Lecture Notes in Economic and Mathematical Systems

By: Michael Puhle

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Paperback | 4 January 2008

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1 The tools of modern portfolio theory are in general use in the equity markets, either in the form of portfolio optimization software or as an accepted frame- 2 work in which the asset managers think about stock selection. In the ?xed income market on the other hand, these tools seem irrelevant or inapplicable. Bond portfolios are nowadays mainly managed by a comparison of portfolio 3 4 risk measures vis a vis a benchmark. The portfolio manager's views about the future evolution of the term structure of interest rates translate th- selves directly into a positioning relative to his benchmark, taking the risks of these deviations from the benchmark into account only in a very crude 5 fashion, i.e. without really quantifying them probabilistically. This is quite surprising since sophisticated models for the evolution of interest rates are commonly used for interest rate derivatives pricing and the derivation of ?xed 6 income risk measures. Wilhelm (1992) explains the absence of modern portfolio tools in the ?xed 7 income markets with two factors: historically relatively stable interest rates and systematic di?erences between stocks and bonds that make an application of modern portfolio theory di-cult. These systematic di?erences relate mainly to the ?xed maturity of bonds. Whereas possible future stock prices become more dispersed as the time horizon widens, the bond price at maturity is 8 ?xed. This implies that the probabilistic models for stocks and bonds have 1 Starting with the seminal work of Markowitz (1952).

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Non-Fiction Accounting & Finance Finance Investment & Securities Mathematics Optimisation Linear Programming Business & Management Operational Research Applied Mathematics

Acknowledgements	p. v
Abbreviations	p. xi
Commonly Used Symbols	p. xiii
Introduction	p. 1
Bond Market Terminology	p. 5
Characteristics of Bonds	p. 5
Interest Rates	p. 6
Term Structure of Interest Rates	p. 8
Estimating the Term Structure of Interest Rates	p. 9
Classical Theories of the Term Structure of Interest Rates	p. 10
Arbitrage-Free Term Structure Theories	p. 11
Empirical Properties of the Term Structure of Interest Rates	p. 11
Term Structure Modeling in Continuous Time	p. 13
Introduction	p. 13
Interest Rate Modeling Approaches	p. 14
Heath/Jarrow/Morton (1992)	p. 17
Introduction	p. 17
Dynamics of Traded Securities	p. 18
Arbitrage-Free Pricing	p. 19
Excursus: The HJM Drift Condition	p. 20
The Short Rate of Interest	p. 21
Special Cases	p. 22
Vasicek (1977)	p. 23
Introduction	p. 23
Derivation of Zero-Coupon Bond Prices	p. 23
Properties	p. 26
Hull/White (1994)	p. 30
Introduction	p. 30
Derivation of Zero-Coupon Bond Prices	p. 31
Properties	p. 35
Summary and Conclusion	p. 39
Static Bond Portfolio Optimization	p. 41
Introduction	p. 41
Static Bond Portfolio Selection in Theory	p. 41
A Short Review of Modern Portfolio Theory	p. 41
Application to Bond Portfolios	p. 43
Obtaining the Parameters	p. 48
One-Factor Vasicek (1977) Model	p. 51
Two-Factor Hull/White (1994) Model	p. 60
Static Bond Portfolio Selection in Practice	p. 66
Introduction	p. 66
Active Bond Portfolio Selection Strategies	p. 67
Passive Bond Portfolio Selection Strategies	p. 77
Summary and Conclusion	p. 82
Dynamic Bond Portfolio Optimization in Continuous Time	p. 85
Introduction	p. 85
Bond Portfolio Selection Problem in a HJM Framework	p. 87
Dynamics of Prices and Wealth	p. 87
The Hamilton/Jacobi/Bellman Equation	p. 89
Derivation of Optimum Portfolio Weights	p. 91
The Value Function for CRRA Utility Functions	p. 94
Special Cases	p. 96
One-Factor Vasicek (1977) Model	p. 96
Two-Factor Hull/White (1994) Model	p. 100
International Bond Investing	p. 105
Introduction	p. 105
Model Setup	p. 106
Derivation of the Optimum Portfolio Weights	p. 109
Interpretation of the Optimum Portfolio Weights	p. 111
Numerical Example	p. 112
Summary and Conclusion	p. 113
Summary and Conclusion	p. 115
Heath/Jarrow/Morton (1992)	p. 119
Dynamics of Zero-Coupon Bonds	p. 119
Arbitrage-Free Pricing	p. 120
HJM Drift Condition	p. 121
Special Case: Hull/White (1994)	p. 122
Dynamic Bond Portfolio Optimization	p. 123
Dynamic Bond Portfolio Optimization	p. 125
Vasicek (1977)	p. 125
Hull/White (1994)	p. 125
International Bond Portfolio Selection	p. 126
References	p. 127
List of Tables	p. 135
List of Figures	p. 137
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Lecture Notes in Economic and Mathematical Systems

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