The Transmission of Monetary Policy
in the
Commercial Paper Market
Chris Downing∗
August 2, 2001
1
Introduction
Commercial paper (CP) is an unsecured debt instrument of up to 270 days maturity issued
by investment–grade financial and nonfinancial corporations. In this paper, I study how
expected changes in the Federal Reserve’s target rate for federal funds are expressed in
the CP market.1 I focus on two linkages between the commercial paper market and the
market for federal funds. First, I study how risk premia on commercial paper are related to
expectations of changes in policy. The results indicate that risk premia in the commercial
paper market appear to rise when the Federal Reserve enters a cycle of policy tightenings
or easings, consistent with the relatively greater policy risk investors in CP must accept. In
addition, risk premia shift during year–end, when liquidity concerns and shifts in borrowing
and lending patterns induce higher premia in the CP market.
The second linkage that I focus on is the quantity response of commercial paper issuance
to expected changes in policy. Specifically, I examine how the maturity structure of com∗
This paper contains preliminary results. Please do not cite the results herein. This paper represents the
views of the author and does not necessarily represent the views of the Federal Reserve System or members
of its staff. Please contact the author at: Federal Reserve Board, Mail Stop 89, Washington, DC 20551.
Phone: (202) 452–2378. Fax: (202) 728–5887. E-Mail: cdowning@frb.gov.
1
The federal funds rate (fed funds) is the interest rate on funds traded by banks to bring their reserves
in line with regulatory requirements.
1
mercial paper reflects expectations. The results suggest that investors (issuers) modify the
maturities of CP that they buy (sell) as a hedge against the possibility of errors in their
policy forecasts. In effect, maturities “pile up” around the FOMC meeting dates, as expectations for a policy change take shape. In turn, these pileups of maturities feed back into
prices, as the heavy expected rollovers induce liquidity premia in subsequently issued CP. In
short, knowing the maturity structure of outstanding CP helps one to predict yields over a
short horizon, and indeed, market participants often point to heavy expected maturities as
a factor that helps to determine day–to–day prices.
These issues are important because, as illustrated in figure 1, the market for commercial
paper issued by domestic US corporations is immense, having grown in recent years to nearly
three times the size of the market for US Treasury bills. As shown in table 1, much of the
daily activity in the market is in the financial sector, although nonfinancial corporations
account for a significant share of daily activity, as well. The CP market is a primary issue
market, with deals settled in cash on the day of issue, and the secondary market is thin,
consisting primarily of liquidity provided by the major dealers. These features of the market
make active risk management in commercial paper difficult, and most investors follow buy–
and–hold strategies with respect to their CP holdings. As a result, relative to many other
short–term financial instruments, a position in longer–dated CP directly exposes an investor
to significant policy risk, in the sense that investors’ expectations for policy may turn out to
be incorrect, and the CP must be held to maturity.
As shown in figure 2, commercial paper yields closely track the target rate for federal
funds, the primary instrument of Federal Reserve credit policy, presumably owing to arbitrage. Commercial banks are active buyers and sellers of both commercial paper and federal
funds, and are quick to exploit any significant divergences between the prices of money in the
two markets. The close relationship between CP and the federal funds target rate, as well
as the effective federal funds rate, is underscored in table 2. The table displays univariate
statistics for the spread between the AA–financial CP rates and the fed funds target, as well
2
as the spread of CP to the effective funds rate.2 As shown, overnight CP rates deviate from
the target by just over one basis point, on average, and from the effective fed funds rate by
less than a basis point. Both deviations exhibit substantial variation, of course, due to a
wide variety of factors such as quarter– and year–end liquidity effects, pressures that arise
on corporate tax days, timing issues, and the like.
Since commercial paper is a short–term instrument, and is to a certain degree priced
by arbitrage against the federal funds rate, the CP market is a direct channel through
which monetary policy affects the activity of firms in the corporate sector. Indeed, many
of the largest investment–grade corporations maintain commercial paper programs, often of
significant size, as shown in table 3. The table displays the number of firms with commercial
paper programs, and measures of the size of the programs, for domestic US firms sorted into
total asset size quintiles.3 The bulk of commercial paper issuers reside in the uppermost
size quintile - firms with total assets greater than $1.4 billion in value. For these firms,
commercial paper liabilities are, on average, 12 percent of total liabilities, and 33 percent
of current liabilities. Hence, changes in credit policy translate almost immediately into
economically significant increases or decreases in the cost of servicing commercial paper, and
thereby, ceterus paribus, into decreases or increases in the companies’ cash flow positions.
It is important, therefore, to understand how monetary policy affects both the pricing and
maturity structure of commercial paper.
This paper is organized as follows. In section 2, I develop the relevant theoretical issues
and discuss related literatures, and in section 3, I present the results of my empirical work.
Section 4 summarizes the results and concludes with some ideas for future research.
2
The effective federal funds rate is the rate that prevails in the market. The effective rate will deviate
from the target due to imprecision in the Fed’s estimates of the amount of reserves required in order to
maintain the target.
3
The sources for these figures are COMPUSTAT and the Federal Reserve’s commercial paper database.
3
2
Theory
Let Yt,t+m denote the yield on commercial paper issued at time t and maturing at time t+m.4
In other words, Yt,t+m is the interest rate on a spot loan made at time t to be repaid at t + m.
Let Ft,t+m denote the yield, at time t, on a forward contract to issue overnight commercial
paper at time t + m − 1 to mature at time t + m. A forward overnight loan made zero periods
forward is just a spot overnight loan, so Yt,t+1 = Ft,t+1 .
In order to rule out riskless arbitrage opportunities, CP issued with two days to maturity
should yield the same as overnight CP rolled over at the forward overnight rate:
(1 + Yt,t+2 )2 = (1 + Yt,t+1 ) (1 + Ft,t+2 ) ,
(1)
(1 + Ft,t+2 ) = (1 + Yt,t+2 )2 (1 + Yt,t+1 )−1 .
(2)
which means that:
This process can be iterated forward; in general, the formula for the relationship between
forward overnight rates and adjacent spot term rates is given by:
(1 + Ft,t+m ) = (1 + Yt,t+m )m (1 + Yt,t+m−1 )−(m−1) .
(3)
Hence, given the yield curve on a particular day, it is a straightforward task to compute the
associated forward yield curve.
In the absence of risk and liquidity premia, arbitrage between the fed funds and CP
markets would force the overnight CP rate to the target. If in addition agents were rational
and term premia were zero, then forward overnight rates would provide unbiased forecasts of
future spot overnight rates. Thus, we could use the forward overnight CP rates to forecast
the future path of the fed funds target rate. However, term premia are not zero, which,
4
In what follows, unless stated otherwise, all yields should be interpreted as daily yields. In addition,
unless stated otherwise, all time intervals are in days.
4
together with the existence of credit and liquidity premia, produces forward overnight rates
that are biased predictors of future spot overnight rates.
To examine these issues more closely, suppose we model the relationship between the
forward overnight CP rate and the expected spot overnight rate as:
h
(1)
i
Ft,t+m = Et Yt+m−1,t+m + t+m−1 ,
(4)
where (1) is a random error term with finite mean and variance. Suppose further that the
relationship between the overnight CP rate and the target is given by:
(2)
Yt+m−1,t+m = Rt+m−1,t+m + t+m−1 ,
(5)
where R is the target rate and (2) is again a random error. Substituting (5) into (4), we
have:
Ft,t+m = Et Rt+m−1,t+m + Et t+m−1 ,
(1)
(6)
(2)
where t+m−1 = t+m−1 + t+m−1 . In this formulation, the term Et t+m−1 captures both
expected deviations of the forward overnight rate from the future spot overnight CP rate,
as well as expected deviations of the future spot overnight rate from the future fed funds
target. This construction makes clear that the “gross risk premium” t+m−1 captures the
effects of factors common to both the CP and fed funds markets, such as term premia, as
well as market–specific default and liquidity premia.5 The predictable components of these
factors, as represented by Et t+m−1 , are priced into forward rates, and thus term spot rates.
5
Typically (though not uniformly), in the term structure literature the label “term premium” is applied to
the difference between current forward spot rates and expected future spot rates. Since these models usually
focus on debt that is free from the possibility of default, and the models abstract away from considerations
of market liquidity, the term premium can be interpreted as the marginal increment to return that arises
purely from the extension of maturity and the greater interest rate uncertainty that this entails. The “gross
risk premium” incorporates this compensation, as well as compensation for taking on additional default and
liquidity risk (also commonly referred to as “rollover risk”). In what follows, I will often refer to the gross
risk premium as simply the “risk premium.”
5
If we next difference forward overnight rates, we obtain:
Ft,t+m+s − Ft,t+m = Et ∆m,s R + Et ∆m,s ,
(7)
where ∆m,s R = Rt+m+s−1,t+m+s − Rt+m−1,t+m and ∆m,s = t+m+s−1 + t+m−1 . The difference
in forward rates s periods apart produces the expected change in the target over the period,
plus the expected change in risk premia. If the function relating risk premia to maturity
is well behaved, equation (7) indicates that, for small s, changes in forward overnight rates
will produce accurate assessments of market participants’ expectations for future policy. For
example, if the risk premium function is relatively flat, so that Et ∆m,s ≈ 0 for small s, then
Ft,t+m+s − Ft,t+m ≈ Et ∆m,s R
Of course, carrying out these calculations is complicated by the fact that expectations are
not directly observable, so it is not possible to make direct measurements of Et Rt+m−1,t+m in
order to infer something about t+m−1 . One approach to this problem is to simply ask market participants what they believe future interest rates will be. This approach is generally
regarded as unreliable, and its usefulness is limited by the fact that repeated measurements
of beliefs are not usually available. A second approach is to build a model of expectations
generation. Indeed, the literature is replete with such models.6 A drawback to this approach
is that it entails strong assumptions about the information set upon which investors condition their expectations.7 A third approach examines risk premia outside of the confines
of structural models by assuming that realizations of the fed funds rate m periods hence
are unbiased forecasts of Et Rt+m−1,t+m - in other words, that expectations are rational.8 A
key question addressed in this literature is whether Et t+m−1 is constant through time, or
whether it might exhibit predictable variation through time.
6
For example, see Vasicek (1977), Brennan and Schwartz (1979), Cox, Ingersoll and Ross (1985), Heath,
Jarrow and Morton (1992), Longstaff and Schwartz (1992), among many others.
7
Hence to the extensive literature on the theory of interest rate expectations formation must be appended
the vast literature on the empirical testing of these models. For a textbook introduction and overview of the
literature, see Campbell, Lo and MacKinlay (1997).
8
This assumption is not without its critics. Froot (1989) argues for a survey–based approach. For surveys
of this literature, see see Melino (1988), Shiller (1990), and Campbell (1995).
6
The empirical work in this paper is best placed in the context of the literature on empirical
tests of the expectations hypothesis, since the primary goal of this work is the examine how
expectations for monetary policy are reflected in risk premia, broadly defined to include term
premia. The work has implications for the literature on structural models of expectations
formation, as well, because I focus on particular factors that might help explain the process
of expectations formation. To the extent that the evidence is persuasive, the results point
the way toward factors that should be included in realistic structural models.
3
Results
In this section, I employ a two step empirical analysis of term premia in the CP market.
First, I use data on realized yields to estimate equation (6) under the assumption that
Et t+m = f (m), with the aim of identifying plausible forms of the function f . Drawing
from the structural modeling literature, I focus particular attention on the possibility that
volatility in the federal funds target, as generated by FOMC policy, might shift this function.
In addition, I examine how the function shifts at year–end, when important liquidity effects
come into play in the CP market. In both respects, we find evidence of time variation in risk
premia, one source attributable to FOMC policy actions, and the second source attributable
to year–end liquidity effects. Moreover, we find that the maturity structure of outstanding
CP appears to partially determine risk premia.
3.1
Data and Yield Curve Measurements
The commercial paper yield curves that I use were constructed using transactions data from
the Depository Trust Company. The raw data comprise a comprehensive database of daily
transactions.9 For this study, the data cover each business day from January 2, 1998 through
June 21, 2001, for a total of 861 daily observations. I merged the transactions data against
9
The Depository Trust Company handles clearing and settlement of between 95 and 99 percent of trades
on the commercial paper market.
7
credit rating and industry information obtained from a variety of sources. I then extracted
trades by domestic financial and nonfinancial CP programs with at least two ’1’ short–term
ratings (the highest), and no short–term ratings below ’1’, and at least one AA long–term
rating, using ratings from Standard and Poor’s, Moody’s, and Fitch IBCA.10 In other words,
I selected CP issued by programs of the highest quality, in order to remove as much of the
credit premium as possible from the yields on the commercial paper. Next, for each day, I
computed the face–value weighted median discount yield at each maturity. Finally, I fit a
smooth curve through the median yields using locally weighted least squares, as discussed
in Downing and Richards (2000). The end result is a daily series of constant–maturity,
zero–coupon yield curves.11
The yield curves were fit with different amounts of smoothing applied to the face–value
weighted medians. The degree of smoothing affects the resulting implied forward rates, as
well, as illustrated in figures 3–5. The top panel of figure 3 shows the fitted yield curves
when the least amount of smoothing is applied to the medians, and the bottom panel shows
the implied forward overnight rates.12 As can be seen, the yields exhibit a great deal of
local variation, and the implied forward overnight rates are chaotic. There are many periods
where the data are sparse and extrapolation leads to negative spot and forward rates. In
sum, these fits are not altogether useful.
On the other end of the spectrum, figure 5 shows the curves that result when the greatest
amount of smoothing is applied to the medians. At this level of smoothing, much of the
local variation in yields has been smoothed away. Neverthless, the forward rates retain a fair
10
The use of long–term ratings excludes most asset–backed CP issuers because most ABCP programs do
not issue long–term debt. It is desirable to exclude these trades because asset–backed CP incorporates a
fluctuating “structure premium” over CP issued by standalone programs.
11
It should be emphasized that this procedure does not suffer from the coupon effect on observed yields,
because all of the data are yields on newly issued discount paper. Thus, the first–stage estimation of yield
curves really amounts to little more than nonparametric smoothing of median discount rates. In effect, we
are directly estimating the discount function itself.
12
The value s1 reported in the figure refers to the proportion of the data that is used in each local regression.
For example, s1 = 0.1 means that ten percent of the data is used in each local regression. This parameter
setting is inversely related to the number of parameters used to fit the data. For example, s1 = 1.0 implies
two parameters - the slope and intercept - while s1 = 0.0 implies a fit that interpolates the raw median
yields.
8
degree of local variation. This is to be expected, because forward rates are, loosely speaking,
derivatives of the yield curve and thus an order of magnitude less smooth than the yield
curve itself. Figure 4 displays the results for an intermediate amount of smoothing. This fit
seems to strike a good balance between local variation and bias reduction, and will serve as
the basis for much of the work to follow.13
Table 4 displays some univariate statistics for the yield curve obtained with an intermediate amount of smoothing (s1 = 0.5). To study the magnitude of any residual credit premia, I
also include univariate statistics on spreads over general collateral repurchase agreements.14
On average, the daily changes in yields amount to a fraction of a basis point, reflecting the
high degree of persistence in interest rates. The average daily change in the overnight rate
is roughly an order of magnitude larger than the term rates, however, indicating the wider
array of liquidity factors that affect overnight rates. Looking at the spreads to overnight
rates, the yield curve on average exhibits about nine basis points of upward slope between
the 90–day maturity and the overnight rate, again with significant variation due to, among
other things, expectations of policy changes, as we shall see. Finally, the spreads to risk–free
repo rates suggest that a credit component remains, even for AA–rated paper, as indicated
by the ten to fifteen basis point spread of AA–CP rates over comparable maturity repo rates.
3.2
Risk Premia
I begin by estimating the risk premium function with the following nonparametric regression:
Ft,t+m − Rt+m−1,t+m = f (m) + t ,
13
(8)
Procedures exist for identifying a degree of smoothing that minimize some measure of expected loss. In
future revisions of this paper, I intend to employ one of these procedures, specifically, the Mallows statistic
(see Cleveland and Devlin (1988)).
14
Longstaff (2001) argues that repo transactions are a realistic alternative to Treasury bills as a proxy for
the risk–free rate. Unlike Treasury bills, repos are pure financial contracts, and thus do not exhibit the technical pressures that often affect Treasury bill yields. Moreover, repos are in fact typically overcollateralized
by pricing the collateral security (usually a Treasury bill) at a discount (the so–called “haircut”) designed
to insure full collateralization even if the price of the collateral should decline during the life of the contract.
9
where f (m) is a smooth function, and t is a normally distributed random error with mean
zero and variance σ 2 . The function f (m) can be thought of as our model for Et t+m−1 in
equation (6) of the previous section. In other words, we are using the ex–post realized errors
of forward rate forecasts of the funds target to estimate a risk premium function that is a
time–invariant function of maturity. The error term t arises from our assumption of rational
expectations - it captures the unpredictable component of the difference between ex–ante
expectations and ex–post realizations.
Figure 6 shows fits of equation (8), where the curves were fit using locally weighted least
squares. As discussed earlier, locally–weighted least squares was also used to estimate the
yield curves in the first step. To examine the robustness of the results against alternative
configurations of the degrees of smoothing used in each step, I recomputed the estimates for
different combinations of the two smoothing parameters. The top panel displays the results
for the least amount of second–stage smoothing (s2 = 0.25), over three levels of first–stage
smoothing (s1 = 0.1, 0.5, 0.9, where 0.1 is very close to the raw face–value weighted median
estimator, and 0.9 is very close to a linear regression of face–value weighted median yields on
maturity). The middle panel displays the results for an intermediate amount of second stage
smoothing (s2 = 0.5), while the bottom panel shows the results when we smooth heavily
in the second stage (s2 = 0.75). As can be seen, for maturities less than 150 days, the
differences between the fits are insignificant.15 Based on these results, in what follows I will
focus exclusively on the fits produced by an intermediate degree of smoothing at each stage
(s1 = 0.5 and s2 = 0.5).
15
This is a preliminary conclusion. The confidence bands that are displayed in the figure 6 should be
treated with caution. The standard errors of the fits have not been adjusted for the errors associated with
the first–stage yield–curve fit. As a result, the confidence bands likely overstate the degree of precision with
which we are estimating the risk premium function. In future revisions of the paper, I plan to make this
correction. It is reasonable to expect that, after this correction, the differences between the fits will be even
less statistically significant.
10
3.3
Risk Premia in Policy Cycles
When the Federal Reserve enters a policy cycle, investors are subject to the risk that the Fed
will change overnight rates, and that the ex–post overnight rate will not align precisely with
investors’ ex–ante expectations. I will call this risk exposure “policy risk.” A key question
is whether exposure to policy risk is reflected in the risk premium function. Looked at from
a slightly different perspective, changes in Fed policy induce additional volatility in interest
rates. Depending on the price of interest rate risk, this additional volatility could result in
significant risk premia in the CP yield curve.
To examine this issue, I split the sample into periods when the Federal Reserve was
actively changing rates, and periods when rates were stable. Observations in the policy cycle
dataset include CP issued within fifteen days of September 29, 1998 through November 16,
1998, within fifteen days of June 30, 1999 through May 15, 2000, and within fifteen days of
January 3, 2001 through June 22, 2001. The fifteen day interval before the first observed
policy change of each cycle is used to capture changes in risk premia that might result from
expectations about the possibility of entering a policy cycle.
Figure 7 shows the resulting fits for policy cycle observations and observations outside
of policy cycles.16 The results indicate that, for maturities less than about 90 days, the risk
premium function tilts upward during policy cycles. The risk premium function then flattens
out, and overlaps non–cycle risk premia out to about 150 days. For terms greater than 150
days, risk premia shoot up dramatically, and increase rapidly with term.17
It is interesting that the risk premium function tilts upward in policy cycles, as opposed
to making a parallel shift. It could be that this reflects the process by which policy change
takes place. With the exception of inter–meeting moves, policy changes occur on fixed dates,
and often after public statements by the Chairman and other Board members have provided
16
Note also that I have removed observations with maturities crossing year–end, in view of the results to
be discussed in the next subsection.
17
It should be noted that daily market trading volumes decline rapidly in maturities greater than 100
days. As a result, the underlying yield curves are estimated with less precision at longer maturities, though
this does not show up in these results because we have not corrected the standard errors.
11
the markets with a good idea of where credit policy is headed. As a result, over a very
short horizon, there is far less uncertainty about the likely path of policy than over a longer
horizon. Moreover, since there are eight policy meetings each year, horizons of roughly six
weeks or more will cross multiple FOMC meeting dates, introducing greater uncertainty.
Hence, an upward tilt in the risk premium function is consistent with the nature of the risks
introduced by the process of policy change.
3.4
Risk Premia at Year–End
In the commercial paper and other short–term money markets, it is well known that money–
market mutual funds (holders of approximately 40% of outstanding CP) and other institutional investors engage in “window dressing” at year–end. Money funds “dress” their
balance sheets for year–end financial statements, which disrupts normal lending patterns,
forcing issuers to turn to lenders who are less familiar with their business situation. The
general perceived level of rollover risk – the risk that an issuer will default because its paper
cannot be rolled over – thus rises.
Figure 8 displays estimates of the risk premium function where we have thrown out
observations occurring in the midst of policy cycles (as identified in the previous subsection),
and split the sample into observations with maturities that cross year–end, and those that
do not. It is evident from figure 8 that there are predictable shifts in the term structure at
year–end. From the figure, it is apparent that the year–end risk premium is, on average,
about 60 basis points out to 70 days maturity, at which time it begins to move up to a
maximum of nearly 120 basis points.
These results suggest that investors are exacting a premium from issuers in order to
hold their paper over year–end. In contrast to the movement of risk premia during policy
cycles, at year–end the risk premium function shifts up roughly in parallel. Like the policy
cycle shifts, however, the moves in risk premia at year–end are consistent with the nature
of the risks associated with the year–end phenomenon. Rollover risk rises on a known date
12
– the end of the year – and there is little to help investors gauge the likely severity of this
risk beyond general notions of the size of the market and the amount of paper that will
be rolled over on or around the end of the year. As a result, the risk associated with the
year–end is more or less constant with maturity. This stands in contrast to the shift in the
risk premium function in policy cycles, where extending maturity would introduce additional
risk by crossing additional FOMC meeting dates.
Examining figures 7 and 8, it is clear that “background” risk premia (that is, risk premia
with year–end and policy–cycle effects removed) are hump–shaped. Background premia rise
monotonically out to about 120 days, and then fall gradually to zero by 270 days. These
results stand in contrast to the results of Longstaff (2001), who found that term premia are
indistinguishable from zero across the very short–term maturity spectrum in the repo market.
We can only suppose at this point that the different shape we find here is attributable to
credit and liquidity differences in the CP and repo markets, although further work remains
to be done in order to fully understand these results.
3.5
Quantity Responses
Because commercial paper is a cash instrument and, due to the shallowness of the secondary
market, is typically held to maturity, market participants often manage their risk exposures
in the CP market by managing the maturity structure of their CP assets and/or liabilities.
For example, when the Fed is expected to tighten credit policy, investors have an incentive
shorten the maturities they buy, as a hedge against policy risk (in other words, they shorten
the average duration of their portfolios). Conversely, when the Fed is expected to ease policy,
issuers have an incentive to issue paper that matures right around the date on which policy
is expected to change.
That these incentives translate into observable behavior is illustrated in figure 9. The
figure displays the fed funds target (dashed line) and the dollar amount of commercial paper
that matured each day (solid line). There is a perceptible upward trend in daily maturities
13
due to the growth in the market. However, around this trend, the upward spikes in maturities
are almost uniformly on dates when the Fed altered policy. In other words, CP maturities
“piled up” around the FOMC date, in anticipation of the change in policy.18
A key question concerns whether these pileups of maturing paper feed back into pricing.
Since most commercial paper is rolled over each day, heavy maturities usually translate into
heavy issuance. Hence yields should tend to be higher on days when maturities are heavy
due to supply pressure. To the extent that investors are aware of the maturity structure of
outstanding paper, expectations of supply pressures on particular days should translate into
premia on paper bought prior to these days, as compensation for the forgone opportunity
to earn a higher yield. To examine whether this is indeed the case, we turn to a parametric
specification.
3.6
Parametric Model
Taken together, the results of the previous subsections suggest the following parametric
specification for risk premia:
Ft,t+m − Rt+m−1,t+m = β0 + β1 Yt + β2 m + β3 (m × Ct )+
β4 m + β5 (m × Ct ) + β6 ln(Mt ) + β7 (ln(Mt ) × Yt )
2
(9)
2
where
Ct =



 1
If date t is in a policy cycle, as defined above, or


 0
Otherwise,
18
The large double downward spikes reflect the influence of Y2K on the CP market. The Bond Market
Association had recommended that CP issuers avoid the two weeks around year–end, a recommendation
that was to a large degree honored. As a result, maturities plummeted right around the turn of the year. A
similar phenomenon was seen at the end of 2000, when significant credit concerns gripped the market.
14
and



 1
If date t + m crosses year–end, or
 0
Otherwise,
Yt = 

and Mt is the fraction of total outstanding CP that is set to mature over the next m days.
Note that here we use weekly observations.
While simple, this specification is rich enough to capture the features of risk premia
identified in the previous subsections. The quadratic piece in m can capture the hump–
shaped “background risk premium” identified in figures 7 and 8. The coefficient β1 captures
the year–end premium, and the coefficients β3 and β5 capture the effects of policy cycles.
Finally, the coefficients β6 and β7 identify liquidity feedback effects. Given the potential
importance of liquidity effects at year–end, I have included the interaction term ln(Mt ) × Yt .
Table 5 displays the results. In general, the coefficients are estimated with a good deal of
precision, though again it should be emphasized that the standard errors should be treated
with caution as they are not corrected for error introduced by the first–stage yield curve
estimation procedure. Likewise, the R2 statistic, while indicating that the specification
picks up about 25 percent of the variation in the dependent variable, should be considered
a provisional estimate.
The results indicate that the year–end premium is 51 basis points, on average, with a
substantial component due to liquidity effects, as indicated by the estimate of β7 . The effect
of policy cycles, captured by β3 , is positive and increasing, as expected, though the estimate
is borderline significant. Moreover, the scale of the coefficient suggests that the effects of
policy cycles are economically significant only at longer maturities, but tails off due to the
negative value of β5 . Overall, the results are in agreement with the nonparametric results of
the previous subsections.
In general, it appears that liquidity effects are only in evidence at year–end. The coefficient β6 is small and insignificant, suggesting that pileups of maturities in the midst of
15
the year do not move risk premia. However, it should be noted that this specification is
heavily biased against finding liquidity effects. Recall from figure 9 that liquidity effects are
in evidence right around FOMC dates. Here we have included all other dates, as well, when
we have less reason to expect to find liquidity effects.19
To make the results more concrete, Figure 10 shows the fitted risk premia at the seven,
thirty and ninety day maturities. As can be seen, risk premia shoot up dramatically at
year–end, and the effects of policy cycles are evident at longer maturities. Risk premia are
otherwise smooth under this specification, since the proportion of maturing paper plays a
minor role in the determination of risk premia except at year–end.
4
Conclusion
In this paper, I studied how expected changes in the Federal Reserve’s target rate for federal
funds are expressed in the commercial paper (CP) market. The results showed that the risk
premium function steepens when the Federal Reserve enters a cycle of policy tightenings or
easings, consistent with the relatively greater policy risk investors in CP must accept. In
addition, risk premia shift up at year–end, when liquidity concerns and shifts in borrowing
and lending patterns induce higher premia in the CP market. Finally, background risk–
premia are hump–shaped, in contrast to the flat zero risk–premium function in the repo
market.
The results also identify an important linkage between risk premia and the amount of
commercial paper that is expected to mature. While most important at year–end, there is
informal evidence that these effects are important around FOMC dates, although formalizing
this evidence is work that remains to be done. The results in hand suggest that when
a relatively greater amount of commercial paper is expected to mature on a given date,
investors in paper issued before this date demand a premium for the forgone opportunity to
19
In future revisions of the paper, I plan to narrow the focus of this parameter to dates right around
FOMC meetings.
16
earn a higher yield on the day of heavy maturities.
References
Brennan, M. J. and Schwartz, E. S.: 1979, A continuous time approach to the pricing of
bonds, Journal of Banking and Finance 3, 133–155.
Campbell, J. Y.: 1995, Some lessons from the yield curve, Journal of Economic Perspectives
9(3), 129–152.
Campbell, J. Y., Lo, A. W. and MacKinlay, A. C.: 1997, The Econometrics of Financial
Markets, Princeton University Press, Princeton, NJ.
Cleveland, W. S. and Devlin, S. J.: 1988, Locally weighted regression: An approach to
regression anaysis by local fitting, Journal of the American Statistical Association
83(403), 596–610.
Cox, J. C., Ingersoll, J. E. and Ross, S. A.: 1985, A theory of the term structure of interest
rates, Econometrica 53(2), 386–407.
Downing, C. and Richards, E.: 2000, Measuring term structures of discount securities. Working Paper.
Froot, K. A.: 1989, New hope for the expectations hypothesis of the term structure of interest
rates, Journal of Finance 44, 283–305.
Heath, D., Jarrow, R. and Morton, A.: 1992, Bond pricing and the term structure of interest
rates: A new methodology for contingent claims valuation, Econometrica 60(1), 77–105.
Longstaff, F. A.: 2001, The term structure of very short–term rates: New evidence for the
expectations hypothesis. forthcoming in Journal of Financial Economics.
17
Longstaff, F. and Schwartz, E.: 1992, Interst rate volatility and the term structure: A
two-factor general equilibrium model, Journal of Finance 47(4), 1259–1282.
Melino, A.: 1988, The term structure of interest rates: Evidence and theory, Journal of
Economic Surveys 2(4), 335–366.
Shiller, R. J.: 1990, The term structure of interest rates, in B. Friedman and F. Hahn (eds),
The Handbook of Monetary Economics, North Holland, Amsterdam.
Vasicek, O.: 1977, An equilibrium characterization of the term structure, Journal of Financial Economics 5, 177–188.
18
Figure 1: Outstanding Commercial Paper and Treasury Bills
1800
Commercial Paper
Treasury Bills
1600
$Bil
1400
1200
1000
800
600
400
1993
1994
1995
1996
1997
1998
1999
2000
Table 1: Average Daily Commercial Paper Market Volumes
Volume Number of Number of
Sector
($Mil)
Issues
Issuers
Total Market 121,784
7,626
705
Financial
91,126
5,138
375
Nonfinancial
30,658
2,488
330
January 4, 2000 - December 29, 2000.
19
Figure 2: Daily AA–Rated Financial Commercial Paper and Federal Funds Target Yields
7.00
Target
90-Day
6.00
5.00
4.00
3.00
01/01/1998
01/07/1998
01/01/1999
01/07/1999
01/01/2000
01/07/2000
01/01/2001
7.00
Target
30-Day
6.00
5.00
4.00
3.00
01/01/1998
01/07/1998
01/01/1999
01/07/1999
01/01/2000
01/07/2000
01/01/2001
7.00
Target
1-Day
6.00
5.00
4.00
3.00
01/01/1998
01/07/1998
01/01/1999
01/07/1999
01/01/2000
01/07/2000
01/01/2001
Date
Table 2: Univariate Statistics for CP Spreads to Fed Funds
Standard
Spread
Mean Deviation N
CP-Target
1.4
14.7 676
CP-Effective
-0.6
13.4 676
Daily data, January 1998-June 2001.
All values in basis points.
Total
Assets
Quartile
1 (largest)
2
3
4
5 (smallest)
Table 3: Average CP Oustandings
Total
Number
Number
CP as Fraction CP as Fraction
Assets
of
of CP
of Total
of Current
($Bil)
Firms
Issuers
Liabilities
Liabilities
>1.4
1,615
339
0.12
0.33
0.4-1.4
1,614
17
0.21
0.47
0.1-0.4
1,616
1
0.54
n.a.
0.03-0.1
1,616
0
–
–
< 0.03
1,616
0
–
–
CP liabilities are weekly averages in 2000, total and
current liabilities are quarterly averages from COMPUSTAT.
20
Figure 3: Yield Curves for s1 = 0.1
Spot Rates
Percent
7
6
5
4
3
250
08jan98
01jan99
01jan00
Date
01jan01
0
50
300
200
150
Days
to Maturity
100
Forward Rates
Percent
7
6
5
4
3
250
08jan98
01jan99
01jan00
Date
01jan01
21
0
50
300
200
150
100 Days to Maturity
Figure 4: Yield Curves for s1 = 0.5
Spot Rates
Percent
7
6
5
4
3
250
08jan98
01jan99
01jan00
Date
01jan01
0
50
300
200
150
Days
to Maturity
100
Forward Rates
Percent
7
6
5
4
3
250
08jan98
01jan99
01jan00
Date
01jan01
22
0
50
300
200
150
100 Days to Maturity
Figure 5: Yield Curves for s1 = 0.9
Spot Rates
Percent
7
6
5
4
3
250
08jan98
01jan99
01jan00
Date
01jan01
0
50
300
200
150
Days
to Maturity
100
Forward Rates
Percent
7
6
5
4
3
250
08jan98
01jan99
01jan00
Date
01jan01
23
0
50
300
200
150
100 Days to Maturity
Table 4: Univariate Statistics for s1 = 0.5
Yield
Mean
Std Dev
1
547.80
63.82
7
548.54
63.84
15
549.77
64.16
30
551.69
65.19
60
554.12
67.58
90
556.80
69.97
Changes in Yield
Mean
Std Dev
-1.52
9.64
-0.21
8.77
-0.21
6.91
-0.21
5.03
-0.23
3.57
-0.24
3.74
Spread to Overnight
Mean
Std Dev
0.83
3.45
1.89
7.87
3.73
15.28
5.88
21.23
8.53
26.16
Spread to Repo
Mean
Std Dev
11.18
11.78
11.56
10.69
13.53
9.66
13.98
12.02
15.44
14.31
9.10
22.21
All values are expressed in basis points, 858 observations.
24
Figure 6: Estimated Risk Premia
Risk Premium (basis pts)
s2=0.25
s1=0.1, confidence band
s1=0.1, fit
s1=0.5, confidence band
s1=0.5, fit
s1=0.9, confidence band
s1=0.9, fit
70
60
50
40
30
20
10
0
50
100
150
200
250
Risk Premium (basis pts)
s2=0.50
s1=0.1, confidence band
s1=0.1, fit
s1=0.5, confidence band
s1=0.5, fit
s1=0.9, confidence band
s1=0.9, fit
70
60
50
40
30
20
10
0
50
100
150
200
250
Risk Premium (basis pts)
s2=0.75
s1=0.1, confidence band
s1=0.1, fit
s1=0.5, confidence band
s1=0.5, fit
s1=0.9, confidence band
s1=0.9
70
60
50
40
30
20
10
0
50
100
150
Days Forward
25
200
250
Figure 7: Risk Premia during Policy Cycles
50
Not Policy Cycle
Policy Cycle
Risk Premium (basis pts)
40
30
20
10
0
50
100
150
Days Forward
200
250
Figure 8: Year–End Risk Premia
140
Not Year-End
Year-End
Risk Premium (basis pts)
120
100
80
60
40
20
0
50
100
150
Days Forward
26
200
250
Figure 9: Maturing Commercial Paper and the Fed Funds Target
175
7
Maturities
Target
Maturities ($ Bil)
125
6
100
75
5
50
Yields (Percentage Points)
150
25
4
0
01jan98
01jan99
01jan00
01jan01
Table 5: Parametric Risk Premium Model
The table displays the OLS coefficient estimates for the specification
Ft,t+m − Rt+m−1,t+m = β0 + β1 Yt + β2 m + β3 (m × Ct ) + β4 m2 + β5 (m2 × Ct ) + β6 ln(Mt ) + β7 (ln(Mt ) × Yt )
Coefficient
β0
β1
β2
β3
β4
β5
β6
β7
Estimate
3.88618
51.10279
0.26269
0.02779
-0.00030909
-0.00140
0.71036
18.31570
N = 26, 306
R2 = 0.25
27
Standard
Error t–Statistic
2.17727
1.78
0.84082
60.78
0.03020
8.70
0.01709
1.63
0.00009861
-3.13
0.00008625
-16.21
1.86648
0.38
5.23612
3.50
Figure 10: Estimated Risk Premia
80
7-Day
30-Day
90-Day
70
60
50
40
30
20
10
0
01jul98
01jan99
01jul99
28
01jan00
01jul00
01jan01