Bond Portfolio Optimization

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Springer Science & Business Media, Jan 8, 2008 - Business & Economics - 140 pages
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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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Contents

Introduction
2
Bond Market Terminology
6
22 Interest Rates
7
23 Term Structure of Interest Rates
9
24 Estimating the Term Structure of Interest Rates
10
25 Classical Theories of the Term Structure of Interest Rates
11
26 ArbitrageFree Term Structure Theories
12
Term Structure Modeling in Continuous Time
13
433 Passive Bond Portfolio Selection Strategies
77
434 Summary and Conclusion
82
Dynamic Bond Portfolio Optimization in Continuous Time
85
52 Bond Portfolio Selection Problem in a HJM Framework
87
522 The HamiltonJacobiBellman Equation
89
523 Derivation of Optimum Portfolio Weights
91
524 The Value Function for CRRA Utility Functions
94
53 Special Cases
96

32 Interest Rate Modeling Approaches
14
33 HeathJarrowMorton 1992
17
332 Dynamics of Traded Securities
18
333 ArbitrageFree Pricing
19
The HJM Drift Condition
20
335 The Short Rate of Interest
21
336 Special Cases
22
34 Vasicek 1977
23
343 Properties
26
35 HullWhite 1994
30
352 Derivation of ZeroCoupon Bond Prices
31
353 Properties
35
36 Summary and Conclusion
39
Static Bond Portfolio Optimization
41
422 Application to Bond Portfolios
43
423 Obtaining the Parameters
48
424 OneFactor Vasicek 1977 Model
51
425 TwoFactor HullWhite 1994 Model
60
43 Static Bond Portfolio Selection in Practice
66
432 Active Bond Portfolio Selection Strategies
67
532 TwoFactor HullWhite 1994 Model
100
54 International Bond Investing
105
542 Model Setup
106
543 Derivation of the Optimum Portfolio Weights
109
544 Interpretation of the Optimum Portfolio Weights
111
545 Numerical Example
112
55 Summary and Conclusion
113
Summary and Conclusion
114
HeathJarrowMorton 1992
119
A2 ArbitrageFree Pricing
120
A3 HJM Drift Condition
121
HullWhite 1994
122
Dynamic Bond Portfolio Optimization
123
Dynamic Bond Portfolio Optimization
124
C3 International Bond Portfolio Selection
126
References
127
List of Tables
134
List of Figures
136
Copyright

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Page 127 - Crane, DB, 1972. A dynamic model for bond portfolio management.
Page 132 - Dynamic Asset Allocation and Fixed Income Management." Journal of Financial and Quantitative Analysis 34: 513-531. Vasicek, O. (1977) "An Equilibrium Characterization of the Term Structure.
Page 7 - It is equal to the dirty price minus accrued interest. The accrued interest is equal to the amount of the next coupon payment multiplied by the proportion of the current inter-coupon period so far elapsed, ie the buyer of the bond "compensates...
Page 7 - The dirty price is the actual amount in return for the right to the full amount of each future coupon payment and the redemption proceeds.