support of a Winner’s Curse and
Champion’s Plague in Canadian Treasury auctions. Bidders shift down their demand
curves to respond to increased market uncertainty. In support of Mares and Shor’s (2003)
prediction, we find that bidders bid a lower price when faced when facing lessened
competition.
In the future work, we will test the impact of when-issued market trading on the
auction performance. One needs to study the when-issued market to pin down the
determinants of
the dependent variables such as bid shading, bid quantity and bid
dispersion. In the Canadian treasury auction, bidders are required to disclose their long or
17
short positions on the when-issued market when they enter the auction. Therefore, our
data set is best suited for an investigation of the linkage between forward trading and the
bidders’ bidding behaviour and auction performance.
Another aspect to examine is how the Bank of Canada’s treasury auctions have
changed over time.
Sundaresan (1994) finds qualitatively different auction results for the
period 1980-1983, which had relatively high interest and market volatility, and the period
1984-1991 for the U.S. treasury markets.
He also shows that the bid-cover ratio is
inversely related to dispersion of the winning bids.
Lastly, the role of information in these auctions is not clear. Mares and Shor
(2003) show that one effect of mergers among bidders is that the pooling information
within bidding rings increases the precision of competing estimates, which leads to more
aggressive bidding. This information effect offsets the effect of less competition on
prices. Their paper demonstrates that the reduction in competition dominates the
informational effect, resulting in lower prices. In the future work, we will empirically
estimate the magnitude of the informational effect.
18
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19
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21
Appendix
Table 1. Sample from a Treasury Bill Auction
Bidder
LJB
FKA
FPB
KVI
LZE
AXG
AXJ
KVI
KVI
FPB
AXJ
LJB
LJB
LZE
TOA
FPB
AXG
AXJ
LJB
LJB
LJB
YPQ
LJB
RWE
AXJ
YPQ
RWE
YPQ
AXG
TOA
LZE
RWE
FKA
FPB
JQS
RFB
Yield
Amount Awarded
(%)
($million)
($million)
5.148
5.165
5.168
5.17
5.18
5.18
5.18
5.184
5.188
5.19
5.19
5.19
5.19
5.198
5.199
5.2
5.2
5.2
5.2
5.2
5.2
5.205
5.208
5.21
5.21
5.213
5.22
5.23
5.236
5.248
5.248
5.25
5.25
5.25
5.3
3
25
50
100
50
31.5
50
10
525
75
50
150
300
100
250
75
100
25
20
100
250
225
100
25
25
200
100
200
100
250
100
200
400
200
200
100
3
25
50
100
50
31.5
50
10
525
75
50
150
300
100
250
75
91.042
22.76
18.208
91.042
227.604
204.844
22
Table 2. Summary statistics of the exogenous variables
Volatility
Mean
Size
Bidders Bids
0.000153 1858.7 18.379 63.422
Standard Deviation 0.000041 716.04
Minimum
0.000137 850
Maximum
3.244 13.718
9
30
0.000865 3990
Observations
883
883
26
117
883
883
Table 3. Summary statistics of the endogenous variables
Mean
0.040
Award
Concentration
0.000514 0.038131 0.0163
0.6686
Standard Deviation
0.069
0.002322 0.051252 0.0570
0.2363
Minimum
Maximum
-0.910
0.850
0.000000 0.000001 -0.2500
0.100000 0.380000 0.5000
0.2100
0.9900
Observations
15466
Discount Dispersion Quantity
15466
23
15466
Profit
883
883
Table 4. Effects of uncertainty and participation on bidding behavior and auction
performance (bidders)
Profit
Award
Concentration
Discount
Dispersion
Quantity
-0.00028
(-2.1239)*
59.2418
(5.4290)*
0.5011E-05
(4.4351)*
0.00380
(9.5631)*
-235.135
(-7.0904)*
-0.141 E-03
(37.6825)*
-0.393E-03
(-2.4453)*
125.238
(9.351)*
0.602E-05
(3.6396)*
0.12E-04
(1.94)**
7.9885
(16.0274)*
-0.20190E-07
(2.18135)*
-0.831E-03
(-7.2972)*
-10.5967
(-1.1158)
-0.14E-04
(-13.0074)*
3M
-0.0182
(-3.9345)*
1.0882
(77.4024)*
-0.004895
(-0.8622)
-0.001388
(-6.569)*
0.09434
(23.4321)*
6M
-0.001326
(-0.3707)
0.79142
(72.813)*
0.01525
(3.47615)*
-0.001147
(-7.0198)*
0.07691
(24.7107)*
1Y
0.00043
(0.12639)
0.7176
(69.433)*
0.01588
(3.8061)*
-0.001064
(-6.8526)*
0.06864
(23.1944)*
2Y
0.09107
(17.4320)*
0.9476
(59.683)*
0.10865
(16.9448)*
-0.000823
(-3.4466)*
0.08919
(19.6161)*
5Y
0.03717
(8.0377)*
0.82127
(58.428)*
0.05331
(9.3917)*
-0.00082
(-3.9025)*
0.07974
(19.811)*
10Y
0.0369
(8.0665)*
0.7854
(56.419)*
0.05329
(9.4803)*
-0.00086
(-4.1496)*
0.07505
(18.828)*
30Y
-0.0222
(-4.777)*
0.6588
(46.5521)*
-0.00590
(-1.03327)
-0.00078
(-3.6676)
0.06272
(15.477)*
R-square
0.1651
0.2129
0.1249
0.0255
0.0197
R-square, adjusted
0.1646
0.2124
0.1243
0.0249
0.0191
Bidders
Volatility
Size
Note: t -statistics are presented in the parenthesis.
* Significant at the 5% level or better
** Significant at the 10% level or better
24
Table 5. Effects of uncertainty and participation on bidding behavior and auction
performance
Profit
Award
Concentration
Discount
Dispersion
Quantity
-0.30E-04
(-0.84228)
59.0854
(5.40838)*
0.6E-05
(4.5594)*
-0.00237
(-21.9365)*
-273.162
(-8.3308)*
-0.122E-03
(-31.8468)*
-0.76E-04
(-1.709)**
124.54
(9.2893)*
0.600E-05
(4.0090)*
0.7E-05
(4.054)*
8.0728
(16.186)*
-0.20110E-07
(1.0723)
-0.443E-03
(-14.191)*
-16.137
(-1.705)**
-0.10E-04
(-9.0068)*
3M
-0.02231
(-5.3964)*
1.24579
(100.39)*
-0.00951
(-1.875)**
-0.001412
(-7.4812)*
0.09484
(26.4874)*
6M
-0.00492
(-1.5454)
0.9763
(102.074)*
0.01176
(3.007)*
-0.001259
(-8.6514)*
0.08328
(30.1756)*
1Y
-0.00305
(-0.9809)
0.9191
(98.622)*
0.01278
(3.353)*
-0.001217
(-8.5847)*
0.0777
(28.8921)*
2Y
0.08708
(17.787)*
1.1490
(78.197)*
0.10473
(17.431)*
-0.000939
(-3.4466)*
0.09578
(22.5897)*
5Y
0.03331
(7.6545)*
1.0426
(79.825)*
0.04982
(9.3294)*
-0.00082
(-4.2026)*
0.08946
(23.7375)*
10Y
0.03329
(7.5173)*
1.0214
(76.836)*
0.05031
(9.2562)*
-0.00107
(-5.3182)*
0.08762
(22.8442)*
30Y
-0.02567
(-5.5222)*
0.9111
(65.2859)*
-0.00834
(-1.4622)
-0.00103
(-4.8713)*
0.07840
(19.4697)*
R-square
0.1649
0.23.21
0.1247
0.0263
0.0289
R-square, adjusted
0.1644
0.23.17
0.1242
0.0257
0.0284
Bids
Volatility
Size
Note: t -statistics are presented in the parenthesis.
* Significant at the 5% level or better
** Significant at the 10% level or better
25
Table 6. Auctions on September 13, 2001
Discount
Dispersion
3-month
All Others
September 13
0.278E-04
0.621E-04
0.316E-05
0.817E-04
(-1.528)**
(-2.025)*
All Others
6-month
0.360E-1-year01
0.456E-03
September 13
0.488E-01
0.628E-03
(1.12)
(-0.99)
All Others
1-year
0.365E-01
0.522E-03
September 13
0.605E-01
0.751E-03
(-2.04)*
(-0.75)
Note: t -statistics are presented in the parenthesis.
* Significant at the 5% level or better
** Significant at the 10% level or better
26
19
94
-0
19 6
94
-0
19 9
94
-1
19 2
95
-0
19 3
95
-0
19 6
95
-0
19 9
95
-1
19 2
96
-0
19 3
96
19 06
96
-0
19 9
96
-1
19 2
97
-0
19 3
97
-0
19 6
97
-0
19 9
98
-0
19 1
98
-0
19 4
98
-0
19 8
98
-1
19 1
99
-0
19 2
99
-0
19 5
99
-0
19 8
99
-1
20 1
00
-0
20 2
00
20 05
00
-08
20
00
-1
20 1
01
-0
20 2
01
-0
20 5
01
-0
20 8
01
-11
monthly average
Figure 1. Monthly Average of All Auctions, 1994. 06 to 2001.12: Number of Bidders and Bids
90
80
70
60
50
bidders
bids
40
y = -0.2342x + 66.751
2
R = 0.4005
Linear (bids)
30
20
10
y = -0.138x + 22.984
2
R = 0.8822
0
auction date
27
Linear (bidders)
19
94
-0
19 6
94
-0
19 9
94
-1
19 2
95
-0
19 3
95
-0
19 6
95
-0
19 9
95
-1
19 2
96
-0
19 3
96
-0
19 6
96
19 09
96
-12
19
97
-0
19 3
97
-0
19 6
97
-0
19 9
98
-0
19 1
98
-0
19 4
98
19 08
98
-1
19 1
99
-0
19 2
99
-0
19 5
99
-0
19 8
99
-1
20 1
00
-0
20 2
00
20 05
00
-08
20
00
-1
20 1
01
-0
20 2
01
-0
20 5
01
-08
20
01
-11
monthly average
Figure 2. Monthly Average of All Auctions, 1994. 06 to 2001.12: Profit and Concentration
1.2
1
0.8
0.6
profit
0.4
concentration
y = -0.0044x + 0.9109
2
R = 0.4644
0.2
0
-0.2
auction date
28
19
94
-0
19 6
94
-0
19 9
94
-1
19 2
95
-0
19 3
95
19 06
95
-0
19 9
95
-1
19 2
96
-03
19
96
-0
19 6
96
-0
19 9
96
-1
19 2
97
-0
19 3
97
-0
19 6
97
-0
19 9
98
-0
19 1
98
-0
19 4
98
-0
19 8
98
-11
19
99
-0
19 2
99
-0
19 5
99
-0
19 8
99
-1
20 1
00
-0
20 2
00
-0
20 5
00
20 08
00
-11
20
01
-0
20 2
01
-0
20 5
01
-0
20 8
01
-11
monthly average
Figure 3. Monthly Average of All Auctions, 1994. 06 to 2001.12: Volatility
0.0006
0.0005
0.0004
0.0003
volatility
0.0002
0.0001
0
auction date
29
19
94
-0
19 6
94
-0
19 9
94
-1
19 2
95
-0
19 3
95
-0
19 6
95
-0
19 9
95
-1
19 2
96
-0
19 3
96
-06
19
96
-0
19 9
96
-1
19 2
97
-0
19 3
97
-0
19 6
97
-0
19 9
98
-0
19 1
98
-04
19
98
-0
19 8
98
-1
19 1
99
-0
19 2
99
-0
19 5
99
-0
19 8
99
-11
20
00
-0
20 2
00
-0
20 5
00
-0
20 8
00
-1
20 1
01
-0
20 2
01
-0
20 5
01
-0
20 8
01
-11
monthly average
Figure 4. Monthly Average of All Auctions, 1994. 06 to 2001.12: Size
4500
4000
3500
3000
2500
size
2000
1500
1000
500
0
auction date
30
19
94
-0
19 6
94
-0
19 9
94
-1
19 2
95
-0
19 3
95
-0
19 6
95
-0
19 9
95
-1
19 2
96
-0
19 3
96
-0
19 6
96
-0
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96
-1
19 2
97
-0
19 3
97
-0
19 6
97
-0
19 9
98
-01
19
98
-0
19 4
98
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98
-1
19 1
99
-0
19 2
99
-0
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99
-0
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99
-11
20
00
-0
20 2
00
-05
20
00
-0
20 8
00
-1
20 1
01
-0
20 2
01
-0
20 5
01
-0
20 8
01
-11
average monthly volatility
Figure 5. Monthly Average of All Auctions, 1994. 06 to 2001.12: 3M, 6M, and 1Y Securities
0.0006
0.0005
0.0004
0.0003
3M
6M
1Y
0.0002
0.0001
0
auction date
31