Applications of state space models in finance

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x Contents 6.2.3.2 The mean reverting model . . . . . . . . . . . . . . . . 96 6.2.3.3 The moving mean reverting model . . . . . . . . . . . . 100 6.2.3.4 The generalized random walk model . . . . . . . . . . . 100 6.2.4 Markov switching based approaches . . . . . . . . . . . . . . . . 105 6.3 Analysis of empirical results . . . . . . . . . . . . . . . . . . . . . . . . . 110 6.3.1 Comparison of conditional beta estimates . . . . . . . . . . . . . 110 6.3.2 In-sample forecasting accuracy . . . . . . . . . . . . . . . . . . . 112 6.3.3 Out-of-sample forecasting accuracy . . . . . . . . . . . . . . . . . 115 6.3.3.1 Step I: Out-of-sample period of 100 weeks to compare all conditional modeling techniques . . . . . . . . . . . 116 6.3.3.2 Step II: Out-of-sample period of ten years to identify the overall best modeling approach . . . . . . . . . . . . . . 119 6.4 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 7 A Kalman filter based conditional multifactor pricing model 123 7.1 Factor modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 7.1.1 Factor taxonomy . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 7.1.1.1 Macroeconomic factors . . . . . . . . . . . . . . . . . . 126 7.1.1.2 Fundamental factors . . . . . . . . . . . . . . . . . . . . 127 7.1.1.3 Momentum and reversal . . . . . . . . . . . . . . . . . . 128 7.1.1.4 Statistical factors . . . . . . . . . . . . . . . . . . . . . 128 7.1.2 Number of factors . . . . . . . . . . . . . . . . . . . . . . . . . . 128 7.1.3 Time-varying factor loadings . . . . . . . . . . . . . . . . . . . . 129 7.2 Specification of a conditional multifactor risk model . . . . . . . . . . . 130 7.2.1 Time series representation . . . . . . . . . . . . . . . . . . . . . . 130 7.2.2 Cross-sectional regressions . . . . . . . . . . . . . . . . . . . . . . 131 7.2.2.1 The Fama-MacBeth approach . . . . . . . . . . . . . . 131 7.2.2.2 Econometric issues . . . . . . . . . . . . . . . . . . . . . 132 7.3 The risk factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 7.3.1 Macroeconomic risk variables . . . . . . . . . . . . . . . . . . . . 134 7.3.1.1 European term structure . . . . . . . . . . . . . . . . . 134 7.3.1.2 Oil price . . . . . . . . . . . . . . . . . . . . . . . . . . 134 7.3.1.3 Dollar . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 7.3.2 Fundamental risk variables . . . . . . . . . . . . . . . . . . . . . 135 7.3.2.1 Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 7.3.2.2 Value-growth-spread . . . . . . . . . . . . . . . . . . . . 135 7.3.3 The market factor . . . . . . . . . . . . . . . . . . . . . . . . . . 136 7.3.4 Summary statistics . . . . . . . . . . . . . . . . . . . . . . . . . . 137 7.4 Empirical results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 7.4.1 Estimation of factor loadings . . . . . . . . . . . . . . . . . . . . 142 7.4.2 Out-of-sample forecasting performance . . . . . . . . . . . . . . . 146 7.4.3 Practical relevance of time-variation in factor loadings . . . . . . 147 7.4.3.1 Risk pricing . . . . . . . . . . . . . . . . . . . . . . . . 147 7.4.3.2 Portfolio management perspective . . . . . . . . . . . . 150
Contents xi 7.5 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 8 Conclusion and outlook 155 A A brief review of asset pricing theory 159 A.1 The discount factor view of asset pricing . . . . . . . . . . . . . . . . . . 159 A.2 The consumption-based model . . . . . . . . . . . . . . . . . . . . . . . 160 A.3 Alternative asset pricing models . . . . . . . . . . . . . . . . . . . . . . . 160 B Figures 163 C Tables 177 References 191
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: Contents ix 4.5 Model selection and
Page 16 and 17: xiv List of figures 6.14 Histograms
Page 19: Notation and conventions The outlin
Page 22 and 23: xx Used abbreviations and symbols L
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Page 29: Preface The work on this book began
Page 33 and 34: Chapter 1 Introduction “Economist
Page 35 and 36: 1.2 Research objectives 3 1.2 Resea
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Page 40 and 41: 8 2 Some stylized facts of weekly s
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30 3 Linear Gaussian state space mo
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Chapter 4 Markov regime switching M
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4.1 Basic concepts 45 R t (%) 20 10
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4.1 Basic concepts 47 probability d
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4.3 Parameter estimation 49 X 1 X 2
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4.3 Parameter estimation 51 4.3.2.1
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4.4 Forecasting and decoding 53 4.4
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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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