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Dietmar Ernst

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Portfolio Management

Theorie und Praxis mit Excel und Matlab

Vorwort
1 Grundlagen des Portfolio Managements
1.1 Was ist unter Portfolio Management zu verstehen?
1.1.1 Was ist ein Portfolio?
1.1.2 Festlegung der Portfolio-Anteile
1.1.3 Das Portfolio Management und die Bedeutung quantitativer Methoden
1.2 Der Investment Management Prozess
1.2.1 Überblick über Portfolioplanung und Portfoliokonstruktion
1.2.2 Planung eines Portfolios und Festlegung von Portfoliorichtlinien
1.2.3 Kapitalanlageklassen und Kapitalmarkterwartungen
1.2.4 Die Strategische Asset Allokation (SAA)
1.2.5 Aktives und passives Kapitalanlagemanagement
1.2.6  Monitoring, Performance-Messung und Feedback
1.3 Überblick über das Risikomanagement
1.3.1 Ziele des Risikomanagement im Portfolio Management
1.3.2 Finanzielle Risiken
1.3.3 Quantitative Risikomaße
1.4 Welche Assetklassen kennt das Portfolio Management?
1.4.1 Übersicht über die verschiedenen Anlageklassen
1.4.2 Traditionelle Assetklassen
1.4.3 Alternative Assetklassen
1.4.4 Weitere Untergliederungsmöglichkeiten der Assetklassen
1.4.5 Korrelationen aller wichtigen Anlageklassen
1.5 Methoden des aktiven und passiven Portfolio Management
1.5.1 Sind Kapitalmärkte effizient?
1.5.2 Das aktive Portfolio Management
1.5.3 Das passive Portfolio Management
1.6 Welche Bedeutung hat die Rendite für das Portfolio Management?
1.6.1 Diskrete Rendite
1.6.2 Geometrische Rendite
1.6.3 Kapitalgewichtete Rendite
1.6.4 Stetige Rendite (logarithmische Rendite)
1.7 Welche Bedeutung hat das Risiko für das Portfolio Management?
1.7.1 Der Risikobegriff
1.7.2 Klassifikation der Risikomaße
1.7.3 Die Quantifizierung von Risiken
1.8 Schlussbetrachtung
1.9 Zusammenfassung
1.10 Fragen zu Kapitel 1
1.11 Anlage
Literaturverzeichnis zu Kapitel 1
2 Mathematische Grundlagen im Portfolio Management
2.1 Grundlagen der Matrizenrechnung
2.1.1 Matrizen
2.1.2 Diagonal- und Einheitsmatrix
2.1.3 Vektoren
2.1.4 Transponieren von Matrizen und Vektoren
2.1.5 Addition und Subtraktion von Matrizen und Vektoren
2.1.6 Multiplikation von Matrizen und Vektoren
2.1.7 Inversion von Matrizen und Vektoren
2.2 Matrizenrechnung in Excel
2.2.1 Allgemeine Darstellung in Excel
2.2.2 Transponieren von Vektoren und Matrizen in Excel
2.2.3 Addition und Subtraktion von Matrizen in Excel
2.2.4 Multiplikation eines Skalars mit einer Matrix in Excel
2.2.5 Multiplikation von Matrizen und Vektoren in Excel
2.2.6 Inversion und Einheitsmatrix in Excel
2.3 Grundlagen der mathematischen Optimierung
2.3.1 Die Ziele des Operations Research und der Portfoliotheorie
2.3.2 Grundlagen der Entscheidungstheorie
2.3.3 Klassifikation der Optimierungsprobleme
2.3.4 Übersicht über die Teilgebiete der Optimierung und des Operations Research
2.3.5 Lineare Optimierungsprobleme
2.3.6 Nicht-lineare Optimierungsprobleme
2.3.7 Optimierungsprobleme unter Unsicherheit
2.4 Einführung in den Excel Solver
2.4.1 Installation des Solvers
2.4.2 Aufruf und Anwendung des Solvers
2.5 Stochastische Prozesse im Portfolio Management
2.5.1 Geschichtlicher Hintergrund
2.5.2 Stochastische Prozesse
2.5.3 Überleitung vom diskreten Random Walk zum stetigen Wiener-Prozess
2.5.4 Der allgemeine Wiener-Prozess
2.5.5 Der Wiener-Prozess für Aktienkurse und im Portfoliomanagement
2.5.6 Die Integration lognormalverteilter Aktienkurse in das Modell
2.5.7 Die Monte-Carlo-Simulation
2.5.8 Die Modellierung stochastischer Prozesse in Excel
2.6 Schlussbetrachtung
2.7 Zusammenfassung
2.8 Fragen zu Kapitel 2
Literaturverzeichnis zu Kapitel 2
3 Grundlagen der modernen Portfoliotheorie
3.1 Die Grundlagen der modernen Portfoliotheorie
3.1.1 Die Annahmen der modernen Portfoliotheorie
3.1.2 Die Bestimmung des Portfoliorisikos im Zwei-Anlagen-Fall
3.1.3 Der Diversifikationseffekt und die Effizienzkurve
3.2 Die Bestimmung von effizienten Portfolios im N-Anlagen-Fall
3.3 Die Auswahl eines optimalen Portfolios
3.3.1 Der „rationale“ Investor
3.3.2 Nutzenfunktionen und Indifferenzkurven
3.3.3 Auswahl eines optimalen Portfolios
3.4 Die Kapitalmarktlinie und die Auswahl eines Portfolios
3.5 Die Wertpapierlinie und das Kapitalmarktgleichgewicht
3.6 Das Capital Asset Pricing Model
3.6.1 Annahmen
3.6.2 Das grundlegende Konzept
3.6.3 Empirische Tests und Kritik
3.7 Modellerweiterungen des CAPM
3.7.1 Das Single-Index-Modell
3.7.2 Systematisches und unsystematisches Risiko
3.7.3 Das Multi-Index-Modell
3.8 Schlussbetrachtung
3.9 Zusammenfassung
3.10 Fragen zu Kapitel 3
Literaturverzeichnis zu Kapitel 3
4 Die Anwendung des aktiven Portfolio Managements
4.1 Die absolute Optimierung im aktiven Portfolio Management
4.1.1 Ermittlung des Minimum-Varianz-Portfolios
4.1.2 Ermittlung des Maximum-Ertrags-Portfolios
4.1.3 Bestimmung eines beliebig effizienten Portfolios
4.1.4 Ermittlung des Tangentialportfolios
4.2 Die relative Optimierung im aktiven Portfolio Management
4.2.1 Bestandteile der relativen Optimierung
4.2.2 Bestimmung der Alpha- und Beta-Faktoren
4.2.3 Aktive Position, aktives Risiko und aktiver Beta-Faktor
4.2.4 Kennzahlen des aktiven Portfolio Managements
4.3 Die Umsetzung der absoluten Portfolio-Optimierung
4.3.1 Vorstellung des Ausgangsportfolios für die absolute Optimierung
4.3.2 Die praktische Umsetzung in Excel
4.3.3 Die praktische Umsetzung in Matlab
4.4 Die Umsetzung der relativen Portfolio-Optimierung
4.4.1 Vorstellung des Ausgangsportfolios für die relative Optimierung
4.4.2 Die praktische Umsetzung in Excel
4.4.3 Die praktische Umsetzung in Matlab
4.5 Schlussbetrachtung
4.6 Zusammenfassung
4.7 Fragen zu Kapitel 4
Literaturverzeichnis zu Kapitel 4
5 Anwendung des passiven Portfolio Managements
5.1 Einführung
5.2 Index Tracking und relative Optimierung
5.3 Index Tracking nach Markowitz
5.4 Index Tracking mit Hilfe von Regression
5.5 Index Tracking auf Grundlage der linearen Optimierung
5.6 Praktische Umsetzung in Excel
5.6.1 Index Tracking und relative Optimierung
5.6.2 Index Tracking nach Markowitz
5.6.3 Index Tracking auf Grundlage der Regression unter Nebenbedingungen
5.6.4 Index Tracking und lineare Optimierung
5.7 Praktische Umsetzung in Matlab
5.8 Schlussbetrachtung
5.9 Zusammenfassung
5.10 Fragen zu Kapitel 5
Literaturverzeichnis zu Kapitel 5
6 Verfahren der robusten Portfolio-Optimierung
6.1 Grundlegende Problematik der klassischen Optimierung
6.1.1 Auswirkungen des Schätzfehlers auf die Zusammensetzung von Portfolios
6.1.2 Die einzelnen Komponenten des Schätzfehlers und deren Auswirkungen
6.1.3 Größe der Schätzfehler für die verschiedenen Parameter
6.2 Übersicht über die Modelle und Methoden der robusten Optimierung
6.3 Modifikation der Input-Parameter
6.3.1 Robuste Schätzer
6.3.2 Geschrumpfte Schätzer
6.4 Modifikation des Modells
6.4.1 Der Ansatz nach Black-Litterman
6.4.2 Der Ansatz des Resamplings
6.5 Schlussbetrachtung
6.6 Zusammenfassung
6.7 Fragen zu Kapitel 6
Literaturverzeichnis zu Kapitel 6
7 Performance-Messung
7.1 Der Performance-Begriff
7.2 Absolute Performancemaße
7.2.1 Diskrete Renditen
7.2.2 Stetige Renditen
7.2.3 Arithmetische Rendite
7.2.4 Geometrische Rendite
7.2.5 Geldgewichtete Renditen
7.2.6 Varianz und Standardabweichung
7.2.7 Volatilität
7.3 Relative Performancemaße
7.3.1 Aktive Performancemaße
7.3.2 Passive Performancemaße
7.4 Schlussbetrachtung
7.5 Fragen zu Kapitel 7
Literaturverzeichnis zu Kapitel 7
Stichwortverzeichnis

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