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Measuring Risk in Fixed Income Portfolios using Yield Curve Models

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  • João Caldeira

    ()

  • Guilherme Moura

    ()

  • André Santos

    ()

Abstract

We propose a novel approach to measure risk in fixed income portfolios in terms of value-at-risk (VaR). We obtain closed-form expressions for the vector of expected bond returns and for its covariance matrix based on a general class of dynamic factor models, including the dynamic versions of the Nelson-Siegel and Svensson models, to compute the parametric VaR of a portfolio composed of fixed income securities. The proposed approach provides additional modeling flexibility as it can accommodate alternative specifications of the yield curve as well as alternative specifications of the conditional heteroskedasticity in bond returns. An empirical application involving a data set with 15 fixed income securities with different maturities indicate that the proposed approach delivers accurate VaR estimates. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • João Caldeira & Guilherme Moura & André Santos, 2015. "Measuring Risk in Fixed Income Portfolios using Yield Curve Models," Computational Economics, Springer;Society for Computational Economics, vol. 46(1), pages 65-82, June.
  • Handle: RePEc:kap:compec:v:46:y:2015:i:1:p:65-82
    DOI: 10.1007/s10614-014-9438-7
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    as
    1. Giot, Pierre & Laurent, Sebastien, 2004. "Modelling daily Value-at-Risk using realized volatility and ARCH type models," Journal of Empirical Finance, Elsevier, vol. 11(3), pages 379-398, June.
    2. Victor DeMiguel & Lorenzo Garlappi & Raman Uppal, 2009. "Optimal Versus Naive Diversification: How Inefficient is the 1-N Portfolio Strategy?," Review of Financial Studies, Society for Financial Studies, vol. 22(5), pages 1915-1953, May.
    3. McCulloch, J Huston, 1971. "Measuring the Term Structure of Interest Rates," The Journal of Business, University of Chicago Press, vol. 44(1), pages 19-31, January.
    4. Almeida, Caio & Vicente, José, 2009. "Are interest rate options important for the assessment of interest rate risk?," Journal of Banking & Finance, Elsevier, vol. 33(8), pages 1376-1387, August.
    5. Lorenzo Cappiello & Robert F. Engle & Kevin Sheppard, 2006. "Asymmetric Dynamics in the Correlations of Global Equity and Bond Returns," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(4), pages 537-572.
    6. Gimeno, Ricardo & Nave, Juan M., 2009. "A genetic algorithm estimation of the term structure of interest rates," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2236-2250, April.
    7. Jones, Charles M. & Lamont, Owen & Lumsdaine, Robin L., 1998. "Macroeconomic news and bond market volatility," Journal of Financial Economics, Elsevier, vol. 47(3), pages 315-337, March.
    8. Christoffersen, Peter F, 1998. "Evaluating Interval Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 841-862, November.
    9. Robert F. Engle & Simone Manganelli, 2004. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 367-381, October.
    10. Manabu Asai & Michael McAleer, 2009. "Multivariate stochastic volatility, leverage and news impact surfaces," Econometrics Journal, Royal Economic Society, vol. 12(2), pages 292-309, July.
    11. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. " On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    12. Engle, Robert F & Ng, Victor K, 1993. " Measuring and Testing the Impact of News on Volatility," Journal of Finance, American Finance Association, vol. 48(5), pages 1749-1778, December.
    13. Asai, M. & Caporin, M., 2009. "Block Structure Multivariate Stochastic Volatility Models," Econometric Institute Research Papers EI 2009-51, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    14. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    15. de Goeij, Peter & Marquering, Wessel, 2006. "Macroeconomic announcements and asymmetric volatility in bond returns," Journal of Banking & Finance, Elsevier, vol. 30(10), pages 2659-2680, October.
    16. Ferreira, Miguel A., 2005. "Forecasting the comovements of spot interest rates," Journal of International Money and Finance, Elsevier, vol. 24(5), pages 766-792, September.
    17. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2006. "Volatility and Correlation Forecasting," Handbook of Economic Forecasting, Elsevier.
    18. Santos, André A.P. & Nogales, Francisco J. & Ruiz, Esther & Dijk, Dick Van, 2012. "Optimal portfolios with minimum capital requirements," Journal of Banking & Finance, Elsevier, vol. 36(7), pages 1928-1942.
    19. Miguel A. Ferreira, 2005. "Evaluating Interest Rate Covariance Models Within a Value-at-Risk Framework," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 3(1), pages 126-168.
    20. Diebold, Francis X. & Li, Canlin, 2006. "Forecasting the term structure of government bond yields," Journal of Econometrics, Elsevier, vol. 130(2), pages 337-364, February.
    21. Michael McAleer, 2009. "The Ten Commandments For Optimizing Value-At-Risk And Daily Capital Charges," Journal of Economic Surveys, Wiley Blackwell, vol. 23(5), pages 831-849, December.
    22. de Goeij, P. C. & Marquering, W., 2006. "Macroeconomic announcements and asymmetric volatility in bond returns," Other publications TiSEM bc4389f3-bad2-4e5b-b996-3, Tilburg University, School of Economics and Management.
    23. Paolo Zaffaroni, 2007. "Contemporaneous aggregation of GARCH processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(4), pages 521-544, July.
    24. Bollerslev, Tim, 1990. "Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model," The Review of Economics and Statistics, MIT Press, vol. 72(3), pages 498-505, August.
    25. Nelson, Charles R & Siegel, Andrew F, 1987. "Parsimonious Modeling of Yield Curves," The Journal of Business, University of Chicago Press, vol. 60(4), pages 473-489, October.
    26. Diebold, Francis X. & Rudebusch, Glenn D. & Borag[caron]an Aruoba, S., 2006. "The macroeconomy and the yield curve: a dynamic latent factor approach," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 309-338.
    27. Santos, André A.P. & Moura, Guilherme V., 2014. "Dynamic factor multivariate GARCH model," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 606-617.
    28. Vlaar, Peter J. G., 2000. "Value at risk models for Dutch bond portfolios," Journal of Banking & Finance, Elsevier, vol. 24(7), pages 1131-1154, July.
    29. Koopman, Siem Jan & Mallee, Max I. P. & Van der Wel, Michel, 2010. "Analyzing the Term Structure of Interest Rates Using the Dynamic Nelson–Siegel Model With Time-Varying Parameters," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(3), pages 329-343.
    30. Galeano, Pedro & Ausín, M. Concepción, 2010. "The Gaussian Mixture Dynamic Conditional Correlation Model: Parameter Estimation, Value at Risk Calculation, and Portfolio Selection," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(4), pages 559-571.
    31. Jeremy Berkowitz & James O'Brien, 2002. "How Accurate Are Value-at-Risk Models at Commercial Banks?," Journal of Finance, American Finance Association, vol. 57(3), pages 1093-1111, June.
    32. Raffaella Giacomini & Halbert White, 2006. "Tests of Conditional Predictive Ability," Econometrica, Econometric Society, vol. 74(6), pages 1545-1578, November.
    33. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    34. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
    35. Sébastien Laurent & Luc Bauwens & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109.
    36. Andrew Harvey & Esther Ruiz & Neil Shephard, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Oxford University Press, vol. 61(2), pages 247-264.
    37. Torben G. Andersen & Luca Benzoni, 2009. "Stochastic volatility," Working Paper Series WP-09-04, Federal Reserve Bank of Chicago.
    38. Ferstl, Robert & Hayden, Josef, 2010. "Zero-Coupon Yield Curve Estimation with the Package termstrc," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 36(i01).
    39. André A. P. Santos & Francisco J. Nogales & Esther Ruiz, 2013. "Comparing Univariate and Multivariate Models to Forecast Portfolio Value-at-Risk," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 11(2), pages 400-441, March.
    40. Michiel De Pooter, 2007. "Examining the Nelson-Siegel Class of Term Structure Models," Tinbergen Institute Discussion Papers 07-043/4, Tinbergen Institute.
    41. Patrick Hagan & Graeme West, 2006. "Interpolation Methods for Curve Construction," Applied Mathematical Finance, Taylor & Francis Journals, vol. 13(2), pages 89-129.
    42. Zakoian, Jean-Michel, 1994. "Threshold heteroskedastic models," Journal of Economic Dynamics and Control, Elsevier, vol. 18(5), pages 931-955, September.
    43. Christoffersen, Peter & Hahn, Jinyong & Inoue, Atsushi, 2001. "Testing and comparing Value-at-Risk measures," Journal of Empirical Finance, Elsevier, vol. 8(3), pages 325-342, July.
    44. Engle, Robert, 2002. "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 339-350, July.
    45. McCulloch, J Huston, 1975. "The Tax-Adjusted Yield Curve," Journal of Finance, American Finance Association, vol. 30(3), pages 811-830, June.
    46. Gita Persand & Chris Brooks, 2003. "Volatility forecasting for risk management," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 22(1), pages 1-22.
    47. Ser-Huang Poon & Clive W.J. Granger, 2003. "Forecasting Volatility in Financial Markets: A Review," Journal of Economic Literature, American Economic Association, vol. 41(2), pages 478-539, June.
    48. Tsunehiro Ishihara & Yasuhiro Omori, 2009. "Multivariate Stochastic Volatility with Cross Leverage," CARF F-Series CARF-F-191, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    49. Rafael B. Rezende & Mauro S. Ferreira, 2013. "Modeling and Forecasting the Yield Curve by an Extended Nelson‐Siegel Class of Models: A Quantile Autoregression Approach," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 32(2), pages 111-123, March.
    50. Engle, Robert F, 1990. "Stock Volatility and the Crash of '87: Discussion," Review of Financial Studies, Society for Financial Studies, vol. 3(1), pages 103-106.
    51. Bianchi, Francesco & Mumtaz, Haroon & Surico, Paolo, 2009. "The great moderation of the term structure of UK interest rates," Journal of Monetary Economics, Elsevier, vol. 56(6), pages 856-871, September.
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    Cited by:

    1. Anthony H. Tu & Cathy Yi-Hsuan Chen, 2016. "What Derives the Bond Portfolio Value-at-Risk: Information Roles of Macroeconomic and Financial Stress Factors," SFB 649 Discussion Papers SFB649DP2016-006, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    2. Schlütter, Sebastian, 2017. "Scenario-based capital requirements for the interest rate risk of insurance companies," ICIR Working Paper Series 28/17, Goethe University Frankfurt, International Center for Insurance Regulation (ICIR).

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