Bond Relative Value Models and Term Structure of Credit Spreads: A Practitioner’s Approach

1. Bond Relative Value Models and Term Structure of Credit Spreads: A Practitioner’s Approach Slides prepared by Kurt Hess, University of Waikato Management School Department of Finance

2. Relative Value “Detecting relative value refers to the process of comparing the potential returns of alternative investments” Kurt Hess, WMS kurthess@waikato.ac.nz

3. Motivation / IntroductionWhy bond relative value models? Yield Curve Modelling -Traditional YTM Benchmarking -JP Morgan Discount Factor Model -Extended Nelson & Siegel Modelling Credit Spreads AGENDA Kurt Hess, WMS kurthess@waikato.ac.nz

4. Why relative value models for bonds? Determined cash flows (FIXED INCOME) make them probably more useful than models in other e.g. equity area (P/E comparisons) Widely used in industry but not all taken seriously by academic literature as some lack theoretical foundation Motivation Kurt Hess, WMS kurthess@waikato.ac.nz

5. Why relative value models for bonds? Academic literature applies them for empirical work but actual implementations useful for practitioners are usually not documented Motivation Kurt Hess, WMS kurthess@waikato.ac.nz

6. For the practitioner, there are two fundamental factors that drive pricing of fixed income instruments Introduction Interest Rate Credit Risk Kurt Hess, WMS kurthess@waikato.ac.nz

7. Interest rates modelling as stochastic processes (Vasicek, CIR) not suitable for bond pricing in the markets (only for suicidal bond traders or for interest rate derivatives) Most “useful” models are thus calibrated to the market yield curve ( and volatilities), e.g Lee (1986), HJM (1992), Libor market model Introduction – Interest Rate Modelling approaches: Kurt Hess, WMS kurthess@waikato.ac.nz

8. This means we need static term structure of interest rate models First fitting attempts early 20th century and Durand (1942) Seminal models by McCulloch (1971,1975) and Nelson & Siegel (1987) Introduction – Interest Rate Modelling approaches (cont’d): Kurt Hess, WMS kurthess@waikato.ac.nz

9. Merton (1974) type structural models or reduced form models (e.g. Jarrow, Lando & Turnbull 1997) Collin-Dufresne et al. (2001): Many factors impact credit spread but the dominant one remains elusive. They postulate “local supply/demand shocks”.. Introduction – Credit Spread Modelling approaches: Kurt Hess, WMS kurthess@waikato.ac.nz

10. Introduction – Implementations • All models described here are available from the author’s website:http://www.mngt.waikato.ac.nz/kurt/frontpage/ModelingTopicList.htm • They are all adaptations of industry implementations (CS First Boston) Kurt Hess, WMS kurthess@waikato.ac.nz

11. Yield Curve Modelling Three models implemented and described • Traditional YTM Benchmarking • Simple polynomial through YTM curve • JP Morgan Discount Factor Model • Models discount factor as polynomial • Extended Nelson & Siegel • Zero rates modelled by combination of exponential function Kurt Hess, WMS kurthess@waikato.ac.nz

12. Yield Curve Modelling Generating Buy / Sell Signals Kurt Hess, WMS kurthess@waikato.ac.nz

13. Yield Curve Modelling - YTM Yield to maturity YTM) / redemption yield: • Weakness recognised early (Schaefer, 1977): implies flat term structure, i.e. reinvesting each coupon at same rate • However still appropriate (and widely used) in less liquid bond markets (e.g. corporate bonds) where it is “more than good enough” Kurt Hess, WMS kurthess@waikato.ac.nz

14. Yield Curve Modelling - YTM Example printout Swiss Government Yield Curve Kurt Hess, WMS kurthess@waikato.ac.nz

15. JP Morgan model derives zero rates from a basket of bonds of equal credit quality (e.g. government bonds) by modeling discount function (usually better behaved) as a polynomial. Option to set some boundary conditions (at time t=0) JPM Discount Function Model Kurt Hess, WMS kurthess@waikato.ac.nz

16. Screenshot for sample of NZ Govt Bonds JPM Discount Function Model Kurt Hess, WMS kurthess@waikato.ac.nz

17. Models spot rate as three components Functional form requiresnumerical methods to fit curve Only “arbitrage free” model shown here. Extended Nelson & Siegel (1987) m Kurt Hess, WMS kurthess@waikato.ac.nz

18. Extended Nelson & Siegel (1987) Kurt Hess, WMS kurthess@waikato.ac.nz

19. Credit spread most popular yardstick for practitioners to assess bonds subject to default risk Absolute level less important than relative spread Research shows that it compensates for more than just default risk(Fons 1994, Elton et al. 2001) Modelling Credit Spreads Kurt Hess, WMS kurthess@waikato.ac.nz

20. Shape of “true” term structure of credit spreads is contentious Structural model predict “humped” shape (tested e.g. in Fons 1994, p.30) Helwege & Turner (1999) seem to confirm intuition of practitioners: no hump Many market participants just assume fixed spread. Modelling Credit Spreads Kurt Hess, WMS kurthess@waikato.ac.nz

21. Modelling Credit Spreads Parallel Shift of Benchmark Curve Credit Spread Kurt Hess, WMS kurthess@waikato.ac.nz

22. Modelling Credit Spreads Shape Parameters Term Structure of Credit Spreads T∞ Short-term characteristics of credit spreads Long-term characteristics Kurt Hess, WMS kurthess@waikato.ac.nz

23. Modelling Credit Spreads Wide range of shapes can be set in model: Kurt Hess, WMS kurthess@waikato.ac.nz

24. Modelling Credit Spreads Example output of summary statistics YTM based model. Could be used to calibrate S∞ Kurt Hess, WMS kurthess@waikato.ac.nz

25. Conclusion Pragmatic fitting method for yield curves and credit spreads … • From a practitioner’s view point the most simple ones are often the most suitable ones. YTM models were/are very popular because users understand “what was going on” • More advanced models often have too many parameters which are difficult to estimate and/or lack intuitive meaning. Kurt Hess, WMS kurthess@waikato.ac.nz