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

Pan, Jiening (2015)

Permanent URL: https://etd.library.emory.edu/concern/etds/wm117p22r?locale=en
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Abstract

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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