Essays on Non-linearities in Stock and Bond Returns: A Density-Based Approach Open Access

Pan, Jiening (2015)

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The dissertation consists of three essays that revolve around non-linearities embedded in asset returns. In the first essay "The Role of Slope Heterogeneity in Bond Excess Returns Predictability", I investigates bond excess return forecastability using current forward rates. The dynamics of excess return are modeled non-parametrically. Estimation shows heterogeneous slopes for independent variables, indicating the existence of non-linearity. Empirically, I find this non-linearity plays an important role in excess return prediction both in- and out-of-sample. By including non-linearity in the model, the in-sample R2 jumps to as high as 91%. Meanwhilelagged forward rates are no longer statistically significant, in contrast to the results documented in previous research. The out-of-sample forecasts also favor the non-parametric model. Findings in this paper suggest a potential important information source embedded in the current forward rates cross-section. Information associated with non-linearity is largely ignored in the existing literature as it is averaged out by linear model settings. The second essay "Do Non-Linearities Matter in the Yield Curve?" tries to answer the question that do non-yield variables contain information beyond what is contained in the yield curve? Using a non-linear factor extracted from the yield curve, I find nonyield factors, which are constructed from a large panel of macro-finance data, are no longer significant in predicting future bond excess returns both in- and out-of-sample. Moreover, my non-linear factor generates countercyclical and business cycle frequency bond risk premia. The findings underscore the importance of non-linearities embedded in the term structure, suggesting a fully spanned term structure model with non-linear state factors may be capable of matching features observed in the data. In the third essay "A Test on Asymmetric Dependence" (joint with Prof. Maasoumi, Lei Jiang and Ke Wu), we provide a model-free test for asymmetric dependence between stock and market returns, based on the Kullback-Leibler mutual information measure. Our test has greater power in small samples than previous tests of asymmetric correlation proposed by Hong, Tu and Zhou (2007). Empirically, we find that asymmetric dependence is a prevailing phenomenon in most commonly used portfolios.

Table of Contents

Preface 1

1 The role of slope heterogeneity in bond excess return predictability 10

I Introduction 11

II Econometric framework 13

II.1 Notation 13

II.2 The model 14

II.3 Test joint signicance of predictors 15

III Excess return forecasts 17

III.1 In-sample analysis: current forward rates only 17

III.2 In-sample analysis: with lagged variables 19

III.3 Summary and implications 20

IV Out-of-sample prediction 20

V Concluding remarks 23

1.A Appendix: Local constant estimator 25

1.B Appendix: Bootstrap algorithm and decision rule 26

1.C Appendix: Diebold and Mariano (D-M) test 28

2 Do non-linearities matter in the yield curve? 39

I Introduction 40

II The factors 43

II.1 Factors from the yield curve 43

II.2 The non-yield factors b Ft 46

II.3 The econometric model 46

III Empirical results 47

III.1 Data 47

III.2 In-sample analysis: NPt only 48

III.3 In-sample analysis: non-yield factors 49

III.4 Out-of-sample results 50

III.5 Implications of the ndings 53

IV Risk premia decomposition 53

V Concluding remarks 58

3 A Test on Asymmetric Dependence 72

I Introduction 73

II A Relative Entropy Based Test on Asymmetric Dependence 75

II.1 A relative entropy based measure of exceedance dependence 75

II.2 The non-parametric estimator 78

II.3 Test statistic and its sampling distribution 79

II.4 Asymmetric Dependence vs. Asymmetry in Distribution 81

III Simulation results 82

III.1 Simulation setup 82

III.2 Asymptotic size 84

III.3 Finite sample performance 85

III.4 Robustness of results 87

IV Asymmetric dependence in stock returns 89

IV.1 Data 89

IV.2 Empirical results 89

V Conclusion 90

3.A Appendix: Proofs 92

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