Skip to main content
SpringerLink
Log in

Yield curves from different bond data sets

  • Published:
Review of Derivatives Research Aims and scope Submit manuscript

Abstract

It is well known that zero coupon rates are not observable variables. Their estimation process may be cumbersome and time consuming. We explore the extent to which the set of security prices used in the yield curve construction of three popular interest rate datasets (from the Federal Reserve Board, the US Department of the Treasury, and Bloomberg) may determine the results of different analyses. Using the same US Treasury prices from GovPX and applying the same fitting technique, we estimate zero coupon rates using different baskets of assets, i.e., including/excluding bills, on-the-run, and off-the-run bonds, attempting to mimic those used by each data providers. To illustrate the uncertainty surrounding these alternatives representations of the underlying yield curve, we examine common uses of these data sets in pricing, risk management and macroeconomic purposes. We find significant and sometime overwhelming differences in the volatility term structure, the pricing of interest rate derivatives, and the correlations among different forward rates particularly in both ends of the yield curve. Relevant implications are also observed on a classic test of the expectations hypothesis. The simplest asset basket, which only includes the on-the-run bills and bonds, is probably the one with the best results.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

Similar content being viewed by others

Notes

  1. The most recently issued security of a particular maturity.

  2. As commented below, we replicate the baskets of securities these providers use to fit the Yield Curve (YC). We get intraday market prices of the US Treasury securities from the GovPX dataset. Thus, our sample period is limited for the availability of reliable prices from GovPX. The quality of this dataset deteriorates progressively, and we are forced to discontinue the sampling period at the end of 2006. See more details in the “Appendix”.

  3. A daily updated spreadsheet can be downloaded from the FRB’s website in the section “Finance and Economics Discussion Series” below the Gürkaynak et al. (2007)’s working paper (https://www.federalreserve.gov/econresdata/feds/2006/index.htm). For convenience, this dataset is referred to “the FRB dataset”; however, the website indicates as follows: “Note: This is not an official Federal Reserve statistical release.”.

  4. Thus, this dataset appears simultaneously in the DoT’s website (https://www.treasury.gov/resource-center/data-chart-center/interest-rates/Pages/TextView.aspx?data=yield) and the Fed’s website (https://www.federalreserve.gov/releases/h15/data.htm).

  5. No more details are reported about the specific functions used to estimate the yield curve.

  6. Bloomberg terminal mentions: “The yield curve is built daily with bonds that have either Bloomberg Generic (BGN) prices, supplemental proprietary contributor prices or both. The bonds are subject to option-adjusted spread (OAS) analysis and the curve is adjusted to generate a best fit. (…) Bloomberg Generic Price (BGN) is Bloomberg’s market consensus price (…) Bloomberg Generic Prices are calculated by using prices contributed to Bloomberg and any other information that we consider relevant”

  7. See, e.g., Sarig and Warga (1989), Warga (1992), Fleming (2000), Amihud and Medelson (1991), Krishnamurthy (2002), Sack and Elsasser (2004), Goldreich, Hanke and Nath (2005), Díaz et al. (2006), Vayanos and Weill (2008), Pasquariello and Vega (2009), Díaz et al. (2011), Graveline and McBrady (2011) and Fontaine and García (2012), and Díaz and Escribano (2017).

  8. Intermediaries in the repo market require Treasuries as collateral; for them, on-the-run bonds are appealing securities. These securities may trade on special, i.e., it can be used as collateral to borrow money at a rate below the prevailing general repo rate either because it is more liquid or because of its scarcity caused by a limited supply or a short squeeze.

  9. See, e.g., Duffie (1996), Jordan and Jordan (1997), Krishnamurthy (2002), Fleming (2003), Longstaff (2004), Cherian et al. (2004), Krishnamurthy and Vissing-Jorgensen (2012) and Barnejee and Graveline (2013).

  10. According to BIS (2005), nine out of thirteen central banks currently use either the Nelson and Siegel (1987) model or its extended version suggested by Svensson (1994) to estimate the term structure of interest rates. One of the exceptions is the United States, which applies a “smoothing splines” method.

  11. Even to apply the Nelson and Siegel (1987) technique, Diebold and Li (2006) propose to fix τ1 to simplify the estimation of the remaining three parameters with the advantage of providing better numerical stability.

  12. Andersen and Benzoni (2007) have documented that EGARCH representation for conditional yield volatility provides a convenient and successful parsimonious model for the conditional heteroskedasticity in these series.

  13. The analysis using EGARCH volatilities provide similar results. The corresponding results are available upon request from the authors.

  14. The DoT provides market yields at fixed maturities calculated from composites of quotations obtained by the Federal Reserve Bank of New York. According to the information on the DoT website, the yields are either investment yields or bond-equivalent yields. The formula uses simple interest and day count convention actual/actual. We recalculate this yield as a continuously compound interest rate. No 1-month rates are available in this dataset until August 1, 2001. Prior to this date, we estimate the corresponding interest rate by using cubic interpolation.

  15. The data in Table 7 are reported in annualized percentage points, i.e., the natural monthly variables are multiplied by 1200.

  16. GovPX Inc. was established under the guidance of the Public Securities Association as a joint venture among voice brokers in 1991 to increase public access to US Treasury security prices.

  17. The “standard interest payment” field indirectly provides information to identify callable bonds and TIPS (Treasury Inflation-Protected Securities). We exclude these assets.

  18. See, for instance, Sarig and Warga (1989) and Kamara (1994). In addition, Fleming (2003) emphasizes that GovPX bill coverage is larger than bond and note coverage.

  19. To fix a universal criterion for the entire maturity spectrum and sample period, such as excluding trades for which price or yield-to-maturity (YTM) exceeds certain percentage of the neighbour trades, does not work. Numerous factors imply differences in prices and YTM. For instance, assets with the same maturity and liquidity level but different coupon amounts are traded at different prices; turmoil and flight-to-liquidity periods involve high volatile prices; on-the-run bonds are often traded with a large liquidity premium and should not be considered outliers because they are the most actively traded assets and the market benchmark, etc. Additionally, there are interdealer brokers’ posting errors similar to those mentioned by Fleming (2003).

  20. We do not consider the reported mid yield, which is simple interest with an actual/365 basis, except for more than 6-month remaining maturity bills, which are valued using the bond equivalent yield.

  21. Note that the settlement date is generally one working day after the trading date.

  22. We control for the special size of the first interest payment in just-issued securities.

References

  • Amihud, Y., & Medelson, H. (1991). Liquidity, maturity and the yield on U.S. Treasury securities. Journal of Finance,46, 1411–1425.

    Article  Google Scholar 

  • Andersen, T. G., & Benzoni, L. (2007). Do bonds span volatility risk in the U.S. Treasury market? A specification test for affine term structure models. NBER Working Paper No. W12962.

  • Anderson, N., & Sleath, J. (1999). New Estimates of the U.K. Real and Nominal Yield Curves. Bank of England Quarterly Bulletin, November, 384–392.

  • Andreasen, M. M., Christensen, J. H. E., & Rudebusch, G. D. (2017). Term structure analysis with big data. Federal Reserve Bank of San Francisco, Working Paper 2017-21.

  • Bank of International Settlements. (2005). Zero-coupon yield curves: technical documentation. BIS Papers, No. 25, October.

  • Barnejee, S., & Graveline, J. J. (2013). The cost of short-selling liquid securities. The Journal of Finance,68, 637–664.

    Article  Google Scholar 

  • Black, F., Dermand, E., & Toy, W. (1990). A one-factor model of interest rates and its application to treasury bond options. Financial Analysts Journal,46, 33–39.

    Article  Google Scholar 

  • Bliss, R. R. (1996). Testing term structure estimation methods. Advances in Futures and Options Research,9, 197–231.

    Google Scholar 

  • Bolder, D. J., & Gusba, S. (2002). Exponentials, polynomials, and Fourier series: More yield curve modelling at the bank of Canada. Bank of Canada, Working Paper 2002-29.

  • Bolder, D. J., Johnson, G., & Metzler, A. (2004). An empirical analysis of the Canadian term structure of zero-coupon interest rates. Bank of Canada Working Paper No. 2004-48.

  • Brown, C. G., Cyree, K. B., Griffiths, M. D., & Winters, D. B. (2008). Further analysis of the expectations hypothesis using very short-term rates. Journal of Banking & Finance,32, 600–613.

    Article  Google Scholar 

  • Campbell, J. Y. (1995). Some lessons from the yield curve. Journal of Economic Perspectives,9(3), 129–152.

    Article  Google Scholar 

  • Campbell, J., & Shiller, R. (1991). Yield spreads and interest rates movements: A bird’s eye view. Review of Economic Studies,58, 495–514.

    Article  Google Scholar 

  • Cherian, J. A., Jacquier, E., & Jarrow, R. A. (2004). A model of the convenience yields in on-the-run treasuries. Review of Derivatives Research,7, 29–97.

    Article  Google Scholar 

  • Corsi, F., Mittnik, S., Pigorsch, C., & Pigorsch, U. (2008). The volatility of realized volatility. Econometric Reviews,27(1–3), 46–78.

    Article  Google Scholar 

  • Díaz, A., & Escribano, A. (2017). Liquidity measures throughout the lifetime of the U.S. Treasury bond. Journal of Financial Markets,33, 42–74.

    Article  Google Scholar 

  • Díaz, A., Jareño, F., & Navarro, E. (2011). Term structure of volatilities and yield curve estimation methodology. Quantitative Finance,11(4), 573–586.

    Article  Google Scholar 

  • Díaz, A., Merrick, J. J., & Navarro, E. (2006). Spanish Treasury bond market liquidity and volatility pre- and post-European Monetary Union. Journal of Banking & Finance,30, 1309–1332.

    Article  Google Scholar 

  • Diebold, F. X., & Li, C. (2006). Forecasting the term structure of government bond yields. Journal of Econometrics,130(2), 337–364.

    Article  Google Scholar 

  • Downing, C., & Oliner, S. (2007). The term structure of commercial paper rates. Journal of Financial Economics,83, 59–86.

    Article  Google Scholar 

  • Duffie, D. (1996). Special repo rates. The Journal of Finance,51(2), 493–526.

    Article  Google Scholar 

  • Fleming, M. J. (2000). Financial market implications of the Federal debt paydown. Staff Report, Federal Reserve Bank of New York, No. 120.

  • Fleming, M. J. (2003). Measuring Treasury market liquidity. Federal Reserve Bank of New York Economic Policy Review,9, 83–108.

    Google Scholar 

  • Fontaine, J. S., & García, R. (2012). Bond liquidity premia. Review of Financial Studies,25, 1207–1254.

    Article  Google Scholar 

  • Goldreich, D., Hanke, B., & Nath, P. (2005). The price of future liquidity: Time-varying liquidity in the U.S. Treasury market. Review of Finance,9, 1–32.

    Article  Google Scholar 

  • Graveline, J. J., & McBrady, M. R. (2011). Who makes on-the-run Treasuries special? Journal of Financial Intermediation,20, 620–632.

    Google Scholar 

  • Gürkaynak, R. S., Sack, B., & Wright, J. H. (2007). The U.S. Treasury yield curve: 1961 to the present. Journal of Monetary Economics,54(8), 2291–2304.

    Article  Google Scholar 

  • Jordan, B., & Jordan, S. (1997). An empirical investigation of the repo special rate. The Journal of Finance,52, 2051–2072.

    Article  Google Scholar 

  • Jordan, J. V., & Mansi, S. A. (2003). Term structure estimation from on-the-run Treasuries. Journal of Banking & Finance,27(8), 1487–1509.

    Article  Google Scholar 

  • Kamara, A. (1994). Liquidity, taxes, and short-term yields. Journal of Financial and Quantitative Analysis,29(3), 403–417.

    Article  Google Scholar 

  • Krishnamurthy, A. (2002). The bond/old-bond spread. Journal of Financial Economics,66(2), 463–506.

    Article  Google Scholar 

  • Krishnamurthy, A., & Vissing-Jorgensen, A. (2012). The aggregate demand for Treasury debt. Journal of Political Economy,120(2), 233–267.

    Article  Google Scholar 

  • Levene, H. (1960). Robust tests for equality of variances. In I. Olkin (Ed.), Contributions to probability and statistics: Essays in honor of Harold Hotelling (pp. 278–292). Stanford, CA: Stanford University Press.

    Google Scholar 

  • Longstaff, F. A. (2000). The term structure of very short-term rates: New evidence for the expectations hypothesis. Journal of Financial Economics,58(3), 397–415.

    Article  Google Scholar 

  • Longstaff, F. A. (2004). The flight-to-liquidity premium in U.S. Treasury bond prices. Journal of Business,77, 511–526.

    Article  Google Scholar 

  • McCulloch, J., & Kwon, H. (1993). U.S. term structure data, 1947–1991. Ohio State University Working Paper, pp. 93–96.

  • Mizrach, B., & Neely, C. (2006). The transition to electronic communications networks in the secondary Treasury market. Federal Reserve Bank of St. Louis Review,88(6), 527–541.

    Google Scholar 

  • Nelson, D. B. (1991). Conditional heteroskedasticity in asset returns: A new approach. Econometrica,59(2), 347–370.

    Article  Google Scholar 

  • Nelson, C. R., & Siegel, A. F. (1987). Parsimonious modeling of yield curves. Journal of Business,60, 473–489.

    Article  Google Scholar 

  • Pasquariello, P., & Vega, C. (2009). The on-the-run liquidity phenomenon. Journal of Financial Economics,92, 1–24.

    Article  Google Scholar 

  • Sack, B. P., & Elsasser, R. (2004). Treasury inflation-indexed debt: A review of the U.S. experience. FRBNY Economic Policy Review,10(1), 47–63.

    Google Scholar 

  • Sarig, O., & Warga, A. (1989). Bond price data and bond market liquidity. Journal of Financial and Quantitative Analysis,24(3), 367–378.

    Article  Google Scholar 

  • Svensson, L. E. (1994). Estimating and interpreting forward interest rates: Sweden 1992–1994. Centre for Economic Policy Research, Discussion Paper 1051.

  • Vayanos, D., & Weill, P. (2008). A search-based theory of the on-the-run phenomenon. The Journal of Finance,63, 1361–1398.

    Article  Google Scholar 

  • Warga, A. (1992). Bond returns, liquidity, and missing data. Journal of Financial and Quantitative Analysis,27(4), 605–617.

    Article  Google Scholar 

  • Yallup, P. J. (2012). Models of the yield curve and the curvature of the implied forward rate function. Journal of Banking & Finance,36(1), 121–135.

    Article  Google Scholar 

Download references

Acknowledgements

We are indebted to Zvika Afik, Alain Coën, Manfred Frühwirth, Alois Geyer, Robert Korajczyk, John Merrick, Pietro Millosovich, Alfonso Novales, Christian Speck, Christian Wagner, Josef Zechner and Hairui Zhang for very detailed suggestions. In addition, we would like to thank the anonymous referee for their constructive and valuable comments on this paper. This work was supported by the Spanish Ministerio de Economía, Industria y Competitividad (ECO2017-89715-P). Any errors are solely the responsibility of the authors.

Author information

Authors and Affiliations

  1. Departamento de Análisis Económico y Finanzas, Facultad C. Económicas y Empresariales, Universidad de Castilla-La Mancha, Plaza de la Universidad, 1, 02071, Albacete, Spain

    Antonio Díaz & Francisco Jareño

  2. Departamento de Economía y Dirección de Empresas, Edificio C. Económicas, Universidad de Alcalá, Empr. y Tur., Pz. de la Victoria, s/n, 28802, Alcalá de Henares, Spain

    Eliseo Navarro

Authors
  1. Antonio Díaz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Francisco Jareño
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Eliseo Navarro
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Antonio Díaz.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendix: Technical details of our dataset of government securities prices

Appendix: Technical details of our dataset of government securities prices

GovPX consolidates and posts real-time quotes and trades data from six of the seven major interdealer brokers (with the notable exception of Cantor Fitzgerald).Footnote 16 Collectively, these brokers account for approximately two-thirds of the voice interdealer broker market. In turn, the interdealer market is approximately one-half of the total market (see Fleming 2003). Thus, although the estimated bills coverage exceeds 90% in every year of the Fleming’s GovPX sample (Jan 97–Mar 00), the availability of 30-year bond data is limited because of Cantor Fitzgerald’s prominence in the long-maturity segment of the market. According to Mizrach and Neely (2006), voice-brokered trading volume began to decline after 1999 as electronic trading platforms (e.g., eSpeed, BrokerTec) became available. Indeed, GovPX does not provide aggregate volume and transaction information after May 2001. After ICAP’s purchase of GovPX in January 2005, ICAP PLC was the only broker reporting through GovPX. Therefore, we assume an imperceptible impact from the decline in GovPX market coverage on our estimates because we consider the midpoint prices and yields between the bid and ask prices at 5 pm.

The GovPX dataset contains snapshots of the market situation at 1 pm, 2 pm, 3 pm, 4 pm, and 5 pm. Each snapshot includes detailed individual security information, such as CUSIP, coupon, maturity date, and product type (an indicator of whether the security is trading when issued, on the run, or active off the run). The transaction data available until May 2001 include the last trade time, size, and side (buy or sell), the price (or yield in the case of bills), and the aggregate volume (volume in millions traded from 6 pm on the previous day to 5 pm). The quote data used from June 2001 include the best bid and ask prices (or discount rate actual/360 in the case of bills) and the mid-price and mid-yield (actual/365).

Our initial sample relies on the information at 5 pm, i.e., the last transaction during “regular trading hours” (from 7:30 am to 5:00 pm Eastern Time, ET), if available, and quote data otherwise. Quote prices are used during the last part of the sample period because trading volume information is not reported by GovPX. We complement the GovPX data with official data on the dates for the last issue and the first coupon payment and the coupon rate of each Treasury security.Footnote 17 This information is publicly available on the US Treasury website.

To improve the adjustment at the short end of the yield curve, we initially consider all Treasury bills. In this maturity segment, bills are very more actively traded than old off-the-run notes and bonds, most of which are absorbed into investors’ inactive portfolios.Footnote 18 Liquidity differences in these short-term assets imply large divergences in yields to maturity. Thus, we include only Treasury notes and bonds that have at least 1 year of life remaining. However, we are forced to modify this criterion from 2002 because the number of outstanding bills with terms to maturity between 6 months and 1 year declines considerable during the year 2000, and the 1-year Treasury bill is no longer auctioned as of the beginning of March 2001. Therefore, we also consider Treasury notes and bonds with remaining maturities between 6 and 12 months for the period after 2001.

We also apply other data filters that are designed to enhance the quality of the data. First, we do not include transactions that are associated with “when-issued” and cash management or trades and quotes that are related to callable and flower bonds and TIPS. Second, when two or more securities have the same maturity, we consider only trades and quotes for the youngest security, i.e., the security with the last auction date. Finally, we exclude yields that differ greatly from yields at nearby maturities. We apply an ad hoc filter based on common sense.Footnote 19 In addition, we occasionally observe that deleting a single data point in the set of prices used to fit the yield curve can produce a notable shift in both the parameters and the fitted yields, notably improving the fit. This phenomenon is also noted by Anderson and Sleath (1999).

To control for market conventions, we recalculate the price of each security in a homogeneous procedure to prevent a situation in which the effects of different market conventions depend on maturities and assets. Every price is valued at the trading date on an actual/actual day-count basis. In the case of Treasury bills, we first obtain the price at the settlement date from the last trade price, if available, and from the mid-price between the bid and the ask prices otherwise.Footnote 20 In both cases, the GovPX reported price is a discount rate using the actual/360 basis. Second, we compute the yield-to-maturity as a compound interest rate by using the actual/actual. Third, we calculate “our” price at the trading date by using the yield-to-maturity obtained in the previous step.Footnote 21 In the case of Treasury notes and bonds, the price is directly reported in the data as the last trade price or the mid-price. From this price, we apply the mentioned second and third steps to obtain “our” homogeneous price.Footnote 22

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Díaz, A., Jareño, F. & Navarro, E. Yield curves from different bond data sets. Rev Deriv Res 23, 191–226 (2020). https://doi.org/10.1007/s11147-019-09162-z

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11147-019-09162-z

Keywords

JEL Classification

Search

Navigation