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Journal of Banking & Finance 26 (2002) 1165–1179
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The Canadian treasury bill auction and
the term structure of interest rates
Lise Godbout a, Paul Storer
b,c
, Christian Zimmermann
c,d,*
a
Laurentian Bank of Canada, Montreal, Canada
Western Washington University, Bellingham, WA, USA
c
Center for Research on Employment and Economic Fluctuations, Universit
e du Qu
ebec a Montr
eal,
Montreal, Canada
d
D
epartement des Sciences Economiques, ESG, Universit
e du Qu
ebec a Montr
eal, Case Postale 8888,
succursale Centre-Ville, Montreal, Que., Canada, H3C 3P8
b
Received 8 May 2000; accepted 27 November 2000
Abstract
This paper examines the efficiency of the Canadian treasury bill market as measured by the
performance of the expectations model of the term structure of interest rates. In particular,
market efficiency is shown to depend upon certain institutional features of the treasury bill
auction process. Building on past work by B. Campbell and J.W. Galbraith [Oxford Bulletin
of Economics and Statistics 59 (2) (1997) 265–284], the paper establishes links between rejections of efficiency and high absolute values of the spread between six- and three-month interest
rates. The major contribution of the paper is to then show that a link exists between weeks in
which spreads are large and weeks in which accepted auction yields show a large degree of dispersion. The paper discusses the implications of these findings for the term structure literature
and for possible auction configurations currently under consideration in Canada and the
US. 2002 Elsevier Science B.V. All rights reserved.
JEL classification: E43; G18; E58
Keywords: Term structure of interest rates; Financial markets; Central banks; Canada
*
Corresponding author. Tel.: +1-514-987-3000 (ext. 0277); fax: +1-514-987-8494.
E-mail address: [email protected] (C. Zimmermann).
0378-4266/02/$ - see front matter 2002 Elsevier Science B.V. All rights reserved.
PII: S 0 3 7 8 - 4 2 6 6 ( 0 1 ) 0 0 1 6 1 - 3
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L. Godbout et al. / Journal of Banking & Finance 26 (2002) 1165–1179
1. Introduction
While the efficiency of financial markets is an article of faith for most economists,
this faith has rarely been justified by empirical testing. For example, when simple
models of the term structure relationship between short-term and long-term interests
are combined with the assumption of rational expectations of future short-term
rates, the joint hypothesis of rationality and efficiency is most frequently rejected.
Blinder (1997) noted that the expectations model of the term structure ‘‘. . .miserably
iserably fails a variety of empirical tests’’ and described this as one of two ‘‘critical
failings of the standard macro model that cry out for theoretical and empirical
repair’’. This paper advances the process of empirical repair by examining the
factors that contribute to the rejection of the basic expectations model of the term
structure.
Explanations for this rejection have in the past tended to focus upon the existence
of time-varying liquidity premiums or other departures from the simple expectationsdriven arbitrage model. Recently, work by Campbell and Galbraith (1997) examined
the impact of liquidity premiums in a non-parametric regression framework. Their
results suggest that the rejection of the model might be due to periods when the absolute value of the ‘‘spread’’, the difference between the six- and three-month treasury bill rates, is larger than normal. The authors analyzed US and Canadian data
and found that ‘‘for typical values of the spread (values not too far from the median), the expectations theory appears to hold. . .’’ (p. 280). They reconciled this with
the above-mentioned rejections of the theory for complete samples by observing that
‘‘. . . the expectations theory does not hold for large absolute values of the spread’’
(p. 280).
The issue of the performance of the term structure model is currently of significant
relevance for several reasons. First, as Blinder points out, the term structure of interest rates plays a crucial role in understanding the transmission of monetary policy
from short-term interest rates to long-term rates. The Federal Reserve has greatest
influence over the Fed funds rate through open market operations and the Bank
of Canada uses the technique of draw-down and re-deposit to influence the overnight
loan rate. The link between these instruments of policy and longer-term rates relevant for investment and consumption decisions is provided by the term structure
of interest rates.
This paper shows that the periods of large spreads identified by Campbell and
Galbraith (C–G) correspond to identifiable periods of unusual activity in the Canadian treasury bill market. By allowing us to understand better what features of financial markets explain the findings of C–G, we make progress toward Blinder’s goal of
rehabilitating the theory of the term structure.
There are also Canadian regulatory issues that make this analysis highly topical.
The Bank of Canada and the Department of Finance have been revising the rules
governing the auction of Government of Canada securities. The motivation for these
revisions was the preservation of the integrity of the auction process. A recent Bank
of Canada discussion paper (Bank of Canada, 1998) explains that: ‘‘The primary
concern addressed in this paper is the risk that the auction process may be used to
L. Godbout et al. / Journal of Banking & Finance 26 (2002) 1165–1179
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manipulate or ‘squeeze’ the market for Government of Canada securities’’. Later, the
discussion paper lists several ‘‘. . . indicators of a possible squeeze in the market. . .’’
which includes ‘‘. . . how far specific issues trade off of the theoretical yield curve’’.
This establishes a potential role for the term structure of interest rates as an indicator
of the integrity of the auction process. This potential role is examined in detail in this
paper.
Finally, there is now a significant difference between the structure of the US treasury bill auction and the treasury bill auction in Canada. In late 1998, the US Treasury decided to use a uniform-price auction for new issues of treasury bills and other
treasury securities. In this system, all bills are awarded at the market-clearing price.
Canada, on the other hand, continues to use a multiple-price system in which bidders
pay the price they bid and the reported yield is the weighted average of all accepted
yields. As explained below, dispersion in bids is related to the performance of the
market and this will have implications for the choice between the US and Canadian
auction systems. In particular, it will be interesting to compare the performance of
term structure models in the two countries once sufficient observations from the
new US system become available. Until now, the term structure relationship has
been very similar in the two countries while this paper suggests that this could change
with the new auction system.
This paper establishes that the term structure model is most likely to fail in those
weeks where yields are highly dispersed at the Canadian treasury bill auction. The
goal of this paper is not to argue that periods of dispersion of accepted yields are
due to a squeeze or other type of market manipulation but rather to show how institutional factors of the auction process can have an impact on the ability of financial markets to fully exploit arbitrage opportunities. We do find, though, that
accepted auction yields are less dispersed in weeks where bid volumes are high
relative to amounts auctioned. Any proposed reform of the auction process should
consider how the process can be constructed to maximize market efficiency as measured by the performance of the expectations model of the term structure of interest
rates.
This link between market efficiency in the term structure relationship and auction
bid dispersion is important given the statements made in 1998 by then Deputy Treasury Secretary Lawrence Summers. Wall Street Journal (1998) states that ‘‘Mr. Summers said the study showed that uniform-price auctions produce a ‘broader
distribution of auction awards’ ’’. This was viewed by the treasury as desirable given
that one reason they began to experiment with uniform-price auctions was the 1991
Salomon Brothers bidding scandal in which bidders were said to have colluded. On
the other hand, Mr. Summers is also quoted as saying that ‘‘uniform-price auctions
can allow the Treasury to make improvements in the efficiency of market operations. . .’’. The results of this paper suggest, however, that an auction method with
greater bid dispersion may have negative impacts upon the functioning of the term
structure relationship.
This study analyzes the relationship between yields on six- and three-month Government of Canada treasury bills. The paper first reviews the expectations theory of
the term structure and then explains how it was tested by C–G. Next, institutional
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features of the Canadian treasury bill market are examined to determine whether the
nature of the auction process can impact the term structure relationship. To determine whether a particular auction was ‘‘unusual’’, data on the range of yields resulting from weekly treasury bill auctions are examined. Weeks with larger than normal
dispersion of yields are shown to be associated with the large spreads which are, in
turn, associated with the rejection of the expectations model of the term structure
according to the work of C–G. The paper ends by considering the implications of
these findings and suggesting avenues for future research.
2. The expectations model of the term structure relationship
The expectations model of the term structure of interest rates is derived from the
combined assumptions of market efficiency and rational expectations. Suppose that
an investor is considering two possible vehicles for a six-month term investment: a
six-month treasury bill or two three-month treasury bills. The current rates of return
for the six-month bill ðR6t Þ and the three-month bill ðR3t Þ are known with certainty
but the three-month rate which will prevail three months in the future ðR3tþ3 Þ is
not known at the time that the decision is made (all interest rates are measured at
quarterly rates). Accordingly, expectations must be formed about the future three3
month rate and this expected three-month forward rate is labeled Ftþ3jt
.
There is also a possible preference for more liquid investments so that the holding
period return for the six-month bill might have to exceed the expected holding period
return for the two three-month bills by a factor of 2h. This yields the following required relationship between expected holding period returns:
3
ð1 þ R6t Þ2 ¼ 2h þ ð1 þ R3t Þð1 þ Ftþ3jt
Þ:
Note that the holding period return on the six-month bill must be squared because
the returns are for three-month periods.
Given that squared and cross-interest rate terms will be smaller than the interest rates themselves, the following linear approximation to this equation is often
used:
1
1 3
R6t h þ R3t þ Ftþ3jt
:
2
2
As currently written, this equation cannot be estimated because the expected future three-month rate is not observable. The assumption of rational expectations
gives
3
Ftþ3jt
¼ R3tþ3 þ etþ3 ;
Eðetþ3 Þ ¼ 0;
etþ3 i:i:d:
Given the approximations and assumptions above, C–G arrive at the following
estimable equation:
L. Godbout et al. / Journal of Banking & Finance 26 (2002) 1165–1179
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R3tþ3 2R6t þ R3t ¼ 2h þ etþ3 :
The left-hand side of this equation is a linear approximation to the forecast error for
the three-month rate three months into the future. To test this specification, the
intercept and slope terms are estimated freely and then the restrictions implied by the
theory are imposed. The estimated equation is
R3tþ3 2R6t þ R3t ¼ a þ bðR6t R3t Þ þ etþ3 ;
and the theory is tested by examining the hypothesis H0 : b ¼ 0. This restriction
essentially says that the forecast error between t and t þ 3 should be orthogonal to
information available at t such as the spread between three- and six-month interest
rates.
This and other slightly different specifications of the arbitrage conditions have
been used in the literature to test the expectations model. Studies such as Shiller
(1979), Shiller et al. (1983), Mankiw and Summers (1984), Fama (1984) and Mankiw
and Miron (1986) have all rejected the restrictions implied by the expectations
model. Despite this, the expectations model continues to be held in high regard
and explanations for its rejection in empirical testing have focused upon data issues
or estimation methods.
3. The Campbell–Galbraith results
One approach to resolving the puzzle of rejections of the model was followed by
Campbell and Galbraith (1993) who investigated the possibility that a few outlier
data points explained the rejection. While sensitivity analysis did not support this explanation, a later study by Campbell and Galbraith (1997) using the non-parametric
kernel estimation methods to test the specification outlined above found that the
model actually explains the data well for small values of the spread between the
six- and three-month rates (R6t R3t ). This suggests that rejections of the model are
due to a systematic problem encountered during periods of large spreads between
three- and six-month rates.
Campbell and Galbraith (1993) also examined the ability of an ARCH-in-mean
(ARCH-M) model to allow for a change in the intercept of the term structure relationship as a function of the level of conditional heteroscedasticity in the error term
of the regression relationship. If it could be established, for example, that the liquidity premium rises in periods where the rate spread is also large then the coefficient b
in the estimated equation could be negative because of a standard missing variables
bias analysis. Essentially, h is negatively correlated with the forecast error on the lefthand side of the estimating equation but is omitted from the regression. If this missing variable is positively correlated with the included (R6t R3t ) variable then the
estimated coefficient b on this included variable will be biased downward from its
true value.
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This paper explains why it could be that the omitted liquidity premium is negatively correlated with the included rate spread (R6t R3t ). We do this by establishing
a link between the included variable and the dispersion of auction yields at the treasury bill auction. We will show that this yield dispersion provides a structural
measure of financial market uncertainty that gives a better measure of the determinants of time varying liquidity premiums than do time-series methods such as the
ARCH-M approach used by Campbell and Galbraith (1997) or Hejazi et al. (2000).
This paper will use weekly data in order to examine the features of the Canadian
treasury bill auction process when the term structure model does not work well due
to large absolute values of the spread between six- and three-month rates. We begin
by establishing that the findings documented by Campbell and Galbraith (henceforth
C–G) also hold in our data. To illustrate this, we first created a quarterly data-set
using one weekly observation per quarter in order to avoid the introduction of a
moving-average error term which violates the assumptions of both OLS regression
and the non-parametric kernel density estimator. 1 It is possible to form 13 separate
quarterly samples of observations from our weekly data covering the 1 January
1970–18 September 1997 period.
C–G used the same average auction yields examined in this paper but used a different sample period (1960–1993). To illustrate the applicability of the C–G results to
our sample period, just one of these 13 samples, the one formed using the first week
of every quarter, is used to show that the C–G result still holds with our data. Similar
results are found when all 13 quarters are used but we only present one set of the
results here since this part of the analysis is essentially just a robustness analysis
of the C–G study with a different sample period. An illustration of the C–G finding
is provided in Fig. 1. This graph plots the right-hand side from the C-G specification
(the interest rate spread) on the horizontal axis and the left-hand side (the forecast
error) on the vertical axis. Under the null hypothesis, the forecast error (the actual
future three-month rate minus its expected rate) should be orthogonal to all available
information such as the spread observed at time t. The OLS regression (see Table 1
and the broken regression line added to Fig. 1) yields a significant negative coefficient for the rate spread variable and this echoes the rejection of the theory found
by C–G.
Fig. 1 also includes a solid line which is the estimated conditional expectation of
the forecast error given the rate spread obtained from a non-parametric kernel density estimate. The difference between the linear OLS conditional expectation and the
kernel estimation is that the kernel method uses a local smoothing technique to allow
the slope of the fitted line to vary smoothly with the values of the independent variables. The smoothing function used in this case was the Gaussian (normal) kernel
1
The possibility of a moving-average process for forecast errors arises whenever the observation
frequency is shorter than the forecast period. For example, forecasts made at week one and week two of a
quarter could both show errors due to new information which arrived at week three. This could introduce
a correlation between errors for adjacent weeks. This problem can only be eliminated by using weekly
observations that are each 13 weeks apart (e.g. one per quarter).
L. Godbout et al. / Journal of Banking & Finance 26 (2002) 1165–1179
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Fig. 1. OLS and non-parametric tests of the term structure relationship (Normal Kernel, bandwidth ¼ 0.0009).
Note: This figure shows the relation between the interest rate spread of three- and six-month Canadian
treasury bills ðR6t R3t Þ and the forecast error ðR3tþ3 2R6t þ R3t Þ from the expectations model of the term
structure. The dotted line represents the fitted values from an OLS regression while the solid line represents
the fitted values from a non-parametric regression of the forecast error on the interest rate spread. The
sample comprises the first week of each quarter from 1 January 1970 to 18 September 1997.
and the bandwidth smoothing parameter was chosen automatically by the EViews
estimation package. 2
The graph shown in Fig. 1 is the same type of graph presented in Fig. 1 of the
C–G paper. Both our graph and those presented by C–G show that the slope is much
steeper for extreme values of the interest rate spread and much closer to zero for ‘‘average’’ values of the spread. This non-parametric result is confirmed by an OLS regression which removes the observations corresponding to the 10 (out of 110) largest
absolute values of the interest rate spread variable. Once these extreme observations
are removed, it is no longer possible to reject the null hypothesis (results from the
restricted regression are in Table 2). It is worth noting that C–G find the same pattern for both Canadian and US treasury bill interest rates.
In the next section of the paper, we go beyond simply confirming what C–G have
already discovered. We link periods in which the rate spread is large in absolute
value to weeks where there was a great deal of dispersion in the rates accepted at the
2
For further information about kernel density estimation see Ullah (1988).
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Table 1
OLS estimation of the term structure model (the dependent variable is the three-month forecast error)
Variable
Coefficient
S.E.
P-value
Constant
Spread (RTB6 ) RTB3)
)0.00035
)1.3184
0.00034
0.4107
0.30
0.002
R2 : 0.087
S.E. of regression: 0.003
Sample: 1970Q1–1997Q2
Durbin–Watson statistic: 1.94
Mean of dependent variable: )0.00084
Number of observations: 110
Table 2
OLS with extreme values of the spread excluded (the dependent variable is the three-month forecast error)
Variable
Coefficient
S.E.
P-value
Constant
Spread (RTB6 ) RTB3)
)0.00067
)1.0220
0.00036
0.5843
0.06
0.083
R2 : 0.030
S.E. of regression: 0.003
Sample: 1970Q1–1997Q2a
a
Durbin–Watson statistic: 2.01
Mean of dependent variable: )0.001
Number of observations: 100
The 10 largest absolute values of the spread were excluded from the regression.
treasury bill auction. We also find that auctions with high degrees of dispersion in
accepted rates tend to have relatively low volumes of submitted bids relative to
the amounts issued. To begin this analysis, the next section of the paper examines
the nature of the auction process for treasury bills in Canada.
4. The Bank of Canada treasury bill auction procedure
Until 16 September 1997, newly issued Government of Canada treasury bills were
auctioned once a week by the Bank of Canada. Since this date, three-month treasury
bills have been auctioned every two weeks. During a September 1997–March 1998
transition period, the maturity of three-month bills was lengthened. Data after 16
September 1997 are not used in this study to avoid introducing effects of this transition into the results. For the weekly auction period analyzed here, the auction
was held on Thursdays through 24 November 1992 but changed to Tuesdays afterward.
The Bank acts as an agent for the Government of Canada and solicits sealed bids
from a group of chartered banks and securities dealers known as primary distributors. These bids specify quantities of bills that the dealers are willing to purchase
at a given price. The Bank of Canada is also able to submit a bid. The Bank can obtain an interest rate below the market equilibrium by submitting a high-price bid but
is not able to raise the interest rate above the market level since low-price bids would
not be accepted.
L. Godbout et al. / Journal of Banking & Finance 26 (2002) 1165–1179
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Over our January 1982–September 1997 sample period, the average spread between six- and three-month treasury bill interest rates was 0.0005, reflecting a normal
positive slope to the term structure. Reported annualized rates used to calculate the
spreads were converted to a quarterly basis using the formula rquarterly ¼ ð1 þ rannual =
91=365
100Þ
1 so that a 6% annualized rate would be entered as 0.0146. The distribution of spread values was roughly symmetric with a standard deviation of
0.00066.
At the treasury bill auction, there can be a non-trivial range of accepted yields if
there is not a large number of bids at the highest price submitted. Typically, the
spread between the highest and lowest yields is small with a median value of
0.45%. There are, however, also many weeks where the highest yield is more than
1% higher than the lowest yield (this is 1% and not one percentage point) and the
maximum difference in our sample is 6%. Large differences in accepted yields may
be indicative of some sort of unusual activity in the market or of a wide range of expectations of market participants. It is plausible that high levels of auction yield dispersion are due to uncertainty in Canadian financial markets, to unexpected
monetary policy intervention, or to manipulation of the market by some participants. During periods with any of these three phenomena, the expectations model
might not function well.
To examine whether there is a link between treasury bill auction yield dispersion
and the term structure model, it is useful to begin by comparing the behavior of yield
dispersion and rate spreads over time. This is first done in Fig. 2 which plots the two
series for the period from 1982 to 1997. This graph shows that periods of heightened
Fig. 2. T-bill spreads and auction dispersion over time.
Note: This figure shows how values for the dispersion of bids (the percentage difference between the highest
and lowest accepted yields at the Canadian t-bill auction) and values of the spread between six- and threemonth t-bill rates have tended to show similar movements over time. The sample is weekly data from 7
January 1982 to 18 September 1997.
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L. Godbout et al. / Journal of Banking & Finance 26 (2002) 1165–1179
dispersion of auction yields also tend to show evidence of above average rate
spreads. This is particularly true of the period through 1985. Given that a significant
tightening of monetary policy occurred in the early 1980s, the heightened auction
dispersion at that time could reflect the difficulty encountered by market participants
as they tried to deal with a new anti-inflationary policy environment.
It is not desirable to use either linear regression analysis or simple correlations to
test the strength of the link between auction yield dispersion and the interest rate
spread. This is because OLS and correlations both measure linear relationships while
periods of extreme values for the spread between three- and six-month interest rates
are related to periods of greater dispersion between high and low auction yields in a
possibly non-linear manner. Given that we do not expect to find a linear relationship,
we choose to investigate this hypothesis by using a binary estimation technique. The
appropriateness of this choice is supported by the non-parametric results provided
below.
To use our binary estimation method, we first define a variable ‘‘extreme’’ which
equals 1 whenever the absolute value of the rate spread exceeds the 90th percentile
value for the sample. In the other 90% of cases, the variable equals 0. We then
use the logit technique to estimate the parameters of the relationship between the
probability of having an extremely large absolute value of the spread and possible
determinants of this unusually large spread. The possible determinants considered
here are:
• the percentage difference between the highest and lowest accepted interest rate,
• the percentage by which the total dollar amount of bids exceeded the dollar
amount of the bills to be auctioned,
• and the level of the three-month treasury bill rate.
The first two variables are used as indicators of unusual activity at the auction,
with the bid amount variable intended to specifically capture supply effects. The interest rate variable is included to allow for the possibility that large values of the
spread simply reflect the level of interest rates.
The result of the logit estimation is provided in Table 3. There is a large and significant positive impact of the auction yield dispersion variable upon the probability
Table 3
Logit estimation for the probability that the spread is ‘‘extreme’’
Variable
Coefficient
S.E.
P-value
Constant
Rate dispersion
Bid volume
Three-month rate
(RTB3)
)3.64
0.81
0.01
10.60
0.70
0.19
0.004
16.37
<0.0001
<0.0001
0.11
0.52
McFadden R2 : 0.035
Log-likelihood: )257.03
Sample: 7 January 1982 –18 September 1997
Number of observations: 820
L. Godbout et al. / Journal of Banking & Finance 26 (2002) 1165–1179
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Fig. 3. The relationship between T-bill spreads and auction dispersion.
Note: This figure shows the relationship between values for the dispersion of bids (the percentage difference
between the highest and lowest accepted yields) at the Canadian t-bill auction and the absolute value of the
spread between six- and three-month t-bill rates. The solid line represents the fitted values from a non-parametric regression of this relationship. The sample is weekly data from 7 January 1982 to 18 September 1997.
of a large yield spread. Interestingly, there is some indication that this relationship
only exists for relatively large values of auction dispersion. Indeed, the scatter diagram in Fig. 3 shows a non-parametric fit to the data points in which there is little
link between the rate spread and auction dispersion for low dispersion levels. It is
only for higher levels of dispersion that a positive link emerges and this on/off nature
of the relationship supports our use of logit regression. The findings of Table 3 and
Fig. 3 lend credence to the belief that something unusual happens to the treasury bill
market whenever there is a large degree of dispersion in auction yields.
Table 4
The link between bid volume and auction dispersion (the dependent variable is rate dispersion ¼ 100 (high ) low)/low)
Variable
Coefficient
S.E.
P-value
Constant
Bid volume
1.356
)0.006
0.061
0.001
< 0:0001
< 0:0001
R2 : 0.169
S.E. of regression: 0.508
Sample: 7 January 1982–18 September 1997
Durbin–Watson statistic: 1.45
Mean of dependent variable: 0.606
Number of observations: 820
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Fig. 4. Auction dispersion and amounts bid.
Note: This figure examines the effect of the degree of over-subscription at the t-bill auction upon auction
dispersion. The degree of over-subscription is measured by the percentage difference between the amount
bid and the amount offered while the dispersion of bids is the percentage difference between the highest
and lowest accepted yields at the Canadian t-bill auction. The solid line is the fitted values from a nonparametric regression between the two variables. The sample is weekly data from 7 January 1982 to 18
September 1997.
The robustness of this finding is strengthened by our result that neither the bid
supply variable nor the level of the interest rate are significant determinants of the
probability of obtaining a large absolute value of the spread. In fact, the bid supply
variable becomes less significant when the interest rate dispersion variable is removed
from the logit regression. It is also interesting that there is a negative relationship between the dispersion of bids and the bid volume variable. This is shown in the OLS
regression of Table 4 and the kernel density estimate of Fig. 4. There is an indication
that high bid dispersion is less likely to occur when the volume of bids becomes large
relative to the value of the treasury bills auctioned.
5. Conclusions
The results of this paper suggest that there is a link between institutional features
of the Canadian treasury bill market and the efficiency of that market as measured
L. Godbout et al. / Journal of Banking & Finance 26 (2002) 1165–1179
1177
by the performance of the expectations theory of the term structure of interest rates.
This result strengthens the findings of C–G who first established a link between
model performance and rate spreads. Beyond this, the results of this paper offer some
insights into the reasons why the expectations model of the term structure may fail in
certain unusual periods. Expectations formation and arbitrage conditions may work
well in financial markets when circumstances are close to ‘‘normal’’ and market participants are able to apply previously learned behavior. Unusual periods lead to mistakes and the ex post finding of apparent non-optimal behavior.
This echoes the corridor analogy of Leijonhufvud (1981). Within this corridor,
classical economic theory works well but it begins to fail once the economy is perturbed sufficiently far from the corridor. Perhaps the two failings of macro theory
cited by Blinder, the term structure and expectations formation, both can be addressed by considering the possibility that such a corridor is relevant in financial
markets.
In addition, the paper points to a new consideration for the Bank of Canada and
the Department of Finance as they seek to modify the auction process. It is important to understand why some weekly auctions have had significantly greater rate dispersion than others. While the degree of dispersion has tended to be smaller since the
1980s, it is still important to understand what features of the auction process are
likely to yield dispersion of accepted bids. Given that high dispersion is associated
with rejections of efficiency and that market efficiency should be a goal of the auction
authorities, further analysis of the determinants and implications of auction yield
dispersion would seem warranted. The paper provides some evidence that periods
of high dispersion in accepted bid rates are related to supply effects. It is also clear
that the explanatory power of bid dispersion in the equation predicting high absolute levels of three-month/six-month spreads is not in any way a proxy for supply
effects.
Finally, the stylized facts uncovered in this paper point to important areas of
research related to the performance of the auction process for US treasury securities. As explained above, the new uniform-price auction method is intended to increase the dispersion of bids at Treasury auctions. This paper shows that
dispersion may have important economic and financial consequences. Future research should compare the performance of financial market relationships under multiple- and uniform-price auction procedures and also examine in greater detail the
possible linkages between time varying liquidity premiums and auction bid dispersion. This could involve the use of comparative studies across countries and over
time.
Acknowledgements
Financial support from the Social Sciences and Humanities Research Council of
Canada and from the Fonds FCAR program of the province of Quebec is gratefully
acknowledged.
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Appendix A. Data appendix
1. Weekly treasury bill auction average yields.
RTB3 – three-month rate: CANSIM series B113903.
RTB6 – six-month rate: CANSIM series B113904.
Both CANSIM series are in annual equivalent rates and were converted to
quarterly rates using the formula:
rquarterly ¼ ð1 þ rannual =100Þ
91=365
1:
2. Treasury bill auction data were provided by Kevin Fettig and Nancy Harvey of
the Bank of Canada.
High – The highest accepted three-month treasury bill yield.
Low – The lowest accepted three-month treasury bill yield.
Offer amount – the dollar value of the three-month bills offered at the auction.
Total amount – the dollar value of all bids received.
3. Constructed variables.
Spread ¼ RTB6 ) RTB3
Forecast error ¼ RTB3(+3) ) 2RTB6 + RTB3
Rate dispersion ¼ 100 (high ) low)/low
Volume ¼ 100 (total amount ) offer amount)/offer amount
Extreme ¼ 1 if ABS(spread) is one of the top 10% values of ABS(spread)
(the top 82 out of 820 observations)
¼ 0 otherwise.
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