Applications of state space models in finance
Applications of state space models in finance
Applications of state space models in finance
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x Contents<br />
6.2.3.2 The mean revert<strong>in</strong>g model . . . . . . . . . . . . . . . . 96<br />
6.2.3.3 The mov<strong>in</strong>g mean revert<strong>in</strong>g model . . . . . . . . . . . . 100<br />
6.2.3.4 The generalized random walk model . . . . . . . . . . . 100<br />
6.2.4 Markov switch<strong>in</strong>g based approaches . . . . . . . . . . . . . . . . 105<br />
6.3 Analysis <strong>of</strong> empirical results . . . . . . . . . . . . . . . . . . . . . . . . . 110<br />
6.3.1 Comparison <strong>of</strong> conditional beta estimates . . . . . . . . . . . . . 110<br />
6.3.2 In-sample forecast<strong>in</strong>g accuracy . . . . . . . . . . . . . . . . . . . 112<br />
6.3.3 Out-<strong>of</strong>-sample forecast<strong>in</strong>g accuracy . . . . . . . . . . . . . . . . . 115<br />
6.3.3.1 Step I: Out-<strong>of</strong>-sample period <strong>of</strong> 100 weeks to compare<br />
all conditional model<strong>in</strong>g techniques . . . . . . . . . . . 116<br />
6.3.3.2 Step II: Out-<strong>of</strong>-sample period <strong>of</strong> ten years to identify the<br />
overall best model<strong>in</strong>g approach . . . . . . . . . . . . . . 119<br />
6.4 Conclud<strong>in</strong>g remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119<br />
7 A Kalman filter based conditional multifactor pric<strong>in</strong>g model 123<br />
7.1 Factor model<strong>in</strong>g . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124<br />
7.1.1 Factor taxonomy . . . . . . . . . . . . . . . . . . . . . . . . . . . 126<br />
7.1.1.1 Macroeconomic factors . . . . . . . . . . . . . . . . . . 126<br />
7.1.1.2 Fundamental factors . . . . . . . . . . . . . . . . . . . . 127<br />
7.1.1.3 Momentum and reversal . . . . . . . . . . . . . . . . . . 128<br />
7.1.1.4 Statistical factors . . . . . . . . . . . . . . . . . . . . . 128<br />
7.1.2 Number <strong>of</strong> factors . . . . . . . . . . . . . . . . . . . . . . . . . . 128<br />
7.1.3 Time-vary<strong>in</strong>g factor load<strong>in</strong>gs . . . . . . . . . . . . . . . . . . . . 129<br />
7.2 Specification <strong>of</strong> a conditional multifactor risk model . . . . . . . . . . . 130<br />
7.2.1 Time series representation . . . . . . . . . . . . . . . . . . . . . . 130<br />
7.2.2 Cross-sectional regressions . . . . . . . . . . . . . . . . . . . . . . 131<br />
7.2.2.1 The Fama-MacBeth approach . . . . . . . . . . . . . . 131<br />
7.2.2.2 Econometric issues . . . . . . . . . . . . . . . . . . . . . 132<br />
7.3 The risk factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132<br />
7.3.1 Macroeconomic risk variables . . . . . . . . . . . . . . . . . . . . 134<br />
7.3.1.1 European term structure . . . . . . . . . . . . . . . . . 134<br />
7.3.1.2 Oil price . . . . . . . . . . . . . . . . . . . . . . . . . . 134<br />
7.3.1.3 Dollar . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134<br />
7.3.2 Fundamental risk variables . . . . . . . . . . . . . . . . . . . . . 135<br />
7.3.2.1 Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135<br />
7.3.2.2 Value-growth-spread . . . . . . . . . . . . . . . . . . . . 135<br />
7.3.3 The market factor . . . . . . . . . . . . . . . . . . . . . . . . . . 136<br />
7.3.4 Summary statistics . . . . . . . . . . . . . . . . . . . . . . . . . . 137<br />
7.4 Empirical results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139<br />
7.4.1 Estimation <strong>of</strong> factor load<strong>in</strong>gs . . . . . . . . . . . . . . . . . . . . 142<br />
7.4.2 Out-<strong>of</strong>-sample forecast<strong>in</strong>g performance . . . . . . . . . . . . . . . 146<br />
7.4.3 Practical relevance <strong>of</strong> time-variation <strong>in</strong> factor load<strong>in</strong>gs . . . . . . 147<br />
7.4.3.1 Risk pric<strong>in</strong>g . . . . . . . . . . . . . . . . . . . . . . . . 147<br />
7.4.3.2 Portfolio management perspective . . . . . . . . . . . . 150