Strategic Asset Allocation in Fixed Income Markets
A Matlab based user's guide
Published on 15. September 2008
192 pages
978-0-470-72107-0 (ISBN)
Description
* Matlab is used within nearly all investment banks and is arequirement in most quant job ads. There is no other book writtenfor finance practitioners that covers this
* Enables readers to implement financial and econometric modelsin Matlab
* All central concepts and theories are illustrated by Matlabimplementations which are accompanied by detailed descriptions ofthe programming steps needed
* All concepts and techniques are introduced from a basiclevel
* Chapter 1 introduces Matlab and matrix algebra, it serves tomake the reader familiar with the use and basic capabilities ifMatlab. The chapter concludes with a walkthrough of a linearregression model, showing how Matlab can be used to solve anexample problem analytically and by the use of optimization andsimulation techniques
* Chapter 2 introduces expected return and risk as centralconcepts in finance theory using fixed income instruments asexamples, the chapter illustrates how risk measures such asstandard deviation, Modified duration, VaR, and expected shortfallcan be calculated empirically and in closed form
* Chapter 3 introduces the concept of diversification andillustrates how the efficient investment frontier can be derived -a Matlab is developed that can be used to calculate a given numberof portfolios that lie on an efficient frontier, the chapter alsointroduces the CAPM
* Chapter 4 introduces econometric tools: principle componentanalysis is presented and used as a prelude to yield-curve factormodels. The Nelson-Siegel model is used to introduce theKalman-Filter as a way to add time-series dynamics to the evolutionof yield curves over time, time series models such as VectorAutoregression and regime-switching are also presented
* Supported by a website with online resources -www.kennyholm.com where all Matlab programs referred to in the textcan be downloaded. The site also contains lecture slides andanswers to end of chapter exercises
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Ken Nyholm works in the Risk Management Division of the European Central Bank, focusing on the practical implementation of financial and quantitative techniques in the area of fixed income strategic asset allocation for the bank's domestic and foreign currency portfolios, as well as asset and liability management for pensions. Ken holds a PhD in finance and has published numerous articles on yield curve modelling and financial market microstructure. Ken has extensive teaching and communication experience obtained from university courses at the master level, as well as conference speaking engagements, and central banking seminars.
Content
1. Introduction.
1.1 Strategic Asset Allocation.
1.2 Outline of the Book.
2. Essential Elements of Matlab.
2.1 Introduction.
2.2 Getting started.
2.3 Introductorymatrix algebra.
2.4 Organising data.
2.5 Creating functions.
2.5.1 Branching and looping.
2.5.2 An example of a simple function.
2.5.3 Calling functions in Matlab Rø.
2.6 The linear regression.
2.6.1 The basic setup.
2.6.2 Maximumlikelihood.
2.7 Some estimation examples.
2.8 A brief introduction to simulations.
2.8.1 Generating correlated randomnumbers.
3. Fixed-Income Preliminaries.
3.1 Introduction.
3.2 Spot rates and yields.
3.3 Forward rates.
3.4 Bond pricing functions.
4. Risk and Return Measures.
4.1 Introduction.
4.2 RiskMeasures.
4.2.1 Value-at-risk and Expected Shortfall.
4.2.2 Duration and modified duration.
4.3 Fixed-Income Returns.
5. Term Structure Models.
5.1 Introduction.
5.2 Not-Necessarily Arbitrage FreeModels.
5.2.1 Nelson and Siegel.
5.2.2 Svensson and Soderlind.
5.3 Arbitrage-FreeModels.
5.3.1 Vasicek.
5.3.2 Multi-factormodels: an example.
6. Asset Allocation.
6.1 Introduction.
6.2 Efficient portfolios.
6.3 Diversification.
6.4 Theminimumvariance portfolio.
6.5 Asset weight constraints.
6.6 The Capital Asset PricingModel.
7. Statistical Tools.
7.1 Introduction.
7.2 The Vector Auto Regression.
7.2.1 Order of integration.
7.3 Regime switchingmodels.
7.3.1 Introduction.
7.4 Yield curvemodels in state-space form.
7.4.1 The Nelson-Siegelmodel in state-space.
7.5 Importance Sampling.
7.5.1 Some theory.
7.5.2 An example.
8. Building graphical user interfaces.
8.1 Introduction.
8.2 The "guide" development environment.
8.3 Creating a simple GUI.
8.3.1 Plotting the yield curve.
8.3.2 Estimating ? and yield curve factors.
9. Useful Formulas and Expressions.
9.1 Introduction.
9.2 Matrix operations.
9.2.1 Definitions.
9.2.2 Sum.
9.2.3 Product.
9.2.4 Transpose.
9.2.5 Symmetricmatrix.
9.2.6 The Identitymatrix.
9.2.7 Determinant.
9.2.8 Rank.
9.2.9 Inverse.
9.2.10 Trace.
9.2.11 Powers.
9.2.12 Eigenvalues and eigenvectors.
9.2.13 Positive definite.
9.2.14 Matrix differentiation.
9.3 Decompositions.
9.3.1 Triangular.
9.3.2 Cholesky.
9.3.3 Eigenvalue.
9.4 Basic rules.
9.4.1 Index rules.
9.4.2 Logarithmrules.
9.4.3 Simple derivatives.
9.4.4 Simple integrals.
9.5 Distributions.
9.5.1 Normal.
9.5.2 Multivariate normal.
9.5.3 Vasicek's limiting distribution.
9.6 Functions.
9.6.1 Linear (affine) function.
9.6.2 Quadratic function.
9.6.3 General polynominals.
9.6.4 Exponential.
9.6.5 Logarithm.
9.6.6 Error function.
9.6.7 Inverse.
9.7 Taylor series approximation.
9.8 Interest rates, returns and portfolio statistics.
9.8.1 Cummulative arithmetic return.
9.8.2 Average arithmetic return.
9.8.3 Cummulative geometric return.
9.8.4 Average geometric return.
9.8.5 Compounding of interest rates.
9.8.6 Portfolio statistics.
