The Transmission of Monetary Policy in the Commercial Paper Market

Transcription

1 The Transmission of Monetary Policy in the Commercial Paper Market Chris Downing August 2, 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 Please do not cite the results herein.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 Phone: (202) Fax: (202) 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

2 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

3 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

4 2 Theory Let Y t,t+m denote the yield on commercial paper issued at time t and maturing at time t+m. 4 In other words, Y t,t+m is the interest rate on a spot loan made at time t to be repaid at t+m. Let F t,t+m denote the yield, at time t, on a forward contract to issue overnight commercial paperattimet+m 1 tomatureattimet+m. A forward overnight loan made zero periods forward is just a spot overnight loan, so Y t,t+1 = F t,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 + Y t,t+2 ) 2 =(1+Y t,t+1 )(1+F t,t+2 ), (1) which means that: (1 + F t,t+2 )=(1+Y t,t+2 ) 2 (1 + Y t,t+1 ) 1. (2) 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 + F t,t+m )=(1+Y t,t+m ) m (1 + Y t,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

5 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: F t,t+m = E t [ Yt+m 1,t+m + ɛ (1) t+m 1], (4) where ɛ (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: Y t+m 1,t+m = R t+m 1,t+m + ɛ (2) t+m 1, (5) where R is the target rate and ɛ (2) is again a random error. Substituting (5) into (4), we have: F t,t+m = E t R t+m 1,t+m + E t ɛ t+m 1, (6) where ɛ t+m 1 = ɛ (1) t+m 1 + ɛ (2) t+m 1. In this formulation, the term E t ɛ 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 ɛ 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 E t ɛ 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

6 If we next difference forward overnight rates, we obtain: F t,t+m+s F t,t+m = E t m,s R + E t m,s ɛ, (7) where m,s R = R t+m+s 1,t+m+s R t+m 1,t+m and m,s ɛ = ɛ t+m+s 1 +ɛ 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 E t m,s ɛ 0 for small s, then F t,t+m+s F t,t+m E t 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 E t R t+m 1,t+m in order to infer something about ɛ 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 E t R t+m 1,t+m - in other words, that expectations are rational. 8 A key question addressed in this literature is whether E t ɛ 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

7 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 E t ɛ 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

8 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 s 1 reported in the figure refers to the proportion of the data that is used in each local regression. For example, s 1 =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, s 1 =1.0 implies two parameters - the slope and intercept - while s 1 =0.0 implies a fit that interpolates the raw median yields. 8

9 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 (s 1 =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: F t,t+m R t+m 1,t+m = f(m)+ɛ t, (8) 13 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

10 where f(m) is a smooth function, and ɛ 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 E t ɛ 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 ɛ 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 (s 2 = 0.25), over three levels of first stage smoothing (s 1 =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 (s 2 =0.5), while the bottom panel shows the results when we smooth heavily in the second stage (s 2 =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 (s 1 =0.5 ands 2 =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

11 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, 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

12 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

13 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

14 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: F t,t+m R t+m 1,t+m = β 0 + β 1 Y t + β 2 m + β 3 (m C t )+ β 4 m 2 + β 5 (m 2 C t )+β 6 ln(m t )+β 7 (ln(m t ) Y t ) (9) where 1 If date t is in a policy cycle, as defined above, or C t = 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

15 and 1 If date t + m crosses year end, or Y t = 0 Otherwise, and M t 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 β 1 captures the year end premium, and the coefficients β 3 and β 5 capture the effects of policy cycles. Finally, the coefficients β 6 and β 7 identify liquidity feedback effects. Given the potential importance of liquidity effects at year end, I have included the interaction term ln(m t ) Y t. 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 R 2 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 β 7. The effect of policy cycles, captured by β 3, 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 β 5. 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 β 6 is small and insignificant, suggesting that pileups of maturities in the midst of 15

16 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

17 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, Campbell, J. Y.: 1995, Some lessons from the yield curve, Journal of Economic Perspectives 9(3), 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), Cox, J. C., Ingersoll, J. E. and Ross, S. A.: 1985, A theory of the term structure of interest rates, Econometrica 53(2), 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, 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), 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

18 Longstaff, F. and Schwartz, E.: 1992, Interst rate volatility and the term structure: A two-factor general equilibrium model, Journal of Finance 47(4), Melino, A.: 1988, The term structure of interest rates: Evidence and theory, Journal of Economic Surveys 2(4), 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,

19 Figure 1: Outstanding Commercial Paper and Treasury Bills Commercial Paper Treasury Bills $Bil Table 1: Average Daily Commercial Paper Market Volumes Volume Number of Number of Sector ($Mil) Issues Issuers Total Market 121,784 7, Financial 91,126 5, Nonfinancial 30,658 2, January 4, December 29,

20 Figure 2: Daily AA Rated Financial Commercial Paper and Federal Funds Target Yields Target 90-Day /01/ /07/ /01/ /07/ /01/ /07/ /01/ Target 30-Day /01/ /07/ /01/ /07/ /01/ /07/ /01/ Target 1-Day /01/ /07/ /01/ /07/ /01/ /07/ /01/2001 Date Table 2: Univariate Statistics for CP Spreads to Fed Funds Standard Spread Mean Deviation N CP-Target CP-Effective Daily data, January 1998-June All values in basis points. Table 3: Average CP Oustandings Total Total Number Number CP as Fraction CP as Fraction Assets Assets of of CP of Total of Current Quartile ($Bil) Firms Issuers Liabilities Liabilities 1 (largest) >1.4 1, , , n.a , (smallest) < ,616 0 CP liabilities are weekly averages in 2000, total and current liabilities are quarterly averages from COMPUSTAT. 20

21 Figure 3: Yield Curves for s1 =0.1 Spot Rates Percent jan98 01jan99 01jan00 Date 01jan Days to Maturity Forward Rates Percent jan98 01jan99 01jan00 Date 01jan Days to Maturity 21

22 Figure 4: Yield Curves for s1 =0.5 Spot Rates Percent jan98 01jan99 01jan00 Date 01jan Days to Maturity Forward Rates Percent jan98 01jan99 01jan00 Date 01jan Days to Maturity 22

23 Figure 5: Yield Curves for s1 =0.9 Spot Rates Percent jan98 01jan99 01jan00 Date 01jan Days to Maturity Forward Rates Percent jan98 01jan99 01jan00 Date 01jan Days to Maturity 23

24 Table 4: Univariate Statistics for s1 = Yield Mean Std Dev Changes in Yield Mean Std Dev Spread to Overnight Mean Std Dev Spread to Repo Mean Std Dev All values are expressed in basis points, 858 observations. 24

25 Figure 6: Estimated Risk Premia s 2 =0.25 Risk Premium (basis pts) Risk Premium (basis pts) Risk Premium (basis pts) s 1 =0.1, confidence band s 1 =0.1, fit s 1 =0.5, confidence band s 1 =0.5, fit s 1 =0.9, confidence band s 1 =0.9, fit s 2 =0.50 s 1 =0.1, confidence band s 1 =0.1, fit s 1 =0.5, confidence band s 1 =0.5, fit s 1 =0.9, confidence band s 1 =0.9, fit s 2 =0.75 s 1 =0.1, confidence band s 1 =0.1, fit s 1 =0.5, confidence band s 1 =0.5, fit s 1 =0.9, confidence band s 1 = Days Forward 25

26 Figure 7: Risk Premia during Policy Cycles 50 Not Policy Cycle Policy Cycle 40 Risk Premium (basis pts) Days Forward Figure 8: Year End Risk Premia 140 Not Year-End Year-End 120 Risk Premium (basis pts) Days Forward 26

27 Figure 9: Maturing Commercial Paper and the Fed Funds Target Maturities Target 7 Maturities ($ Bil) Yields (Percentage Points) jan98 01jan99 01jan00 01jan01 4 Table 5: Parametric Risk Premium Model The table displays the OLS coefficient estimates for the specification F t,t+m R t+m 1,t+m = β 0 + β 1 Y t + β 2 m + β 3 (m C t )+β 4 m 2 + β 5 (m 2 C t )+β 6 ln(m t )+β 7 (ln(m t ) Y t ) Standard Coefficient Estimate Error t Statistic β β β β β β β β N =26, 306 R 2 =

28 80 70 Figure 10: Estimated Risk Premia 7-Day 30-Day 90-Day jul98 01jan99 01jul99 01jan00 01jul00 01jan01 28