Applications of state space models in finance

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4 1 Introduction missing. Chapter 6 aims to close this gap by investigating the time-varying behavior of systematic risk for eighteen pan-European sectors, also referred to as industry portfolios. Using weekly data over the period 1987–2005, time-variation in beta is modeled by a bivariate t-GARCH(1,1) model, a bivariate stochastic volatility model estimated via efficient Monte Carlo likelihood, four Kalman filter based approaches as well as two Markov switching models. The main purpose of the chapter is to compare the performance of these modeling techniques including non-standard procedures such as Markov switching and stochastic volatility. Overall, the respective ex-ante forecast performances of the various modeling approaches indicate that the random walk process combined with the Kalman filter is the most accurate in describing and forecasting the time-varying behavior of sector betas in a European context. The analysis of the dynamics in the relationship between financial variables represents an exciting area of research, motivated by both economic arguments and empirical findings. However, it is not yet clear to what degree the modeling of change is relevant in practice. The third contribution of this thesis is an empirical analysis of the practical relevance of taking time-variation in factor loadings explicitly into account. A multifactor pricing framework that relates pan-European industry portfolios to systematic macroeconomic and fundamental risks is considered. Chapter 7 focuses on the question whether an explicit consideration of the changing importance of macroeconomics and fundamentals on European sectors can be exploited in a profitable way, either from a risk management or from a portfolio management perspective. The selection of common factors is based on the latest findings of the anomalies literature. Covering an out-of-sample period of ten years, the proposed conditional multifactor pricing model employs a market factor, three macroeconomic factors and two fundamental factors, which are motivated by the well-known three-factor model by Fama and French (1993). The stochastic process of conditional betas is modeled as individual random walks. Estimation of the model over time using the Kalman filter yields series of estimated conditional factor loadings. These are used as explanatory variables in a cross-sectional regression approach that follows Fama and MacBeth (1973). Traditionally, the Fama-MacBeth approach utilizes constant coefficients as instruments. In order to get an indication of the importance of conditional betas for the pricing of risk, in this thesis a modified formulation with time-varying sensitivities as instruments is employed. The question whether employing conditional factor loadings to derive return forecasts leads to more profitable portfolios is examined based on a series of backtests. The main results of this chapter indicate that time-varying betas carry implications for the prediction of returns, and less so for the analysis of risk. 1.3 Organization of the thesis This thesis deals with the modeling of change in the context of widely used concepts in finance. To link the theoretical and practical parts, Chapter 2 introduces the set of sector return series and reviews their major empirical properties. The stylized facts reveal that the paradigm of stable sensitivities has to be questioned. This motivates the use of more advanced time series concepts to analyze the time-varying importance attached
1.3 Organization of the thesis 5 to common systematic risks for pan-European industry portfolios. The stylized facts serve as a guide toward selecting the modeling techniques to be employed in the course of this thesis. Chapter 3 gives a general treatment of the class of linear Gaussian state space models and introduces the Kalman filter and smoother. Chapter 4 introduces the theoretical conception of Markov regime switching, in which the hidden dynamics are modeled as being discrete. Both modeling approaches, Kalman filtering and Markov switching, are employed to model changing coefficients directly. Chapter 5 reviews the two most important concepts of capturing conditional heteroskedasticity, which are used to derive indirect estimates of conditional betas: ARCH and stochastic volatility. Various simulation-based procedures to estimate the latter are discussed. Chapter 6 applies the selected time series concepts to model and forecast time-varying market betas for pan-European industry portfolios. Chapter 7 analyzes the practical relevance of explicitly considering conditionality in factor loadings by applying the Kalman filter to a multifactor pricing model with macroeconomic and fundamental variables. The chapter introduces a synthesis of the classical Fama-MacBeth approach with time-varying betas and conducts a series of backtests on which the evaluation is based. Chapter 8 summarizes the main results and offers suggestions for future research.
Page 1: Sascha Mergner Applications of Stat
Page 4 and 5: erschienen im Universitätsverlag G
Page 6 and 7: Bibliographische Information der De
Page 9 and 10: Contents List of figures . . . . .
Page 11 and 12: Contents ix 4.5 Model selection and
Page 13: Contents xi 7.5 Concluding remarks
Page 16 and 17: xiv List of figures 6.14 Histograms
Page 19: Notation and conventions The outlin
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Page 29: Preface The work on this book began
Page 33 and 34: Chapter 1 Introduction “Economist
Page 35: 1.2 Research objectives 3 1.2 Resea
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Page 77 and 78: 4.1 Basic concepts 45 R t (%) 20 10
Page 79 and 80: 4.1 Basic concepts 47 probability d
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4.4 Forecasting and decoding 55 mod
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Chapter 5 Conditional heteroskedast
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5.1 Autoregressive conditional hete
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5.2 Stochastic volatility 65 or the
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5.2 Stochastic volatility 67 5.2.1.
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5.2 Stochastic volatility 69 likeli
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5.2 Stochastic volatility 71 linear
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5.2 Stochastic volatility 73 3. An
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5.3 Multivariate conditional hetero
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84 6 Time-varying market beta risk
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Chapter 7 A Kalman filter based con
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7.1 Factor modeling 125 uncondition
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7.1 Factor modeling 127 predictabil
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7.1 Factor modeling 129 usefulness,
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7.2 Specification of a conditional
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7.3 The risk factors 133 Table 7.1:
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7.3 The risk factors 135 introduced
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7.3 The risk factors 137 auxiliary
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7.4 Empirical results 139 Table 7.4
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7.4 Empirical results 141 are consi
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7.4 Empirical results 145 β TS 0.4
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7.4 Empirical results 153 cumulativ
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Chapter 8 Conclusion and outlook Th
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Conclusion and outlook 157 cannot o
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Appendix A Brief review of asset pr
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A.3 Alternative asset pricing model
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Appendix B Figures
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Figures 165 β t β t β t 2.0 1.5
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Appendix C Tables
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Tables 179 Table C.1 — continued
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Tables 181 Table C.3: In-sample mea
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Tables 183 Table C.5: Out-of-sample
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Tables 185 Table C.7: Parameter est
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Tables 187 Table C.7 — continued
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Tables 189 Table C.8: Out-of-sample
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References Abell, J. D. and T. M. K
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References 193 Bulla, J. (2006). Ap
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References 195 Fabozzi, F. J. and J
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References 197 Harvey, A. C., E. Ru
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References 199 Lie, F., R. Brooks,
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References 201 Shephard, N. (1993).
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State space models play a key role
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Applications of state space models in finance

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