The Term Structure of Commercial Paper Rates

The Term Structure of Commercial Paper Rates (cid:3) Chris Downing and Stephen Oliner Federal Reserve Board April 2, 2004 Abstract This paper tests the expectations hypothesis in the market for commercial paper. Our main dataset, which is new to the literature, consists of daily indexes constructed from the actual market yields for nearly all commercial paper issued by U.S. corporations between January 1998 and August 2003. We show that the term premia built into commercial paper yields rise dramatically at year-end, causing the expectations hypothesis to be rejected. However, once we control for these predictable year-end e(cid:11)ects, we (cid:12)nd the reverse|that commercial paper yields largely conform with the expectations hypothesis. Key words: Term structure; Expectations hypothesis; Commercial paper Classi(cid:12)cation: E43 This paper has bene(cid:12)ted fromdiscussionswith GeertBekaert,JimClouse,FrancisLongsta(cid:11),andBrian Sack; the authors thank Jonathan Wright for useful econometric advice and for providing computer code to calculate robust con(cid:12)dence intervals; all errors and omissions remain the responsibility of the authors. The viewsexpressedarethoseoftheauthorsandshouldnotbeattributedtotheBoardofGovernorsoftheFederal ReserveSystemorits sta(cid:11). Pleaseaddresscorrespondenceto (Downing): FederalReserveBoard,MailStop 93, Washington, DC 20551. Phone: (202) 452-2378. Fax: (202) 728-5887. E-Mail: cdowning@frb.gov. (Oliner): Federal Reserve Board, Mail Stop 66, Washington, DC 20551. Phone: (202) 452-3134. Fax: (202) 452-5296. E-Mail: soliner@frb.gov.

1 Introduction Interest in the expectations hypothesis of the term structure of interest rates dates back at least a century, largely because it is rooted in one of the most basic concerns of capital market participants: Is one better o(cid:11) committing funds for a long or short period? Tests of theexpectationshypothesisalsocommandattentionbecausetheyshedlightontheformation of expectations, the operation of (cid:12)nancial markets, and the transmission of monetary policy through the markets. Accordingly, an enormous amount of research has been devoted to testing the expectations hypothesis.1 In general, although not uniformly, the expectations hypothesis has been rejected in various U.S. credit markets.2 Recently, however, Longsta(cid:11) (2000) found strong empirical support for the expectations hypothesis in the market for domestic U.S. repurchase agreements of less than 90 days maturity. Longsta(cid:11)’s results raise the question of whether the expectations hypothesis holds in other very short-term U.S. credit markets. This paper tests the expectations hypothesis in the market for commercial paper. Commercial paper (CP) is an unsecured debt instrument of up to 270 days’ maturity issued by investment-grade corporations. Firms use CP to (cid:12)nance inventories, to provide bridge (cid:12)nancing in connection with various transactions, and for day-to-day cash management. The commercial paper market is large, with approximately $1.3 trillion outstanding at the end of 2003. In the fourth quarter of 2003, daily placements of commercial paper averaged about $100 billion, principally in maturities of 90 days or less, and each day an average of about 1For surveysofthis literature,seeMelino (1988)andShiller (1990);Campbell, LoandMacKinlay(1996) provide a textbook treatment. 2The empirical evidence from foreign markets has been somewhat more supportive of the expectations hypothesis. See Hardouvelis (1994),Gerlachand Smets (1997), Dahlquist and Jonsson(1995),and Bekaert, Hodrick and Marshall (2001). Gerlach and Smets (1997) suggest that the better performance of the expectations hypothesis in some foreign markets owes to the greater predictability of short rates in those markets. 1

500 (cid:12)rms issued new paper. Despite this active new-issue market, secondary trading is thin, consisting primarily of trades between the major dealers and investors who wish to liquidate their holdings.3 In addition to having limited liquidity, commercial paper is subject to default. Hence, the di(cid:11)erence in expected returns between a long-term position in commercial paper and a strategy of rolling over shorter-term paper will reflect not only the usual premia that compensate investors for interest-rate risk, but also premia to compensate for default risk. Testing the expectations hypothesis in the commercial paper market is of interest for several reasons. First, this test o(cid:11)ers additional evidence on the expectations hypothesis for very short-term interest rates, where only limited research has been conducted.4 Second, as mentioned above, commercial paper is a defaultable instrument traded in a relatively thin secondary market. Accordingly, tests of the expectations hypothesis in this market o(cid:11)er insights into the interaction of default and liquidity risk with the expectations hypothesis. Third, commercial paperratesarestronglyinfluenced bymonetarypolicy. Hence, our results have implications for the transmission of monetary policy to private interest rates.5 Weconductourmaintestsoftheexpectationshypothesisusingacomprehensive database oncommercial paper yields published bytheFederalReserve. This database, which is newto theliterature, consistsofdailyindexesconstructedfromtheactualmarketyieldsonnearlyall commercial paper issued by U.S. (cid:12)rms, beginning in January 1998. Using these transactionsbaseddata,weshowthattermpremia forcommercialpaperjumpupatyear-end, causing the expectations hypothesis to be rejected. The year-end jump probably reflects a combination 3For further discussion of the commercial paper market, see Stigum (1990). 4Besides Longsta(cid:11) (2000), the only studies we are aware of that have characterized the overnight to 90day portion of the yield curve are Simon (1990), Roberds, Runkle and Whiteman (1996), Balduzzi, Bertola and Foresi (1997), Lange, Sack and Whitesell (2003), and Swanson (2004). 5For recentstudies thathighlightthe roleofthe expectationshypothesis inthe transmissionofmonetary policy, see Rudebusch (1995), Balduzzi et al. (1997), Kozicki and Tinsley (2001), and Roush (2001). 2

of factors. One contributing factor appears to be \window dressing" on the part of some large institutional investors. Just prior to releasing their year-end (cid:12)nancial statements, these investors evidently have an incentive to temporarily substitute Treasury bills and other safe instrumentsfortheirholdingsofcommercialpaper|especiallylower-gradepaper|topresent a strong balance sheet to investors.6 Another likely factor is the desire of commercial paper issuers to lock-in longer-term funding over year-end when conditions in overnight markets tend to be volatile. Their willingness to pay a premium for this insurance boosts the yield on longer-term commercial paper at year-end. We then test whether the expectations hypothesis holds after controlling for these predictable year-end e(cid:11)ects. The key result of the paper is that, with these controls in place, we (cid:12)nd strong support for the expectations hypothesis in the commercial paper market. Evidently, the term premia in commercial paper yields are fairly stable other than at year-end.7 For completeness, we also conduct the same tests with daily yield indexes constructed from dealer quotes spanning March 1989 to August 1997. Although these indexes served as the Federal Reserve’s o(cid:14)cial series on commercial paper yields until 1997, they are less accurate than the indexes based on actual transactions, and the Fed stopped publishing the dealer quotes when the transaction data became available. In contrast to the transactions data, the yields based on dealer quotes reject the expectations hypothesis, even after controlling for year-end e(cid:11)ects. One possible explanation for the di(cid:11)erent results is that the dealer-quote data are of 6Thisargumentrequiresthatdemandforcommercialpaperbeinelastic,sothatotherinvestorsdonot(cid:12)ll the void at prevailing yields. See Musto (1997) and Musto (1999) for additional discussions of the window dressing hypothesis. 7The days following the terrorist attacks of September 11, 2001 are a notable exception. The attacks severely disrupted the operation of the commercial paper market, an unanticipated event that produced sharp movements in realized term premia. We treat these observations as outliers to prevent them from a(cid:11)ecting our conclusions. 3

inferior quality|perhaps containing stale quotes, for example|and do not accurately reflect the dynamics of commercial paper rates. An alternative explanation relates to the conduct of monetary policy. As documented by Lange et al. (2003) and Swanson (2004), the Federal Open Market Committee (FOMC) has taken many steps since the late 1980s to make its views on the economy and its policy actions more transparent. Among these steps, the FOMC began in February 1994 to announce policy changes on the day of its meetings and to explain the reasons for the change. Likely reflecting the greater transparency of monetary policy, Lange et al. found that the federal funds rate became more predictable starting in 1994 and that the expectations hypothesis performed far better after that point than in earlier years.8 We obtain similar results when we split the dealer-quote data for CP rates at February 1994: the earlier data soundly reject the expectations hypothesis, but we (cid:12)nd more support for the hypothesis from 1994 on. This (cid:12)nding suggests that the later period covered bythetransactionsdata(1998-2003)mayhelpexplainthedi(cid:11)eringresultsgeneratedbythese data and the full sample of dealer quotes. If we had a longer history for the transactions data, we could run a more de(cid:12)nitive test of this explanation. However, in the absence of such a test, we cannot rule out that the inferior quality of the dealer-quote data also plays a role. The only previous tests of the expectations hypothesis with commercial paper yields appear to have been conducted by Fama (1986) and Cook and Hahn (1990), neither of which dealt with year-end e(cid:11)ects. Both studies rejected the expectations hypothesis using dealer-quote indexes, consistent with our results based on the pre-1994 dealer-quote data. This paper is organized as follows. In section 2, we review the theory of the expectations 8Swanson(2004)(cid:12)nds some deteriorationin the predictability of the federalfunds rate since 2001. However, for the period since 1994 as a whole, he concludes that increased predictability remains a robust feature ofthe data andthat changesinFOMC transparencyhavelikely helped to make the funds rate more predictable. 4

hypothesis and our speci(cid:12)cation of time-varying term premia. Section 3 discusses our data andeconometricresults, andsection4concludes withsome(cid:12)nalthoughtsontheimplications of our results and some directions for future work. 2 Theory 2.1 The Expectations Hypothesis Denote by r(m;t) the interest rate at time t on a spot loan to be repaid at time t+ m (a discount bond of maturity m). Similarly, let f(m;t+i;t) denote the interest rate at time t on a forward loan that starts at time t + i and ends at time t + i + m. We measure both r(m;t) and f(m;t+i;t) on a continuously compounded and annualized basis. Using m = 1 to denote an overnight maturity, we can write the following relationships between forward overnight rates and future spot overnight rates: f(1;t+0;t)−r(1;t) = 0 (1) f(1;t+1;t)−r(1;t+1) = (cid:23) (2) t+1 f(1;t+2;t)−r(1;t+2) = (cid:23) (3) t+2 . . . f(1;t+m−1;t)−r(1;t+m−1) = (cid:23) (4) t+m−1 where the (cid:23) are random errors. Equation 1 states that, by de(cid:12)nition, the forward overnight (cid:1) rate zero days ahead equals the current spot overnight rate. Equations 2-4 state that the forward overnight rate set at time t for time t+i (i = 1;2;:::;m−1) will di(cid:11)er from the 5

spot overnight rate realized at time t+i by the random amount (cid:23) . t+i To develop a test of the expectations hypothesis, we (cid:12)rst add the elements on each side of equations 1-4, producing: t+Xm−1 t+Xm−1 (f(1;i;t)−r(1;i)) = (cid:23) : (5) i i=t i=t+1 Noting that the m-period continuously-compounded spot rate r(m;t) equals the average of t+Pm−1 the forward overnight rates over its term (r(m;t) = 1 f(1;i;t)), we have: m i=t t+Xm−1 t+Xm−1 r(m;t)m = r(1;i)+ (cid:23) : (6) i i=t i=t+1 Next, multiply equation 6 by 1 , subtract r(1;t) from both sides, and rearrange terms, m producing: 1 t+Xm−1 1 t+Xm−1 r(1;i)−r(1;t) = (r(m;t)−r(1;t))− (cid:23) : (7) m m i i=t i=t+1 t+Pm−1 Now introduce (cid:12)(cid:3) = 1, and write (cid:23) as the sum of a predictable component, (cid:11)(cid:3) , m i m;t i=t+1 and a mean-zero error term, (cid:15)(cid:3) , which produces: m;t 1 t+Xm−1 1 1 r(1;i)−r(1;t) = − (cid:11)(cid:3) +(cid:12)(cid:3) (r(m;t)−r(1;t))− (cid:15)(cid:3) : (8) m m m;t m m m;t i=t Equation 8 can be rewritten in the following equivalent but more convenient form that we use for our regression tests: 1 t+Xm−1 r(m;t)− r(1;i) = (cid:11) +(cid:12) (r(m;t)−r(1;t))+(cid:15) ; (9) m m;t m m;t i=t 6

where (cid:11) (cid:17) 1(cid:11)(cid:3) , (cid:12) (cid:17) 1 − (cid:12)(cid:3), and (cid:15) (cid:17) 1(cid:15)(cid:3) . Under rational expectations, (cid:15) m;t m m;t m m m;t m m;t m;t is uncorrelated with information available at time t, including the yields appearing on the right-hand side of equation 9. As a result, the (cid:11) and (cid:12) coe(cid:14)cients can be estimated m;t m consistently with ordinary least squares. The expectations hypothesis rules out anytime variationintermpremia.9 Interms of the coe(cid:14)cients in equation 9, we characterize the expectations hypothesis with the restrictions (cid:11) = (cid:11) , a time-invariant constant for each maturity m, and (cid:12) = 0 for all m. The m;t m m so-called pure expectations hypothesis further requires that (cid:11) = 0. In other words, under m the expectations hypothesis, the di(cid:11)erence between an m-period yield and the average of the overnight yields over the same period equals a constant, possibly equal to zero, plus expectational error. 2.2 Year-End Premia in the Commercial Paper Market Predictable year-end e(cid:11)ects are a key component of term premia at all maturities in the commercial paper market. We illustrate these e(cid:11)ects for the 30-day maturity in (cid:12)gure 1; the other maturities exhibit qualitatively similar year-end e(cid:11)ects and so are omitted for the sake of brevity. Panel A of the (cid:12)gure shows 30-day term premia for CP issued by the highest quality (cid:12)rms|those with short-term credit ratings of A1/P1 and long-term bond ratings of AA or better.10 The term premia are computed as the di(cid:11)erence between the 30-day CP rate and the average overnight CP rate over the same 30-day period. The panel 9Many di(cid:11)erent versionsofthe expectations hypothesis have appearedin the literature. At longermaturities, some forms of the expectations hypothesis are inconsistent with each other. However, for maturities as short as we consider here, the various forms of the expectations hypothesis are virtually the same (see Longsta(cid:11) (2000) for further discussion). 10Standard and Poor’s and Moody’s both issue short-term ratings on a three-point scale (1, 2, and 3), with 1 being the highest and 3 being the lowest. Standardand Poor’spre(cid:12)xes their short-termratings with an ’A’, while Moody’s uses a ’P’. Thus, an A1/P1 rating means that the (cid:12)rm received a ’1’ rating by both rating agencies. 7

displays both the dealer-quote data (1989-1997) and the transaction-based data (1998-2003) that we discuss at length in section 3.1 below.11 Panel B shows 30-day term premia for CP issued by A2/P2-rated (cid:12)rms with long-term bond ratings of BBB or A|issuers with credit quality substantially below those in the upper panel; this series begins in 1998 because the dealer-quote data for this rating class are very limited. As can be seen, the 30-day term premium tends to jump as year-end approaches, with the largest increases for A2/P2-rated issuers. This additional premium then disappears as soon as year-end passes. The size of the spike varies from year to year, and we allow for this variation in our empirical tests of the expectations hypothesis. In recent years, the largest jump occurred in advance of the century date change at the end of 1999. Year-end e(cid:11)ects in other money markets are more muted, on balance, than those in the commercial paper market. For example, as shown in (cid:12)gure 2, term premia do tend to rise at year-end in the markets for repurchase agreements (panel A) and federal funds (panel B). However, for repurchase agreements (\repo"), the year-end increases are relatively small and are often di(cid:14)cult to distinguish from the variation throughout the rest of the year. For federal funds, the year-end increases in the term premium are roughly on par with those for AA-rated commercial paper but are much smaller than the spikes observed for A2/P2 paper. These di(cid:11)erences likely help to explain why Longsta(cid:11) (2000) could not reject the expectations hypothesis in the repo market even without controls for year-end e(cid:11)ects and why Lange et al. (2003) found that the expectations hypothesis has performed reasonably well in the federal funds market since the early 1990s, again without year-end controls. Year-end e(cid:11)ects are evident as well in the quantity of commercial paper outstanding. 11The break in the series reflects the Fed’s switch from dealer quotes to the transactions data. Although 30-day rates based on the transactions data are available back to the beginning of 1997, the series for overnight rates starts a year later, which prevents us from using the 1997 data. 8

Figure3displays thelevelofoutstandingcommercialpaperfor\tier-1"and\tier-2"issuers.12 The lower panel indicates that CP outstanding for tier-2 issuers declines systematically at year-end and that the drop is usually reversed in January. This pattern is much less evident for tier-1 issuers, further indicating that year-end e(cid:11)ects are concentrated among lowerquality (cid:12)rms. Another notable feature of the CP market is that the volume of maturing paper declines markedly at year-end. Figure 4 illustrates this point by showing the average maturity structure of outstanding commercial paper at two points in December{the (cid:12)rst Wednesday of the month (panel A) and the third Wednesday (panel B). The bars depict the average amount of paper, as of the indicated date, that is set to mature in the maturity ranges shown on the horizontal axis. The dotted vertical lines indicate year-end, and the solid lines indicate the average maturity structure for all other Wednesdays.13 The distributions of outstanding paper reveal a pronounced drop in the amount of paper maturing around year-end. As year-end approaches, the maturity structure tends to shift toward longer-dated paper, with the amount of CP maturing after year-end being substantially greater than would be predicted by the average maturity structure of paper at other times of the year. This paucity of maturing paper, combined with the limited amount of secondary market trading, points to a fall-o(cid:11) in market liquidity at year-end. One explanation for these year-end patterns focuses on \window dressing" by some in- 12Rule2a-7oftheInvestmentCompanyActof1940limitsthecreditriskthatmoneymarketmutualfunds may bear by restricting their investments to \eligible" securities. An eligible security must carry one of the two highest ratings (\1" or \2") for short-term obligations from at least two of the nationally recognized statistical ratings agencies (which currently consist of Standard and Poor’s, Moody’s, and Fitch IBCA). A tier-1 security is an eligible security rated \1" by at least two of the rating agencies; a tier-2 security is an eligible security that is not a tier-1 security. We employ this quality split in order to display lengthy time series, as the Federal Reserve data provide only a limited history for CP outstanding based on the A1/P1 versus A2/P2 split. 13We use Wednesdays for the (cid:12)gure because the Federal Reserve releases its data on CP outstanding at a weekly-Wednesday frequency. 9

vestors in the commercial paper market (Musto (1997, 1999)). According to the Federal Reserve’s Flows of Funds accounts, approximately one-half of all outstanding commercial paper is held by money market mutual funds, insurance companies, and pension funds. Most of these entities report on their portfolio holdings at year-end, and they show some propensity to window dress their balance sheets by temporarily substituting higher-quality investments for their usual holdings. Given this behavior, lower-quality issuers likely would have to o(cid:11)er a yield premium to induce investors to hold their paper over year-end. Rather than paying such a premium, some issuers might (cid:12)nd it less costly to turn to other forms of (cid:12)nance at year-end, which would help explain the drop in outstanding paper.14 A second explanation focuses onuncertainty in short-term (cid:12)nancing markets at year-end. Overnight interest rates tend to be highly volatile at that time of year because of the large| and variable|increases in demand for cash by (cid:12)nancial institutions, non(cid:12)nancial businesses, and individuals. Figure 5 depicts one measure of this heightened rate volatility. As shown, the deviation of the federal funds rate from its target tends to be substantially larger around year-end than during the rest of the year. To the extent that this volatility is transmitted to other very short-term instruments like overnight commercial paper, (cid:12)rms might be willing to insure against this interest-rate risk by issuing longer-maturity paper in lieu of rolling over paper every day. The spike in term premia around year-end shown in (cid:12)gure 1 could partly reflect the price that issuers are willing to pay for this insurance. 14Window dressingby moneyfund managersmightalsohelp explainthe year-endpricinge(cid:11)ects observed in the Treasury bill market. If enough CP investors move their funds into Treasury bills for a short time aroundyear-end,this flow could cause the temporary increase in Treasurybill prices documented by Du(cid:11)ee (1996). 10

2.3 Time Variation in Term Premia The foregoing discussion suggests that term premia in the commercial paper market might rise at year-end as compensation for increases in liquidity risk, investors’ aversion to holding lower-quality assets at that time, and heightened interest-rate risk. It is important to highlight that these year-end factors are predictable|and thus get embedded in the structure of commercial paper yields. This stands in contrast to unpredictable events, such as sudden defaults by large issuers (owing to fraud, for example) or the terrorist attacks of September 11, 2001, which have important but unanticipated e(cid:11)ects on the market. In our rational expectations framework, it is only anticipated events that can systematically shift term premia. As we showed in (cid:12)gure 1, the amplitude of the year-end jump in term premia varies markedly both over time and with credit quality. Our analysis of year-end e(cid:11)ects suggests that a realistic speci(cid:12)cation of term premia ought to consist of three components: (i) the standard time-invariant component that is present at all times; (ii) a component that rises as year-end approaches; and (iii) a component that can capture the e(cid:11)ects of heightened interest-rate volatility and reduced market liquidity right around year-end. To allow for these sources of variation, we use the following speci(cid:12)cation for term premia: X (cid:11) = (cid:11) + ((cid:11) +(cid:11) (cid:28) +(cid:11) (cid:28)2 +(cid:11) (cid:28)3 )DX +(cid:11) D ; (10) m;t m;0 m;yr;1 m;yr;2 m m;yr;3 m m;yr;4 m m;yr;t m;yr;5 yr;t yr where yr = 1998;:::;2002 for the transactions-based data and yr = 1989;:::;1996 for the dealer-quote data. In this speci(cid:12)cation, the coe(cid:14)cient (cid:11) represents the usual time-invariant component m;0 of the term premium|component (i) above. Component (ii) is modeled using a cubic speci- 11

(cid:12)cation in time that is in e(cid:11)ect only near year-end. Speci(cid:12)cally, the variable DX equals m;yr;t one when the observation date t is before, and the maturity date t+m is after, December 26 of the year indexed by yr. We allow DX to switch on for maturities slightly before m;yr;t year-end because (cid:12)gure 4 suggests that year-end e(cid:11)ects begin to be seen about a week before the turn of the year. When this dummy variable equals one, the variable (cid:28) counts the m number of days from December 26 of the given year to the maturity date t+m. The cubic term in (cid:28) allows the speci(cid:12)cation to capture a wide range of time patterns for the year-end term premium. Finally, component (iii) is modeled with the dummy variable D , which yr;t equals one when the observation date t is between December 22 of the year indexed by yr and January 10 of the following year. Hence the coe(cid:14)cient (cid:11) captures any level shifts in m;5 term premia right around year-end, when, as we discussed earlier, liquidity in the market appears low and short-term interest rates are relatively volatile. Allowing the coe(cid:14)cients to vary across years introduces additional flexibility. In the next section, we test traditional speci(cid:12)cations of term premia, as well as our new speci(cid:12)cation that incorporates year-end premia. 3 Data and Estimation Results 3.1 Data Large investment-grade corporations in the United States typically maintain commercial paper programs, often of signi(cid:12)cant size. The bulk of commercial paper issuers reside in the top size quintile of publicly traded corporations|(cid:12)rms with total assets, at book value, of more than $1.4 billion in 2003. For this top quintile of (cid:12)rms, commercial paper accounts, on 12

average, for30percent oftheircurrentliabilities, makingitanimportantsourceofshort-term credit.15 We employ two sources of daily data on commercial paper yields.16 Our primary source consists of the commercial paper discount yields currently published by the Federal Reserve Board for AA-rated and A2/P2-rated domestic non(cid:12)nancial companies. We focus on maturities of 90 days or less because the market for longer-maturity paper is quite thin. The Federal Reserve Board constructs these yield indexes from transaction-level data supplied by the Depository Trust Company, which handles clearing and settlement for more than 95 percent of all commercial paper trades in the United States. Federal Reserve sta(cid:11) (cid:12)t a smooth curve to the transaction-level data. The end result is a daily series of constant-maturity, zero-coupon yields.17 Our yield data cover each business day from January 2, 1998 through August 1, 2003, for a total of 1,365 daily observations. The upper two panels of table 1 display summary statistics for these transactions-based yields. For AA-rated issuers (top panel), yields rise very little with increases in maturity, resulting in a mean spread between 90-day and overnight paper of only 3.09 basis points. In contrast, for A2/P2-rated issuers (middle panel), the mean 90-day spread is 19.09 basis points, reflecting the greater default and liquidity risks in this part of the market. The yields for both AA and A2/P2 paper are highly autocorrelated at all maturities, consistent with the behavior of other short-term interest rates. We also make use of a second database, consisting of dealer quotes on yields for com- 15These (cid:12)gures are calculated using the Federal Reserve’s commercial paper database and Compustat. 16The yield indices used to construct the term premia are from the Federal Reserve’s daily commercial paper release. Details can be found at: http://www.federalreserve.gov/Releases/cp/about.htm. 17Thisproceduredoesnothavetodealwiththee(cid:11)ectofcouponsonobservedyieldsbecausetheunderlying data pertain to newly-issued discount instruments. Thus, the smoothing procedure directly estimates the discount function itself, as opposed to extracting the discount function implied by the prices of coupon securities. 13

mercial paper issued by a generic AA-rated domestic corporation, collected by the Federal Reserve Bank of New York between February 27, 1989 and August 29, 1997.18 Over this period, the New York Fed surveyed the major dealers each day and constructed unweighted averages of the rates reported for various maturities. The lower panel of table 1 displays summary statistics for these data. As shown, the longer-term yields from the dealer survey exhibit higher spreads to overnight rates than the transactions-based AA yields, reaching 14.59 basis points at the 90-day maturity. One possible explanation for the higher spreads is that, while the dealers were instructed to report yields for AA-rated corporations, they may have in fact provided yields for (cid:12)rms of lesser credit quality.19 3.2 A First Look at Term Premia To characterize term premia in the commercial paper market, table 2 reports estimates of the following regression: 1 t+Xm−1 r(m;t)− r(1;i) = (cid:11) +(cid:15) ; (11) m m m;t i=t where (cid:11) represents the average term premium at maturity horizon m, and (cid:15) is a meanm m;t zero error term. Recalling equation 9, this speci(cid:12)cation imposes the restrictions from the expectations hypothesis|namely, that (cid:11) is time-invariant and that (cid:12) equals zero|and m;t m then estimates the average term premium conditional on these restrictions. As shown in the upper two panels of the table, the transactions data clearly indicate that term premia are non-zero, with the exception of the shortest maturity (7 days) for the 18The New York Fed surveyeddealers going back to the 1960s,but only for a limited range of maturities. In order to make our results comparable across the two sources of data, we restrict our analysis of the dealer-quote data to the period over which the dealer survey included the widest range of maturities. 19See Cook and Lawler (1983) for further discussion of the New York Fed’s dealer survey. 14

highest-quality issuers. On average, AA-rated issuers pay 3.50 basis points more to place 30-day paper than to roll overnight paper for 30 days, while A2/P2-rated issuers pay 12.76 basis points more; over a 90-day horizon, these premia rise to 11.93 basis points for AA issuers and 27.85 basis points for A2/P2 issuers.20 Based on these results, we would clearly reject the pure expectations hypothesis in the commercial paper market. The dealer-quote data support a similar conclusion. The estimates of term premia in the lower panel are highly signi(cid:12)cant and larger in size than those based on the transactions data for AA (cid:12)rms, the part of the market to which the quotes should apply. In fact, for every maturity, the estimated term premium is closer to the premium for A2/P2-rated (cid:12)rms than to that for AA-rated (cid:12)rms. 3.3 Tests of the Expectations Hypothesis 3.3.1 Maturity-Speci(cid:12)c Term Premia We (cid:12)rst consider the evidence for the standard version of the expectations hypothesis that allows term premia to vary by maturity but not over time: 1 t+Xm−1 r(m;t)− r(1;i) = (cid:11) +(cid:12) (r(m;t)−r(1;t))+(cid:15) : (12) m m m m;t i=t In contrast to equation 11, this speci(cid:12)cation tests whether (cid:12) = 0 rather than imposing m that restriction a priori. Table 3 displays the estimates of (cid:11) and (cid:12) , along with their m m t-statistics. The t-statistics are corrected for the overlap in the errors. However, as is well known in the term structure literature, interest rates are highly persistent, a feature that 20These results contrastwith those in Longsta(cid:11)(2000),who found a 90-dayterm premium of just 3 basis points using data on repurchase agreements. We would expect term premia to be greater in the commercial paper market both because repo contracts are almost free of default risk and because these contracts are more liquid than commercial paper. 15

can lead to distortions in the distributions of conventional test statistics (Bekaert, Hodrick and Marshall (1997)). Hence for each maturity the (cid:12)nal two columns of the table display the critical values for a 95 percent con(cid:12)dence interval that maintains the correct test size in the presence of a regressor with a (possibly large) autoregressive root (Cavanagh, Elliott and Stock (1995)).21 Based on the transactions data for AA-rated issuers, we (cid:12)nd some support for the expectations hypothesis. The point estimates of (cid:12) at the 60- and 90-day maturities are relatively m close to zero (0.13 and 0.04, respectively); comparing the t-statistics to the lower and upper critical values, these coe(cid:14)cient estimates are also statistically insigni(cid:12)cant. The point estimate of (cid:12) at the 7-day maturity is somewhat larger at 0.29, but it too is insigni(cid:12)cant. At m the same time, the estimate of (cid:12) is signi(cid:12)cantly di(cid:11)erent from zero at the 15- and 30-day m maturities. In contrast to these mixed results based on the data for AA-rated issuers, we decisively reject the expectations hypothesis with the data for A2/P2-rated issuers and with the dealer-quote data. For both sets of data, the estimate of (cid:12) is well above zero and highly m signi(cid:12)cant at every maturity. The estimates of (cid:11) are all signi(cid:12)cantly di(cid:11)erent from zero, with the exception of the m 7-day maturity for AA-rated issuers. Thus, as in table 2, we obtain strong evidence against the pure expectations hypothesis. The estimates of (cid:11) using the dealer-quote data are again m more similar to those for A2/P2-rated issuers than for AA-rated issuers, underscoring our concerns about the accuracy of the dealer-quote data. 21Bekaert et al. (1997) develops a Monte Carlo approach for correcting the size of the test statistics in (cid:12)nite samples. This method is implemented by Longsta(cid:11) (2000) for very short-term repo data. We have implemented this procedure on all of the data here, but found that the data generating process (4-factor VAR-GARCH) tended to produce too many explosive paths for the Monte Carlo results to be reliable. 16

3.3.2 Controlling for Time Variation in Term Premia We now consider the evidence for the expectations hypothesis after we control for the rise in term premia around year-end and for the idiosyncratic e(cid:11)ects of the September 11 terrorist attacks. In this case, our speci(cid:12)cation is given by: t+Pm−1 r(m;t)− 1 r(1;i) = (cid:11) +(cid:12) (r(m;t)−r(1;t))+ m m;0 m i=t P ((cid:11) +(cid:11) (cid:28) +(cid:11) (cid:28)2 +(cid:11) (cid:28)3)DX +(cid:11) D + (13) m;yr;1 m;yr;2 m m;yr;3 m m;yr;4 m m;yr;t m;yr;5 yr;t yr (cid:11) SX +(cid:11) S +(cid:15) : m;6 m;t m;7 t m;t For the transaction data, yr = 1998;:::;2002, while for the dealer-quote data, yr = 1989;:::;1996. The variables DX , D , and (cid:28) are as de(cid:12)ned in section 2.3, and m;yr;t yr;t m SX and S are variables designed to control for the e(cid:11)ects of the September 11 attacks on m;t t the CP market. These attacks severely disrupted the computer networks that money-market participants rely on to carry out their transactions. With some banks unable to transfer the funds necessary to redeem maturing commercial paper, a sizable portion of the paper that came due in the days following the attacks could not be honored.22 Moreover, a large number of issuers could not roll over maturing paper. Many of these issuers instructed their banks to draw down liquidity backup lines in order to make payments on maturing paper, producing substantial draws at the discount window at the Fed.23 These market disruptions produced signi(cid:12)cant pricing e(cid:11)ects in the commercial paper 22Thesituationwasanalagoustoanindividualattemptingtocashacheck,andupon(cid:12)ndingthenecessary funds unavailable, returning the next day to try again. In the jargon of the money markets, the maturity presentments were \failed" and presented again the next day. 23For a full description of the Federal Reserve’s response to the stresses in the U.S. (cid:12)nancial system, see the Monetary Report to Congress, February 2002,available at: http://www.federalreserve.gov/boarddocs/hh/2002/February/FullReport.htm. 17

market. Yields on the Tuesday of the attacks showed little change from Monday, but they likely reflected pricing on deals done in the morning before the attacks.24 On Wednesday, yields on overnight paper jumped about 30 basis points for AA-rated issuers, and about 60 basis points for A2/P2 issuers.25 Overnight yields rose further on Thursday and Friday, as operational risks in the clearance and settlement systems remained signi(cid:12)cant, raising the possibility of defaults. Then, on the Monday following the attacks, yields dropped precipitously, owing in part to a 50 basis point cut in the target federal funds rate just prior to the reopening of the equity markets, as well as to the sizable liquidity injections by the Fed in the days following the attacks. Rates continued to gyrate for the remainder of the month, but by the beginning of October, the market had largely stabilized. To account for these e(cid:11)ects, we introduce the dummy variable SX which takes the m;t value one when the observation date t is before September 11, 2001 and the maturity date t+m is after September 11. When SX equals one, the yields at date t were una(cid:11)ected m;t by September 11, but all of the overnight yields realized after September 11|which we use to construct term premia|were highly elevated. We also introduce the variable S , which t equals one when the observation date t is between September 11 and September 18, 2001, a period during which all maturities|including overnight paper|bore the imprint of September 11. We treat the observations that are dummied out in this way as outliers resulting from a singular event that ought not influence our conclusions regarding the expectations hypothesis.26 24The commercial paper market is a \morning market" in the sense that nearly all of the deals are completed before noon, in order to facilitate same-day settlement. 25The Fed’s calculation of yields on these days was hampered by the sharp drop in market liquidity, and the (cid:12)gures cited here should be regarded as merely indicative. 26While these September 11 dummy variables are similar in their construction to the year-end dummy variableswe introducedearlier,their interpretationisverydi(cid:11)erent. Whereasthe year-enddummies control for the influence of predictable events on term premia, the September 11 dummy variables are being used to removethe influence of an unpredictable one-time eventduring the period coveredby our transactions data. 18

Table 4 presents the estimates of the (cid:11) and (cid:12) coe(cid:14)cients in equation 13; the tables m;0 m in appendix A.2 display the estimates of all of the year-end and September 11 coe(cid:14)cients. Based on the transactions data, we (cid:12)nd strong support for the expectations hypothesis once we control for year-end e(cid:11)ects and September 11.27 For AA-rated commercial paper, the point estimates of (cid:12) are now much closer to zero than they were absent these controls m (except for 90-day paper, for which (cid:12) was already close to zero). Moreover, comparing the m t-statistics to the robust critical values in the last two columns of the table, we see that all of the slope coe(cid:14)cient estimates are statistically insigni(cid:12)cant. For A2/P2-rated commercial paper, we (cid:12)nd that the point estimates of (cid:12) are also in the neighborhood of zero. Only the m estimate at the 30-day maturity is statistically signi(cid:12)cant. The results for the dealer-quote data, shown in the bottom panel of the table, provide much less support for the expectations hypothesis. The point estimates of (cid:12) shrink in m size after controlling for year-end e(cid:11)ects, but they remain statistically signi(cid:12)cant except at the 7-day maturity. In addition, these coe(cid:14)cient estimates are generally larger than those obtained with the transactions data. As noted earlier, year-end changes in term premia are a dominant characteristic of commercial paper yields. Table 5 quanti(cid:12)es this fact by comparing the adjusted-R2 statistics from the standard regression (equation 12) with those from the speci(cid:12)cation that accounts for year-end e(cid:11)ects and September 11 e(cid:11)ects (equation 13). In every case, the R2 rises dramatically with the inclusion of these controls. Indeed, for the 90-day AA-rated transaction data, the R2 rises from essentially zero to nearly 60 percent, and most of the other table entries show a jump of at least 30 percentage points.28 27IfweomittheSeptember11dummyvariables,ourqualitativeresultsareunchanged,butsomecoe(cid:14)cients are less precisely estimated. 28In every regression, the September 11 dummy variables account for only a small part of the increase in R2. Forthe AA-rateddata,the September 11 dummy variablescontribute between three and14percentage 19

3.3.3 Year-End and September 11 E(cid:11)ects Recall that equation 13 includes a cubic polynomial function to capture the movements in term premia as year-end approaches. Figures 6 and 7 plot this estimated function for 30day commercial paper yields.29 As shown in (cid:12)gure 6, using the transactions-based data, we (cid:12)nd that term premia for both AA- and A2/P2-rated issuers vary considerably from year to year. However, more often than not, the term premia display a concave pattern, initially rising and then declining as the issue date approaches year-end. This pattern was especially pronouncedin1999,justaheadofthecenturydatechange. Inthatyear,termpremiainitially shot up on concerns that computer bugs could hinder the functioning of (cid:12)nancial markets but plummeted shortly before the turn of the year, at least in part because the Federal Reserve committed to provide substantial liquidity in the event of a market disruption. In contrast to 1999, year-end premia were muted in some other years, notably for AA-rated issuers in 2001 and 2002. The year-to-year variation shown in (cid:12)gure 6 is highly signi(cid:12)cant: Using a standard F-test, the null hypothesis that the year-end coe(cid:14)cients are equal across the years is rejected with more than 95 percent con(cid:12)dence for both rating classes. Figure 7 displays the analogous estimates for the dealer-quote data. The pattern of yearend term premia again varies across years. In 1990|a recession year|term premia kept rising as year-end approached, reaching an extremely high level. However, in 1992, 1993, and 1994, term premia peaked well before year-end, and in 1995, they were consistently small. As with the transactions data, an F-test indicates that these di(cid:11)erences are highly points to the increase in R2, while for the A2/P2 data, these controls contribute between one and six percentage points. 29These plots are based on the estimates of (cid:11) 30;yr;1 ;:::;(cid:11) 30;yr;4 shown in tables A.1-A.3 in appendix A.2. Thebulk oftheestimatedcoe(cid:14)cientsarestatisticallysigni(cid:12)cant;thus,wecanrejectthehypothesisthatthe plots in each panel equal a horizontal line drawn at zero. To conserve space, we focus here on the 30-day maturity; the qualitative features of the estimates for the other maturities are similar. 20

signi(cid:12)cant. The estimates of the September 11 coe(cid:14)cients are displayed in table 6. The coe(cid:14)cient (cid:11) shows the estimated change in term premia in the period just before September 11, m;6 when m-day paper was priced without knowledge of the terrorist attacks but at least some of the subsequently realized overnight yields entering the calculated term premia pertain to days after September 11. As can be seen, the estimate of this coe(cid:14)cient is negative for 7-day paper and then turns positive for longer maturities. This sign change reflects the dynamics in overnight rates discussed above|rates rose in the days following September 11 but then fell sharply a week later when the Federal Reserve unexpectedly cut the federal funds rate by 50 basis points. The coe(cid:14)cient for 7-day paper picks up only the short-lived rise in overnight rates, which drives down the calculated term premium, while the coe(cid:14)cients for longer maturities reflect the unanticipated decline in overnight rates after the Fed’s rate cut. The other September 11 coe(cid:14)cient, (cid:11) , shows the e(cid:11)ect on term premia for m-day paper m;7 issued during the week after the terrorist attacks. All of the estimates of this coe(cid:14)cient are positive and highly signi(cid:12)cant, indicating the presence of a sizable term premium for paper placed between September 11 and September 18. 3.3.4 Reconciling the Dealer-Quote and Transactions-Based Results Contrary to the results we obtained with the transactions data, the dealer-quote data generally reject the expectations hypothesis even after controlling for year-end e(cid:11)ects. One factor behind the di(cid:11)ering results could be the lower quality of the dealer-quote data. The ideal way to test this explanation would be to estimate equation 13 with the dealer-quote and transactions data over exactly the same period. Because we know that the transactions data accurately reflect the prevailing yields in the commercial paper market, any di(cid:11)erence in 21

estimation results would have to arise from problems with the dealer quotes. However, the two datasets have no time periods in common, which prevents us from running this test. Accordingly, we cannot rule out that di(cid:11)erences in data quality help explain the divergent results. Nevertheless, we can test an alternative explanation that relates to the conduct of monetary policy. As noted in the introduction, Lange et al. (2003) document that the FOMC has taken many steps over the past (cid:12)fteen years to make monetary policy more transparent, which has enabled market participants to better anticipate policy actions. Indeed, Lange et al. found that the federal funds rate became much more predictable starting in February 1994, when the FOMC began to announce policy changes and the rationale for these actions shortly after the conclusion of its meetings. Consistent with the greater predictability of the funds rate, Lange et al. showed that the expectations hypothesis performed considerably better in the federal funds market after February 1994 than before.30 These developments in the federal funds market have direct implications for our tests of the expectations hypothesis in the commercial paper market. As shown in (cid:12)gure 8, both overnight CP rates (panel A) and longer-term yields (panel B) closely track the FOMC’s target for the federal funds rate. Thus, we might expect the performance of the expectations hypothesis in the commercial paper market to have improved over the course of the 1990s, as it did for federal funds. If that were the case, this pattern could help explain why the more recent transactions-based dataprovidefarmoresupport fortheexpectations hypothesis than do the earlier dealer-quote data. We examine this argument by splitting our dealer-quote data into two subsamples. The 30The link between the predictability of interest rate changesand the expectations hypothesis is analyzed in depth by Mankiw and Miron (1986); for related work, see Balduzzi et al. (1997), Gerlach and Smets (1997), and Rudebusch (1995). 22

(cid:12)rst subsample covers the period from the beginning of the sample to February 4, 1994, the date of the FOMC meeting that corresponds to the Lange et al. breakpoint; the second subsample includes the rest of the dealer-quote data. Tables 7 and 8 present the coe(cid:14)cient estimates from re-running both the standard regression and the speci(cid:12)cation with year-end controls on each subsample. For the earlier subsample, the top panel of table 7 shows that the standard regression decisively rejects the expectations hypothesis, as the estimate of (cid:12) m is well above zero and highly signi(cid:12)cant at every maturity. Adding the year-end controls does not materially change this conclusion; as shown in the lower panel, the estimates of (cid:12) m become smaller but they remain signi(cid:12)cant at all maturities except seven days. Turning to table 8, we (cid:12)nd somewhat more support for the expectations hypothesis in the later subsample once we control for year-end e(cid:11)ects. As shown in the lower panel of the table, the estimates of (cid:12) at the 7-, 15-, and 30-day maturities are close to zero and m statistically insigni(cid:12)cant. The estimates for 60- and 90-day maturities are signi(cid:12)cant, but they are much smaller in size than their counterparts in table 7. Overall, these results are consistent with the view that the greater transparency of monetary policy accounts, at least in part, for the better performance of the expectations hypothesis in recent years. 4 Conclusion In this paper, we rigorously tested the expectations hypothesis in the market for commercial paper. Our tests relied on daily yield indexes constructed by the Federal Reserve Board from the actual market yields for virtually all commercial paper issued by U.S. corporations. These transactions-based indexes provide an extremely accurate summary of market yields from 1998 onward. For completeness, we ran a parallel set of tests on the dealer-quote data 23

that the Federal Reserve published before the transactions data became available; the dealer quotes are less accurate than the transactions-based indexes, but they span a longer period and have been used in previous research. Both datasets reject the traditional speci(cid:12)cation of the expectations hypothesis that requires the term premium for a given maturity to be constant over time. This rejection is not surprising, as term premia typically rise in the commercial paper market at year-end, especially for lower-rated paper. Some plausible explanations for this year-end e(cid:11)ect include \window dressing" by institutional investors, who hold a substantial amount of commercial paper, as well as a desire by issuers to insure against volatile interest rates and the attendant increase in rollover risk around year-end. After we control forthese year-end e(cid:11)ects, we (cid:12)nd strong support for theexpectations hypothesis using the transactions data|the key result in the paper. The dealer-quote data, in contrast, largely reject the expectations hypothesis even after controlling for year-end e(cid:11)ects. We argued that at least some of this di(cid:11)erence likely reflects the increasing predictability of short-term interest rates over the 1990s, though we cannot rule out that the lower quality of the dealer-quote data also contribute to this result. Finally, we should note that we have relied exclusively on composite yield indexes to carry out these tests. Our results with the transactions-based indexes indicate that the expectations hypothesis is valid for the \average (cid:12)rm" in the commercial paper market. However, the extent to which the hypothesis holds for individual (cid:12)rms remains an open question and would be an important topic for future research. 24

Figure 1: Term Premia for 30-Day Commercial Paper The (cid:12)gureshows termpremia for 30-daycommercialpaper issuedby non(cid:12)nancial(cid:12)rms ratedAA (panelA) andA2/P2(panelB).Eachdailyobservationiscalculatedasthe di(cid:11)erencebetweenthe 30-dayrateandthe average of the overnight rates subsequently realized over the term of the 30-day rate. The data in panel A cover the period from February 27, 1989 to August 1, 2003, with a break from August 30, 1997 to January 1, 1998. The data in panel B coverthe period fromJanuary2, 1998to August 1, 2003. The verticallines in both panels are drawn at year-end. Panel A: AA-rated (cid:12)rms 200 150 100 50 0 -50 stnioP sisaB 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 Panel B: A2/P2-rated (cid:12)rms 200 150 100 50 0 -50 stnioP sisaB 1998 1999 2000 2001 2002 2003 Source: Federal Reserve Board (based on data from the Federal Reserve Bank of New York market survey through 1997 and data from the Depository Trust Company after 1997). 25

Figure 2: Term Premia for 30-Day Repurchase Agreements and Federal Funds The(cid:12)gureshowstermpremiafor30-dayrepurchaseagreements(panelA)andfederalfunds(panelB).Each daily observation is calculated as the di(cid:11)erence between the 30-day rate and the average of the overnight rates subsequently realized over the term of the 30-day rate. The data are daily and cover the period May 21, 1991 through August 1, 2003. The vertical lines in both panels are drawn at year-end. Panel A: Repurchase Agreements 200 150 100 50 0 -50 stnioP sisaB 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 Panel B: Federal Funds 200 150 100 50 0 -50 stnioP sisaB 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 Sources: RepurchaseagreementdataarefromGarbanInternational;federalfunds dataarefromthe Federal Reserve Board. 26

Figure 3: Tier-1 and Tier-2 Commercial Paper Outstanding Thepanelsdisplaythelogofcommercialpaperoutstandingatmonth-endfromJanuary1993throughAugust 2003forall(cid:12)rms inthe indicatedshort-termratingclass. Bothnon(cid:12)nancialand(cid:12)nancial(cid:12)rms areincluded in the samples. A tier-1 security is a money-market mutual fund eligible security rated \1" by at least two of the majorrating agencies;a tier-2security is aneligible security that is not a tier-1 security; allineligible securities are excluded (refer to footnote 12 for further discussion). The vertical lines in both panels are drawn at year-end. Panel A: Tier-1 Firms 7.4 7.2 7.0 6.8 6.6 6.4 6.2 )gnidnatstuO PC fo liB$(nl 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 Panel B: Tier-2 Firms 5.0 4.8 4.6 4.4 4.2 4.0 3.8 3.6 3.4 3.2 )gnidnatstuO PC fo liB$(nl 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 Source: Federal Reserve Board (based on data from the Federal Reserve Bank of New York market survey through 1997 and data from the Depository Trust Company after 1997). 27

Figure 4: Year-End Maturity Structure of Commercial Paper The (cid:12)gure shows the average amount of non(cid:12)nancial and (cid:12)nancial commercial paper outstanding that is scheduled to mature in the indicated date ranges. Panel A shows the average amounts outstanding as of the (cid:12)rst Wednesday of December for all of the years included in the transactions-data sample (1998-2002). PanelB shows the averageamounts outstandingas ofthe third Wednesdayin December for the same years. ThedottedverticallineineachpanelshowstheapproximatelocationofDecember31. Thesolidlineineach panel shows the average maturity structure over all other Wednesdays. Panel A: First Wednesday of December 300 250 200 150 100 50 0 0-7 15-21 29-35 43-49 57-63 71-77 sralloD fo snoilliB Days to Maturity Panel B: Third Wednesday of December 300 250 200 150 100 50 0 0-7 15-21 29-35 43-49 57-63 71-77 sralloD fo snoilliB Days to Maturity Source: Federal Reserve Board, based on data from the Depository Trust Company. 28

Figure 5: Deviation of Federal Funds Rate from Target The (cid:12)gure displays the standard deviations of the daily di(cid:11)erences of the e(cid:11)ective federal funds rate from the intended target rate. The solid line shows the standard deviations for year-end observations, de(cid:12)ned as observations after December 25 of the indicated year or before January 5 of the following year. The dashed line displays the standard deviations for all other observations in the indicated year. 120 100 80 60 40 20 0 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 stnioP sisaB Year-End Other Days Source: Federal Reserve Board. 29

Figure 6: Year-End Term Premia for 30-Day Commercial Paper Rates, Transactions Data The panelsplotthe cubic portionofthe estimatedyear-endtermpremiumfunctions for30-daypaper,given by (cid:11)^m;yr;1+(cid:11)^m;yr;2 (cid:28) m+(cid:11)^m;yr;3 (cid:28) m 2 +(cid:11)^m;yr;4 (cid:28) m 3 for (cid:28) = 0;1;:::;30 and m = 30. When (cid:28) = 0, the maturity date is December 26 and when (cid:28) = 30 the maturity date is 30 days later (January 24 of the following year). The (cid:11)^(cid:1) denote estimated coe(cid:14)cients from the appropriate rows in tables A.1 and A.2. Panel A: AA-Rated Firms 140 120 100 80 60 40 20 0 -20 0 5 10 15 20 25 30 stnioP sisaB t 1998 1999 2000 2001 2002 Panel B: A2/P2-Rated Firms 140 120 100 80 60 40 20 0 -20 0 5 10 15 20 25 30 stnioP sisaB t 1998 1999 2000 2001 2002 30

Figure 7: Year-End Term Premia for 30-Day Commercial Paper Rates, Dealer-Quote Data The panelsplotthe cubic portionofthe estimatedyear-endtermpremiumfunctions for30-daypaper,given by (cid:11)^m;yr;1+(cid:11)^m;yr;2 (cid:28) m+(cid:11)^m;yr;3 (cid:28) m 2 +(cid:11)^m;yr;4 (cid:28) m 3 for (cid:28) = 0;1;:::;30 and m = 30. When (cid:28) = 0, the maturity date is December 26 and when (cid:28) = 30 the maturity date is 30 days later (January 24 of the following year). The (cid:11)^(cid:1) denote estimated coe(cid:14)cients from the appropriate rows in table A.3. Panel A: 1989-1992 140 120 100 80 60 40 20 0 -20 0 5 10 15 20 25 30 stnioP sisaB t 1989 1990 1991 1992 Panel B: 1993-1996 140 120 100 80 60 40 20 0 -20 0 5 10 15 20 25 30 stnioP sisaB t 1993 1994 1995 1996 31

Figure 8: Commercial Paper Rates and the Target Rate for Federal Funds The panels display rates on overnight and 30-day commercial paper issued by AA-rated non(cid:12)nancial (cid:12)rms, alongwith the targetfederalfunds rate. Bothpanels showdaily data coveringthe periodfromFebruary27, 1989 to August 1, 2003, with a break from August 30, 1997 to January 1, 1998. Panel A: Overnight CP and Fed Funds Target Rates 10 9 8 7 6 5 4 3 2 1 tnecreP Fed Funds Target Overnight CP 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 Panel B: 30-Day CP and Fed Funds Target Rates 10 9 8 7 6 5 4 3 2 1 tnecreP Fed Funds Target 30-Day CP 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 Source: Federal Reserve Board. The commercial paper rates are based on data from the Federal Reserve Bank of New York market survey through 1997 and data from the Depository Trust Company after 1997. 32

Table 1: Summary Statistics This table displays univariate statistics for the commercial paper rates used in our empirical analysis. The upper twopanels pertain to the transactions-baseddata fromJanuary2,1998to August 1,2003,for a total of 1,365 daily observations. The lower panel pertains to the dealer-quote data from February 27, 1989 to August 29, 1997, for a total of 2,046 daily observations. The means are expressed in percent; the spreads are expressed in basis points. Transactions data, AA-rated Days to maturity 1 7 15 30 60 90 Mean yield 4.07 4.06 4.08 4.08 4.08 4.10 Std. dev. 1.80 1.80 1.82 1.83 1.84 1.86 Spread to overnight -0.35 0.70 1.04 1.67 3.09 Std. dev. 10.60 15.41 18.09 21.34 24.92 Lag Autocorrelations 1 0.9959 0.9974 0.9979 0.9984 0.9985 0.9985 5 0.9849 0.9890 0.9903 0.9916 0.9924 0.9925 10 0.9791 0.9821 0.9822 0.9833 0.9846 0.9848 Transactions data, A2/P2-rated Days to maturity 1 7 15 30 60 90 Mean yield 4.28 4.31 4.34 4.38 4.43 4.47 Std. dev. 1.80 1.81 1.83 1.83 1.84 1.85 Spread to overnight 3.64 6.47 10.36 15.37 19.09 Std. dev. 13.78 20.14 23.96 25.62 28.49 Lag Autocorrelations 1 0.9956 0.9969 0.9975 0.9979 0.9977 0.9977 5 0.9843 0.9864 0.9868 0.9892 0.9898 0.9906 10 0.9779 0.9786 0.9756 0.9784 0.9802 0.9812 Dealer-quote data Days to maturity 1 7 15 30 60 90 Mean yield 5.43 5.47 5.49 5.51 5.55 5.58 Std. dev. 1.79 1.79 1.78 1.77 1.76 1.75 Spread to overnight 3.62 5.52 7.84 11.56 14.59 Std. dev. 14.17 16.93 17.74 20.75 24.18 Lag Autocorrelations 1 0.9962 0.9975 0.9978 0.9996 1.0014 1.0015 5 0.9907 0.9906 0.9926 0.9954 0.9963 0.9960 10 0.9943 0.9868 0.9911 0.9944 0.9939 0.9939 33

Table 2: Term Premia in the CP Market This table reports the results from estimating equation 11. The term premium on the left-hand side of the equation is computed as the di(cid:11)erence between the term CP rate at the indicated maturity and the average overnight CP rate for the horizon of the term CP rate: t+Xm−1 1 r(m;t)− m r(1;i)=(cid:11) m+(cid:15) m;t ; i=t for m = 7;15;30;60;90 and t = 1;2;:::;T. In the regressions using dealer-quote data, T = 2;046−m. In the regressions using transactions data, T =1;365−m. The estimates of (cid:11) m are expressed in basis points. The t-statistics are adjusted for the overlap in the observations. Transactions data, AA-rated Days to maturity (cid:11) t-stat. m 7 -0.19 -0.46 15 1.57 1.96 30 3.50 2.88 60 7.32 4.14 90 11.93 4.51 Transactions data, A2/P2-rated Days to maturity (cid:11) t-stat. m 7 3.77 6.14 15 7.27 5.89 30 12.76 6.30 60 20.94 6.95 90 27.85 7.13 Dealer-quote data Days to maturity (cid:11) t-stat. m 7 4.33 8.48 15 6.58 7.38 30 9.80 7.83 60 15.45 7.67 90 20.35 7.25 34

Table 3: Tests of the Expectations Hypothesis This table reports the results from estimating equation 12. The term premium on the left-hand side of the equation is computed as in table 2. The term spread on the right-hand side is computed as the di(cid:11)erence betweenthetermCPrateandtheovernightCPrate. Equation12,reproducedhereforconvenience,isgiven by: t+Xm−1 1 r(m;t)− m r(1;i)=(cid:11) m+(cid:12) m(r(m;t)−r(1;t))+(cid:15) m;t : i=t If the expectations hypothesis is true, then (cid:12) m = 0. If the pure expectations hypothesis is true, then (cid:11) m = (cid:12) m = 0. The sample sizes and units are the same as in table 2. The columns labeled \Lower 95% crit." and \Upper 95% crit." display critical values of the t-statistic (corrected for the overlap in the observations)fora95%testthat(cid:12) m =0,wherethe con(cid:12)denceintervalsmaintainthe correctsizeofthe test in the presence of a persistent regressor(Cavanagh et al. (1995)). Transactions data, AA-rated Days to Lower Upper maturity (cid:11) m t-stat. (cid:12) m t-stat. 95% crit. 95% crit. 7 -0.09 -0.23 0.29 1.56 -2.49 1.64 15 1.34 2.61 0.33 1.93 -2.40 1.64 30 3.20 3.41 0.29 2.20 -2.14 1.65 60 7.11 4.14 0.13 1.24 -1.76 1.82 90 11.79 4.39 0.04 0.35 -1.64 2.07 Transactions data, A2/P2-rated Days to Lower Upper maturity (cid:11) m t-stat. (cid:12) m t-stat. 95% crit. 95% crit. 7 1.91 4.50 0.51 4.59 -2.38 1.64 15 3.40 4.52 0.60 4.61 -2.30 1.64 30 6.67 4.95 0.59 4.94 -2.02 1.65 60 13.52 4.16 0.48 3.79 -1.75 1.82 90 21.43 3.99 0.34 2.25 -1.64 1.99 Dealer-quote data Days to Lower Upper maturity (cid:11) m t-stat. (cid:12) m t-stat. 95% crit. 95% crit. 7 2.23 4.78 0.58 3.95 -2.05 1.65 15 3.81 5.96 0.49 3.52 -2.27 1.64 30 6.77 8.42 0.38 4.93 -2.22 1.64 60 11.66 6.98 0.32 4.74 -1.88 1.69 90 16.32 5.79 0.27 4.30 -1.71 1.90 35

Table 4: Tests of the Expectations Hypothesis, Controlling for Time Variation in Term Premia Thistablereportstheresultsfromestimatingequation13. Thetermpremiumandtermspreadarecomputed as in tables 2 and 3. Equation 13 is reproduced here for convenience: t+Pm−1 r(m;t)− m 1 r(1;i)=(cid:11) m;0+(cid:12) m(r(m;t)−r(1;t))+ P i=t ((cid:11) m;yr;1+(cid:11) m;yr;2 (cid:28) m+(cid:11) m;yr;3 (cid:28) m 2 +(cid:11) m;yr;4 (cid:28) m 3)DX m;yr;t+(cid:11) m;yr;5 D yr;t+ yr (cid:11) m;6 SX m;t+(cid:11) m;7 S t+(cid:15) m;t ; The right-hand side includes dummy variables for shifts in term premia around year-end (the DX (cid:1) and D (cid:1)) andfor the e(cid:11)ects of September 11,2001(the SX (cid:1) andS (cid:1)); see the text for details andappendix A.2 for the estimates of the relevant coe(cid:14)cients. If the expectations hypothesis is true, then (cid:12) m =0. The sample sizes and other details about the displayed results are the same as in the previous tables. Transactions data, AA-rated Days to Lower Upper maturity (cid:11) m;0 t-stat. (cid:12) m t-stat. 95% crit. 95% crit. 7 -0.90 -2.63 -0.14 -2.04 -2.38 1.64 15 0.14 0.33 -0.02 -0.35 -2.33 1.64 30 1.05 1.74 0.02 0.65 -1.91 1.64 60 3.26 3.63 -0.03 -0.73 -1.64 2.08 90 5.94 3.83 -0.08 -1.08 -1.64 2.35 Transactions data, A2/P2-rated Days to Lower Upper maturity (cid:11) m;0 t-stat. (cid:12) m t-stat. 95% crit. 95% crit. 7 2.49 5.47 0.11 1.35 -2.42 1.64 15 4.47 6.42 0.11 1.47 -2.38 1.64 30 7.32 7.53 0.13 2.32 -1.84 1.76 60 13.11 5.69 0.01 0.19 -1.64 2.47 90 18.96 4.45 -0.10 -0.75 -1.64 2.81 Dealer-quote data Days to Lower Upper maturity (cid:11) m;0 t-stat. (cid:12) m t-stat. 95% crit. 95% crit. 7 3.12 9.20 0.08 0.97 -2.44 1.64 15 4.38 8.95 0.11 2.74 -2.37 1.64 30 6.09 7.84 0.20 4.28 -2.16 1.64 60 10.13 6.70 0.20 3.89 -1.87 1.64 90 13.37 5.58 0.25 3.97 -1.73 1.94 36

Table 5: Goodness-of-Fit Measures The table compares the adjusted-R2 goodness-of-(cid:12)t measure for the regressions in tables 3 and 4 above. The columns labeled \NoYr-end" showthe goodness-of-(cid:12)tmeasuresfor the regressionsin table 3,while the columns labeled \Yr-end" show the goodness-of-(cid:12)t measures for the corresponding regressions in table 4. The adjusted-R2 (cid:12)gures are in percent. Transactions data AA-rated A2/P2-rated Dealer-quote data Days to No No No maturity Yr-end Yr-end Yr-end Yr-end Yr-end Yr-end 7 7 45 26 48 34 63 15 16 60 43 72 31 65 30 16 66 45 78 20 54 60 4 61 28 73 15 52 90 0 60 14 67 11 49 37

Table 6: September 11 Coe(cid:14)cient Estimates The table displays the estimates of the coe(cid:14)cients on the September 11 dummy variables in equation 13. The relevant portion of that equation is given by: :::+(cid:11) m;6 SX m;t+(cid:11) m;7 S t+::: where the dummy variable SX m;t takes the value one when the observation date t is before September 11, 2001, but the maturity date t+m crosses September 11. The variable S t equals one when the observation date t is between September 11 and September 18, 2001. The estimates of (cid:11) m;6 and (cid:11) m;7 are expressed in basis points. AA-rated Days to Maturity (cid:11) t-stat. (cid:11) t-stat. m;6 m;7 7 -10.36 -6.82 86.21 18.28 15 12.89 1.87 47.95 10.07 30 17.89 2.72 51.97 22.73 60 25.18 3.55 48.29 33.48 90 28.83 2.74 51.95 20.17 A2/P2-rated Days to Maturity (cid:11) t-stat. (cid:11) t-stat. m;6 m;7 7 -16.81 -3.28 82.98 9.13 15 0.48 0.10 49.28 5.93 30 8.11 1.94 39.20 9.95 60 18.20 3.73 36.05 9.38 90 20.37 2.23 37.36 5.63 38

Table 7: Tests of the Expectations Hypothesis on Dealer-Quote Data; Early Period The table reports results from estimating equation 13 with the dealer-quote data prior to February 4, 1994. The regression speci(cid:12)cation in the upper panel is identical to that in table 3, while the speci(cid:12)cation in the lower panel is identical to that in table 4. The sample sizes are 1;237−m. Without Year-End Controls Days to Lower Upper maturity (cid:11) t-stat. (cid:12) t-stat. 95% crit. 95% crit. m;0 m 7 2.36 6.36 0.69 5.61 -2.02 1.67 15 4.04 6.61 0.61 4.53 -2.06 1.64 30 7.43 6.51 0.50 5.39 -2.37 1.64 60 13.40 5.71 0.52 6.49 -2.15 1.64 90 19.18 5.11 0.48 6.23 -1.84 1.69 With Year-End Controls Days to Lower Upper maturity (cid:11) t-stat. (cid:12) t-stat. 95% crit. 95% crit. m;0 m 7 2.57 7.08 0.15 1.35 -2.40 1.64 15 3.70 5.85 0.15 2.85 -2.49 1.64 30 6.06 5.73 0.31 5.06 -2.41 1.64 60 11.13 5.47 0.35 4.38 -2.28 1.64 90 15.51 5.03 0.43 4.50 -2.30 1.64 39

Table 8: Tests of the Expectations Hypothesis on Dealer-Quote Data; Late Period The table reports results from estimating equation 13 with the dealer-quote data starting from February 4, 1994. The regression speci(cid:12)cation in the upper panel is identical to that in table 3, while the speci(cid:12)cation in the lower panel is identical to that in table 4. The sample sizes are 832−m. Without Year-End Controls Days to Lower Upper maturity (cid:11) t-stat. (cid:12) t-stat. 95% crit. 95% crit. m;0 m 7 4.11 7.36 0.12 1.27 -2.45 1.64 15 5.83 7.67 0.15 1.75 -2.39 1.64 30 7.05 5.80 0.21 2.18 -2.17 1.64 60 9.54 6.84 0.19 2.34 -2.11 1.64 90 10.39 6.85 0.23 3.64 -1.87 1.71 With Year-End Controls Days to Lower Upper maturity (cid:11) t-stat. (cid:12) t-stat. 95% crit. 95% crit. m;0 m 7 4.73 9.15 -0.10 -1.66 -2.49 1.64 15 6.13 8.49 0.00 0.06 -2.32 1.64 30 7.40 7.27 0.06 1.02 -2.24 1.64 60 9.31 6.93 0.11 2.61 -2.10 1.64 90 9.35 4.38 0.21 4.17 -1.74 1.84 40

A.1 Robust Con(cid:12)dence Intervals Cavanagh et al. (1995) develop formal results for testing the null hypothesis that γ = γ for 0 the recursive system:31 x = (cid:22) +v ; (1−(cid:11)L)b(L)v = (cid:15) ; (A.1) t x t t 1t y = (cid:22) +γx +(cid:15) ; (A.2) t y t−1 2t Pk where b(L) = b Li, b = 1, and (cid:15) = ((cid:15) ;(cid:15) )0 is a martingale di(cid:11)erence sequence with i 0 t 1t 2t i=0 E((cid:15) (cid:15)0) = (cid:27) and corr((cid:15) ;(cid:15) ) = (cid:14). In our implementation, y is the term premium and t t 1t 2t t x is the term spread. The issue is that the term spread contains a large, perhaps unit, t−1 autoregressive root, modeled here as (cid:11) = 1 + c , where c is a (cid:12)xed constant (the \local to T unity" model). Cavanagh et al. (1995) show that the t-statistic for testing γ = γ has a limiting repre- 0 sentation: p t ! (cid:14)(cid:28) + 1−(cid:14)2z; (A.3) γ 1c R J(cid:22)dB where (cid:28) 1c = q R c 1 , J c is the di(cid:11)usion process de(cid:12)ned by dJ c (s) = cJ c (s)ds+dB 1 (s) with (J(cid:22))2 c R1 J (0) = 0, B is a standard Brownian motion, J(cid:22)(s) = J (s)− J (r)dr, and z is a standard c 1 c c c 0 normal random variable that is independent of B and J . The parameter (cid:14) is consistently 1 c estimated by the sample correlation between (cid:15)^ and (cid:15)^ . 1t 2t We construct a conservative test of γ = γ using the extrema of the asymptotic local- 0 to-unity critical values of t . Formally, letting d denote the 100(cid:17)% quantile of the γ tγ;c;(cid:17) p distribution of (cid:14)(cid:28) + 1−(cid:14)2z for a given value of (cid:14), we compute the following \sup-bound 1c 31This appendix is a very brief distillation of a portion of Cavanagh et al. (1995). For more details and additional useful results, the reader is referred to the source. 41

con(cid:12)dence interval" by Monte Carlo simulation: (cid:18) (cid:19) (d ;d(cid:22) ) = infd ;supd : (A.4) (cid:17) (cid:17) c tγ;c;(cid:17) c tγ;c;(cid:17) Intuitively, the procedure amounts to picking the most conservative con(cid:12)dence limits across a sequence of values of c. The following Matlab code details our implementation of the Cavanagh et al. (1995) procedure for calculating the conservative sup-bound con(cid:12)dence intervals:32 function [tstat, crit] = supbound_dum(x, y, d, p); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Computes sup-bound critical values in a regression of % % y(t) on d(t) and x(t-1,1); the routine will also add a constant. % % Autocorrelation robust standard errors are used with truncation % % p. d(t) is a set of calendar dummy variables with number of % % rows equal to the number of rows of y and x and any number of % % columns (subject to computational limits.) % % It is assumed that the number of observations is large enough % % that the number of rows of d can serve as the number of Monte % % Carlo iterations in the calculation of the supbounds. % % NOTE: Before calling this routine, set the seed for Matlab’s % % random number generator if you want results that can be % % replicated exactly. % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% t=size(x,1); q=y(1:t-1); w=[ones(t-1,1) d(1:t-1,:) x(1:t-1)]; k=size(w,2); bhat=inv(w’*w)*w’*q; u=q-w*bhat; z=kron(u,ones(1,k)).*w; for j=1:p+1; lb(:,:,j)=((p+2-j)/(p+1))*z(j:t-1,:)’*z(1:t-j,:); end; %NW sigma=sum(lb,3)+(sum(lb,3)’)-lb(:,:,1); clear lb; a=inv(w’*w)*sigma*inv(w’*w); 32Thisprogramincorporatesminormodi(cid:12)cationstoaprogramkindlyprovidedtotheauthorsbyJonathan Wright. Wemodi(cid:12)edWright’sprogramtoallowforcalendardummyvariablesintheregressionspeci(cid:12)cation. 42

w=[ones(t-1,1) d(2:t,:) x(1:t-1)]; q=x(2:t,:); v=q-(w*inv(w’*w)*w’*q); z=[u v]; for j=1:p+1; lb(:,:,j)=((p+2-j)/(p+1))*z(j:t-1,:)’*z(1:t-j,:); end; %NW sigma=sum(lb,3)+(sum(lb,3)’)-lb(:,:,1); delta=sigma(1,2)/sqrt(sigma(1,1)*sigma(2,2)); tstat=bhat(k)/sqrt(a(k,k)); s=size(d,1); dum=[ones(s,1) d]; dp=dum*inv(dum’*dum)*dum’; b1=zeros(s,1000); sa=zeros(1000,1); stat=zeros(1000,1); sb1=zeros(3,31); sb2=zeros(3,31); u=randn(s,31000)./sqrt(s); eps=randn(1000,31); for k=1:31; alpha=1+((1-k)/1000); b1=filter(1,[1;-alpha],u(1:s,(k-1)*1000+1:k*1000)); b1=b1-dp*b1; sa=sum(b1(1:s-1,1:1000).*u(2:s,(k-1)*1000+1:k*1000))./sqrt(mean((b1.^2))); stat=(delta.*sa’)+(sqrt(1-(delta^2)).*eps(1:1000,k)); stat=sort(stat); sb1(1:3,k)=stat([10;50;100]); sb2(1:3,k)=stat([990;950;900]); end; sb1(1:3,32)=norminv([0.01 0.05 0.10]’); sb2(1:3,32)=norminv([0.99 0.95 0.90]’); crit=[[0.01 0.05 0.10]’ min(sb1’)’ max(sb2’)’]; 43

A.2 Dummy Variable Coe(cid:14)cient Estimates The tables in this appendix display the estimated coe(cid:14)cients on the dummy variables in equation 13 that control for year-end and September 11 e(cid:11)ects. Tables A.1-A.3 report the results from the transactions data for AA-rated (cid:12)rms, the transaction data for A2/P2-rated (cid:12)rms, and the dealer-quote data, respectively. Tables A.4 and A.5 show the estimates for the sample splits on the dealer-quote data. Below each coe(cid:14)cient estimate we report its t-statistic, where the underlying standard errors are adjusted for the overlap in the observations. 44

Table A.1: Dummy Variable Coe(cid:14)cient Estimates for Tests of the Expectations Hypothesis, Controlling for Time-Varying Term Premia, Transactions Data, AA-Rated Firms Daysto Maturity Year (cid:11) (cid:11) (cid:11) (cid:11) (cid:11) (cid:11) (cid:11) m;yr;1 m;yr;2 m;yr;3 m;yr;4 m;yr;5 m;6 m;7 7 1998 0.64 21.29 4.65 -1.0915 4.37 0.09 13.78 7.18 -11.1876 1.02 7 1999 82.03 33.10 -0.96 -0.9390 -4.88 10.14 5.52 -0.83 -3.1403 -2.96 7 2000 -10.36 1.71 0.87 -0.1747 7.54 -1.09 2.05 2.45 -3.2217 0.85 7 2001 -0.72 3.21 0.20 -0.1088 0.85 -10.36 86.21 -0.82 17.03 2.27 -5.4875 1.21 -6.82 18.28 7 2002 1.38 1.81 0.02 -0.0444 2.54 1.66 6.99 0.30 -11.1876 4.65 15 1998 21.06 8.61 -0.18 -0.0262 1.74 15.78 7.80 -0.97 -2.7824 1.52 15 1999 50.92 20.97 -0.68 -0.0684 0.98 7.42 9.78 -0.76 -1.2795 0.96 15 2000 6.13 0.49 -0.12 0.0188 4.97 4.14 2.30 -0.90 2.2146 0.86 15 2001 -0.76 1.84 0.12 -0.0184 0.94 12.89 47.95 -0.55 7.08 0.89 -1.4048 1.87 1.87 10.07 15 2002 -1.12 0.32 0.05 -0.0033 2.45 -2.18 7.30 2.93 -2.7824 4.54 30 1998 12.57 1.08 0.13 -0.0050 8.48 7.17 1.02 1.09 -1.7641 4.29 30 1999 22.91 1.47 0.54 -0.0211 4.58 6.36 0.56 2.06 -3.4145 1.70 30 2000 4.00 0.51 0.11 -0.0034 4.85 6.36 4.50 6.34 -5.8386 1.26 30 2001 8.89 -1.01 -0.02 0.0027 -4.71 17.89 51.97 9.08 -3.66 -0.36 1.9994 -6.53 2.72 22.73 30 2002 1.73 0.05 0.02 -0.0008 0.49 2.86 0.77 3.57 -1.7641 0.92 60 1998 12.23 1.58 -0.04 0.0002 6.13 5.49 2.51 -1.27 0.6707 4.99 60 1999 23.51 1.44 -0.01 -0.0003 0.76 4.77 1.11 -0.09 -0.4062 0.36 60 2000 1.49 0.78 0.01 -0.0002 8.33 1.51 5.82 1.08 -1.3811 2.66 60 2001 6.48 0.36 -0.02 0.0003 -5.86 25.18 48.29 2.92 0.69 -0.85 0.7255 -4.77 3.55 33.48 60 2002 20.95 -2.31 0.08 -0.0007 -1.35 13.58 -8.77 6.37 0.6707 -1.72 90 1998 5.85 -0.01 0.01 -0.0001 2.30 1.92 -0.06 3.28 -4.0165 1.87 90 1999 29.24 2.68 -0.08 0.0005 -5.14 5.43 2.94 -2.66 2.3860 -1.21 90 2000 4.44 0.17 0.02 -0.0002 10.13 2.87 1.24 3.80 -4.0860 2.52 90 2001 14.93 0.18 -0.01 0.0001 -5.41 28.83 51.95 3.91 0.90 -2.22 2.1320 -3.17 2.74 20.17 90 2002 17.85 1.03 -0.04 0.0004 -5.45 6.43 3.13 -4.40 -4.0165 -3.11 45

Table A.2: Dummy Variable Coe(cid:14)cient Estimates for Tests of the Expectations Hypothesis, Controlling for Time-Varying Term Premia,Transactions Data, A2/P2-Rated Firms Daysto Maturity Year (cid:11) (cid:11) (cid:11) (cid:11) (cid:11) (cid:11) (cid:11) m;yr;1 m;yr;2 m;yr;3 m;yr;4 m;yr;5 m;6 m;7 7 1998 4.84 23.99 4.57 -1.1071 1.86 0.51 9.19 5.34 -7.7745 0.30 7 1999 53.70 24.41 0.04 -0.7402 -0.66 9.58 6.67 0.08 -4.7307 -0.39 7 2000 24.21 17.70 0.81 -0.5492 5.72 1.81 8.39 1.43 -4.1092 0.47 7 2001 5.58 0.36 1.67 0.7253 3.63 -16.81 82.98 2.08 0.50 37.93 10.2709 1.31 -3.28 9.13 7 2002 12.19 0.08 -0.57 0.1053 -0.85 6.98 0.34 -6.64 -7.7745 -0.71 15 1998 24.51 5.76 1.62 -0.1289 -1.12 4.95 1.32 1.56 -2.3771 -0.33 15 1999 44.17 20.47 0.40 -0.1349 -1.13 10.55 12.34 1.17 -6.1224 -0.90 15 2000 11.07 10.36 1.11 -0.1039 -16.36 4.98 12.76 4.63 -6.1429 -1.59 15 2001 8.92 5.69 -0.06 -0.0258 12.81 0.48 49.28 5.98 8.60 -0.42 -1.4789 5.03 0.10 5.93 15 2002 -4.17 3.25 0.07 -0.0152 -1.34 -4.33 11.88 1.73 -2.3771 -1.59 30 1998 46.17 3.95 -0.17 0.0013 10.98 15.40 3.55 -1.61 0.5043 6.70 30 1999 33.66 4.12 0.27 -0.0141 11.24 7.07 1.13 0.75 -1.6416 2.47 30 2000 -0.53 5.18 0.12 -0.0065 -28.58 -0.43 15.40 2.59 -4.7210 -4.84 30 2001 21.34 3.63 -0.32 0.0080 2.69 8.11 39.20 14.33 6.06 -4.24 3.5781 1.86 1.94 9.95 30 2002 10.47 0.75 0.01 -0.0009 6.12 5.86 1.06 0.10 0.5043 4.97 60 1998 45.58 4.41 -0.13 0.0010 8.46 19.75 6.01 -4.28 2.6102 4.75 60 1999 31.21 3.08 -0.06 0.0002 4.65 5.64 2.33 -0.93 0.2066 1.84 60 2000 -12.85 1.92 -0.04 0.0010 -24.00 -6.57 5.40 -2.47 3.9108 -5.64 60 2001 33.55 1.79 -0.07 0.0006 -8.97 18.20 36.05 19.27 4.96 -3.73 2.6894 -4.65 3.73 9.38 60 2002 43.89 -3.17 0.12 -0.0011 -1.17 19.66 -9.98 8.44 2.6102 -0.63 90 1998 -8.82 3.08 -0.02 -0.0001 13.77 -1.19 5.51 -1.35 -0.7041 3.22 90 1999 37.83 3.41 -0.08 0.0005 -3.36 5.88 2.77 -2.07 1.6526 -0.54 90 2000 -11.78 0.63 -0.01 0.0002 -15.33 -3.69 2.24 -1.06 2.9103 -2.85 90 2001 10.60 2.83 -0.05 0.0002 -12.15 20.37 37.36 1.57 5.97 -4.89 2.8729 -3.59 2.23 5.63 90 2002 21.58 1.34 -0.03 0.0002 6.21 5.74 4.33 -3.39 -0.7041 2.73 46

Table A.3: Dummy Variable Coe(cid:14)cient Estimates for Tests of the ExpectationsHypothesis, Controllingfor Time-VaryingTermPremia, Dealer-Quote Data Days to Maturity Year (cid:11) m;yr;1 (cid:11) m;yr;2 (cid:11) m;yr;3 (cid:11) m;yr;4 (cid:11) m;yr;5 7 1989 -35.82 10.66 4.45 -0.4876 3.27 -5.74 3.06 10.08 -1.1031 1.71 7 1990 -20.99 61.01 9.03 -2.0625 9.15 -1.44 11.69 7.85 -9.6117 1.62 7 1991 -7.07 49.01 4.78 -1.5415 2.99 -1.67 10.43 11.22 -9.5760 1.09 7 1992 -26.53 6.94 2.73 -0.5276 16.93 -16.47 6.93 18.15 -13.9015 15.81 7 1993 -8.65 4.61 0.82 -0.1586 6.19 -4.99 6.99 8.28 -7.1808 4.17 7 1994 -7.03 7.18 0.48 -0.2235 10.44 -5.68 5.58 3.61 -3.8704 11.31 7 1995 9.98 6.02 -0.27 -0.2164 3.44 4.69 5.00 -5.93 -4.4006 4.34 7 1996 -7.26 7.25 1.78 -0.1833 8.31 -2.68 2.51 4.97 -1.5691 3.58 15 1989 2.98 -0.28 -0.23 0.0420 1.59 1.45 -0.74 -1.19 0.2203 1.23 15 1990 16.06 14.58 0.91 -0.0923 22.98 2.83 11.70 2.59 -4.0051 10.04 15 1991 -7.77 5.13 1.25 -0.0833 3.06 -2.79 7.85 6.33 -6.3428 1.16 15 1992 12.41 6.95 -1.34 0.0577 12.21 5.08 3.89 -3.18 2.6861 5.37 15 1993 1.56 2.07 -0.25 0.0121 5.44 1.45 7.94 -3.29 2.9951 4.52 15 1994 3.81 2.56 -0.18 0.0043 13.70 1.71 5.77 -1.00 0.3634 6.09 15 1995 7.99 1.22 -0.42 0.0295 3.25 4.96 5.90 -3.51 3.3557 3.45 15 1996 6.01 2.99 -0.15 0.0146 8.04 2.58 7.85 -0.90 1.3917 6.43 30 1989 -13.51 0.86 -0.01 0.0017 -3.30 -9.58 2.26 -0.19 0.0290 -2.53 30 1990 23.19 -2.28 0.18 0.0004 32.25 6.26 -1.31 0.84 0.0649 18.75 30 1991 25.32 0.23 -0.07 0.0036 2.85 16.83 0.29 -0.75 1.6264 1.14 30 1992 25.85 5.07 -0.49 0.0101 13.14 10.65 7.78 -8.12 7.4137 9.72 30 1993 9.33 2.57 -0.26 0.0059 3.04 (Continued next page...) 47

Table A.3: (continued) Days to Maturity Year (cid:11) m;yr;1 (cid:11) m;yr;2 (cid:11) m;yr;3 (cid:11) m;yr;4 (cid:11) m;yr;5 7.19 4.63 -5.08 5.3451 2.62 30 1994 18.33 4.04 -0.34 0.0072 13.28 11.82 7.03 -7.32 7.5515 8.38 30 1995 -3.48 0.53 0.02 -0.0010 4.18 -4.20 3.05 0.78 -1.2961 5.00 30 1996 1.02 -0.10 0.03 0.0009 3.96 0.82 -0.31 0.85 0.8156 2.80 60 1989 1.27 -0.91 0.01 0.0002 -6.22 0.75 -5.98 1.82 0.0231 -3.87 60 1990 7.56 3.29 -0.10 0.0011 46.31 2.66 3.94 -2.32 2.0314 16.54 60 1991 23.05 0.71 -0.02 0.0002 -6.94 9.85 0.99 -0.50 0.4289 -2.50 60 1992 4.56 2.39 -0.05 0.0001 8.74 2.66 7.59 -3.39 0.6062 5.60 60 1993 2.42 2.07 -0.08 0.0007 -9.23 1.59 11.85 -9.62 7.5475 -5.31 60 1994 -18.72 1.31 0.03 -0.0008 13.06 -4.80 3.97 2.06 -4.4086 6.60 60 1995 -6.27 -0.01 0.02 -0.0002 10.85 -4.13 -0.05 3.16 -3.1137 6.71 60 1996 -9.35 0.33 -0.02 0.0004 4.24 -6.09 1.42 -1.18 2.1919 2.79 90 1989 15.42 -0.91 0.01 0.0001 -8.30 3.95 -1.93 0.34 0.0048 -2.78 90 1990 14.00 0.31 0.02 -0.0002 55.88 4.41 1.03 1.74 -2.0219 19.71 90 1991 32.12 1.10 -0.03 0.0002 -9.22 11.13 3.28 -2.78 2.1752 -2.85 90 1992 -5.10 -0.28 0.04 -0.0004 9.50 -1.47 -1.24 7.27 -8.7713 4.61 90 1993 -1.32 0.43 -0.01 0.0000 -13.63 -0.50 1.45 -0.83 0.4195 -4.72 90 1994 -5.33 -1.47 0.06 -0.0004 13.15 -1.15 -3.46 4.30 -4.1200 3.89 90 1995 -3.83 -0.52 0.02 -0.0002 5.27 -1.43 -3.45 4.53 -4.2905 2.25 90 1996 -4.42 -0.17 -0.00 0.0001 -0.93 -1.43 -0.59 -0.27 1.2788 -0.42 48

Table A.4: Dummy Variable Coe(cid:14)cient Estimates for Tests of the ExpectationsHypothesis, Controllingfor Time-VaryingTermPremia, Dealer-Quote Data Prior to February 4, 1994 Days to Maturity Year (cid:11) m;yr;1 (cid:11) m;yr;2 (cid:11) m;yr;3 (cid:11) m;yr;4 (cid:11) m;yr;5 7 1989 -38.83 9.47 4.57 -0.4325 3.99 -5.53 2.57 10.13 10.1282 2.04 7 1990 -26.19 56.73 8.79 -1.9341 9.41 -1.74 8.84 8.21 8.2078 1.68 7 1991 -9.31 45.36 4.51 -1.4234 3.88 -1.93 7.51 8.75 8.7497 1.35 7 1992 -27.35 6.05 2.65 -0.4991 17.68 -14.74 4.51 13.58 13.5799 14.96 7 1993 -8.87 4.05 0.77 -0.1433 6.45 -5.34 4.59 6.42 6.4164 4.24 15 1989 3.46 -0.60 -0.29 0.0497 2.36 1.58 -1.31 -1.45 -1.4534 1.72 15 1990 13.86 13.48 0.88 -0.0847 23.29 2.28 8.91 2.53 2.5253 10.12 15 1991 -7.36 4.68 1.18 -0.0765 4.07 -2.64 6.37 5.80 5.7950 1.47 15 1992 12.08 6.40 -1.31 0.0578 13.19 4.75 3.60 -3.20 -3.2009 5.63 15 1993 1.75 1.95 -0.26 0.0130 5.86 1.39 7.28 -3.52 -3.5215 4.50 30 1989 -12.11 0.87 -0.06 0.0037 -3.00 -7.21 1.81 -0.84 -0.8397 -1.92 30 1990 21.47 -2.59 0.14 0.0022 30.46 6.25 -1.75 0.78 0.7767 14.43 30 1991 23.82 -0.01 -0.07 0.0042 3.50 13.38 -0.01 -0.95 -0.9530 1.37 30 1992 22.24 4.26 -0.43 0.0092 13.79 7.80 6.30 -7.41 -7.4077 8.38 30 1993 7.88 1.84 -0.20 0.0048 2.22 4.85 3.23 -4.00 -4.0044 1.56 60 1989 0.73 -0.76 0.00 0.0004 -5.99 0.32 -2.26 0.10 0.0999 -3.01 60 1990 5.14 3.58 -0.13 0.0015 43.44 1.42 3.80 -2.62 -2.6181 12.27 60 1991 21.78 0.73 -0.03 0.0004 -6.20 8.07 0.95 -0.69 -0.6901 -2.05 60 1992 0.47 1.91 -0.04 0.0001 8.89 0.18 4.98 -2.55 -2.5461 4.54 60 1993 -1.16 1.83 -0.07 0.0007 -11.40 -0.47 8.55 -7.98 -7.9831 -4.86 90 1989 14.87 -0.77 -0.00 0.0001 -8.08 (Continued next page...) 49

Table A.4: (continued) Days to Maturity Year (cid:11) m;yr;1 (cid:11) m;yr;2 (cid:11) m;yr;3 (cid:11) m;yr;4 (cid:11) m;yr;5 3.13 -1.40 -0.13 -0.1321 -2.20 90 1990 11.41 0.58 0.00 -0.0001 53.54 2.46 1.21 0.27 0.2705 13.23 90 1991 28.56 1.30 -0.04 0.0003 -8.14 7.85 3.21 -2.94 -2.9418 -2.13 90 1992 -2.07 -0.69 0.04 -0.0003 8.89 -0.46 -2.19 6.02 6.0165 3.40 90 1993 -4.12 0.29 -0.01 0.0001 -17.36 -1.16 0.83 -0.82 -0.8218 -4.44 50

Table A.5: Dummy Variable Coe(cid:14)cient Estimates for Tests of the ExpectationsHypothesis, Controllingfor Time-VaryingTermPremia, Dealer-Quote Data After February 4, 1994 Days to Maturity Year (cid:11) m;yr;1 (cid:11) m;yr;2 (cid:11) m;yr;3 (cid:11) m;yr;4 (cid:11) m;yr;5 7 1994 -5.54 9.94 0.70 -0.3386 9.95 -5.31 10.35 6.75 6.7534 11.58 7 1995 14.45 8.74 -0.39 -0.3186 1.54 8.23 9.00 -6.58 -6.5841 1.50 7 1996 -5.46 13.02 2.33 -0.4017 8.30 -2.17 5.98 8.65 8.6514 4.18 15 1994 4.35 3.16 -0.15 -0.0008 12.78 1.76 6.15 -0.80 -0.7989 5.16 15 1995 5.93 1.47 -0.31 0.0210 1.25 2.92 5.91 -2.00 -1.9973 1.09 15 1996 4.28 3.71 0.06 -0.0034 7.11 1.65 8.04 0.35 0.3464 5.32 30 1994 20.76 5.43 -0.44 0.0087 14.58 12.05 7.60 -7.61 -7.6141 8.59 30 1995 -4.50 0.56 0.02 -0.0009 2.29 -4.66 3.86 0.92 0.9216 2.12 30 1996 -1.50 0.24 0.07 -0.0009 5.50 -1.04 0.90 2.33 2.3348 4.33 60 1994 -11.24 0.89 0.05 -0.0010 16.79 -3.78 3.06 3.94 3.9426 10.78 60 1995 -5.05 0.01 0.02 -0.0002 10.99 -4.00 0.06 3.00 3.0010 7.12 60 1996 -8.07 0.18 -0.00 0.0002 6.70 -6.32 1.25 -0.41 -0.4083 5.84 90 1994 1.47 -1.47 0.06 -0.0004 18.22 0.45 -3.05 3.83 3.8291 7.08 90 1995 0.03 -0.49 0.02 -0.0002 8.06 0.01 -3.49 4.69 4.6876 3.56 90 1996 0.84 -0.30 0.00 0.0000 3.20 0.40 -1.40 0.34 0.3434 2.08 51

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