Applications of state space models in finance

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Chapter 7 A Kalman filter based conditional multifactor pricing model Factor pricing models relate the risk of a portfolio to a possibly multidimensional set of common factors. They are widely employed by academics and investment professionals to analyze risk or to derive return predictions. The quality of a factor model depends on the selection of risk factors and on the estimated factor sensitivities. Using a Kalman filter based conditional multifactor pricing model, this chapter aims at analyzing the time-varying impact of fundamentals and macroeconomics on pan-European industry portfolios. Commercial portfolio risk models, such as BARRA (www.barra.com) or Citigroup’s macro-based European Risk Attribute Model (Brennan et al. 2000), are usually based on single stock returns. They account for potential time-variation in factor sensitivities by assigning more weight to the most recent observations. The conditional modeling approach employed in this chapter is different in both aspects: (i) sectors instead of single stocks are used as dependent variables, and (ii) time-varying factor sensitivities are modeled explicitly as individual stochastic processes. A major advantage of building a factor model on sectors is the reduction of a potential errors-in-variables problem, which typically arises whenever independent variables, such as factor sensitivities in a cross-sectional setting, are measured with error. The proposed conditional multifactor pricing model can be applied to analyze current portfolio risks at the sector-level, to construct sector portfolios and to evaluate the past performance of an implemented sector strategy. Given the results of the available literature on multifactor pricing models and the demonstrated significant relationship between macroeconomics, fundamentals and equity returns, this chapter focuses on the time-variation in macroeconomic and fundamental factor loadings of pan-European sectors. In the previous chapter, the ability of various modeling techniques to model the time-varying behavior of betas have been compared. As the results suggest that the stochastic process of systematic risk can be best described and predicted by a random walk process estimated via the Kalman filter, the same modeling technique is employed here. This is in contrast to the literature where conditional sensitivities are commonly captured either by allowing for an interaction term, by selecting different factors at different times, or by employing a discrete regime-
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Sascha Mergner Applications of Stat
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erschienen im Universitätsverlag G
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Bibliographische Information der De
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Contents List of figures . . . . .
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Contents ix 4.5 Model selection and
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Contents xi 7.5 Concluding remarks
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xiv List of figures 6.14 Histograms
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Notation and conventions The outlin
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xx Used abbreviations and symbols L
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xxii Used abbreviations and symbols
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xxiv Used abbreviations and symbols
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Preface The work on this book began
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Chapter 1 Introduction “Economist
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1.2 Research objectives 3 1.2 Resea
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1.3 Organization of the thesis 5 to
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8 2 Some stylized facts of weekly s
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10 2 Some stylized facts of weekly
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18 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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Page 116 and 117: 84 6 Time-varying market beta risk
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Page 188 and 189: 156 Conclusion and outlook conditio
Page 190 and 191: 158 Conclusion and outlook conduct
Page 192 and 193: 160 Appendix A A.2 The consumption-
Page 194 and 195: 162 Appendix A The APT, introduced
Page 196 and 197: 164 Appendix B β t β t β t 2.0 1
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172 Appendix B β t β t β t 2.0 1
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174 Appendix B β t β t β t 1.2 1
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176 Appendix B cumulative return (%
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178 Appendix C Table C.1: Compariso
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180 Appendix C Table C.2: In-sample
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182 Appendix C Table C.4: Out-of-sa
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184 Appendix C Table C.6: Out-of-sa
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186 Appendix C Table C.7 — contin
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188 Appendix C Table C.7 — contin
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190 Appendix C Table C.9: Fama-MacB
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192 References Baum, L. E. and T. P
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194 References de Jong, P. (1991).
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196 References Giannopoulos, K. (19
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198 References Keim, D. B. and R. F
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200 References Pagan, A. R. (1996).
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202 References Wells, C. (1994). Va
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Applications of state space models in finance

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