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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. Relative Value.

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bond relative value models and term structure of credit spreads a practitioner s approach

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

relative value
Relative Value

“Detecting relative value refers to the process of comparing the potential returns of alternative investments”

Kurt Hess, WMS kurthess@waikato.ac.nz

agenda
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

motivation
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

motivation5
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

introduction
For the practitioner, there are two fundamental factors that drive pricing of fixed income instrumentsIntroduction

Interest Rate

Credit Risk

Kurt Hess, WMS kurthess@waikato.ac.nz

introduction interest rate
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

introduction interest rate8
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

introduction credit spread
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

introduction implementations
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

yield curve modelling
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

yield curve modelling12
Yield Curve Modelling

Generating Buy / Sell Signals

Kurt Hess, WMS kurthess@waikato.ac.nz

yield curve modelling ytm
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

yield curve modelling ytm14
Yield Curve Modelling - YTM

Example printout Swiss Government Yield Curve

Kurt Hess, WMS kurthess@waikato.ac.nz

jpm discount function model
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

extended nelson siegel 1987
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

extended nelson siegel 198718
Extended Nelson & Siegel (1987)

Kurt Hess, WMS kurthess@waikato.ac.nz

modelling credit spreads
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

modelling credit spreads20
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

modelling credit spreads21
Modelling Credit Spreads

Parallel Shift of Benchmark Curve

Credit Spread

Kurt Hess, WMS kurthess@waikato.ac.nz

modelling credit spreads22
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

modelling credit spreads23
Modelling Credit Spreads

Wide range of shapes can be set in model:

Kurt Hess, WMS kurthess@waikato.ac.nz

modelling credit spreads24
Modelling Credit Spreads

Example output of summary statistics YTM based model. Could be used to calibrate S∞

Kurt Hess, WMS kurthess@waikato.ac.nz

conclusion
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