Sustainable Asset Accumulation and Dynamic Portfolio Decisions (eBook)

Preface 6
Acknowledgements 8
Contents 10
List of Figures 14
List of Tables 18
1 Introduction 20
1.1 Institutions, Models and Empirics 21
1.2 Dynamic Programming as Solution Method 23
1.3 Previous Work 24
1.4 Outline and Results 26
2 Forecasting and Low Frequency Movements of Asset Returns 28
2.1 Introduction 28
2.2 Limits on Forecasting Asset Returns 28
2.3 The Use of Periodic Returns 33
2.4 Conclusions 36
3 Portfolio Modeling with Sustainability Constraints 37
3.1 Introduction 37
3.2 Mean-Variance Portfolio Models 39
3.3 Description of Statistical Properties of Returns Data 45
3.3.1 Computing Expected Real Returns on Risky Assets 45
3.3.2 Variance-Covariance and Correlation Matrices and Volatility of Real Returns 48
3.3.3 Eigenvalue and Eigenvector Properties of the Empirical Covariance and Correlation Matrix 51
3.4 Estimation Results of the Portfolio Models 55
3.5 Conclusion 65
Appendix 66
Forecasting the Monthly Consumer Price Inflation 66
Capital Allocation Line and Efficient Frontiers 68
4 Dynamic Saving and Portfolio Decisions-Theory 70
4.1 Introduction 70
4.2 The Model with One Asset and Constant Returns 70
4.2.1 Numerical Results for the Benchmark Model 72
4.2.2 Variation of Risk Aversion, Returns and Discount Rate 74
4.3 Dynamic Consumption and Portfolio Decisions: Two Assets and Time Varying Returns 78
4.3.1 The Model with Time Varying Returns 79
4.3.2 Numerical Results on a Benchmark Case 81
4.3.3 Variation of Risk Aversion 83
4.3.4 Variation of Returns 84
4.3.5 Variation of Time Horizon 86
4.4 A Stochastic Model with Mean Reversion in Returns 90
4.5 Conclusions 93
Appendix 94
The Solution to the Dynamic Decision Problem with One Asset 94
5 Asset Accumulation with Estimated Low Frequency Movements of Asset Returns 97
5.1 Introduction 97
5.2 The Literature and Results 98
5.3 The Dynamic Programming Solution 101
5.4 Varying Risk Aversion Across Investors 102
5.5 Varying Time Horizon Across Investors 106
5.6 Some Conclusions 111
6 Asset Accumulation and Portfolio Decisions with Time Varying Asset Returns and Labor Income 113
6.1 Introduction 113
6.2 Literature and Results 116
6.3 Business Cycles, Asset Returns and Labor Income 119
6.4 Dynamic Decisions on Asset Accumulation 122
6.5 Wealth Disparities 128
6.6 Conclusions 129
7 Continuous and Discrete Time Modeling 131
7.1 Introduction 131
7.2 Literature and Results 132
7.3 Discrete-Time Approximation 135
7.3.1 Euler Method 135
7.3.2 Milstein Method 136
7.3.3 New Local Linearization Method 136
7.3.4 Equivalence of the Euler and NLL Predictors 137
7.4 Empirical Results on Modeling Short Term Interest Rates 138
7.4.1 Specification Test 139
7.4.1.1 Autocorrelation Checking 139
7.4.1.2 Testing Normality 140
7.4.2 Results of Estimating CKLS Model 140
7.5 Searching for New Models 142
7.5.1 Improvement in the Continuous-Time Framework 142
7.5.2 Modeling Autocorrelations in the Estimated Noise 143
7.5.3 Modeling Thick-Tails in the Estimated Noise 145
7.5.4 Model Identification 145
7.5.5 Results 146
7.6 Conclusions 149
Appendix 150
Tables: Estimation Results 150
The Likelihood Function of the Milstein Approximation 152
8 Asset Accumulation and Portfolio Decisions Under Inflation Risk 154
8.1 Introduction 154
8.2 A New Multi-factor Model for Nominal and Inflation-Indexed Bonds 157
8.2.1 The Factors 157
8.2.2 The Nominal Bonds 158
8.2.3 The Inflation Indexed Bonds (IIB) 159
8.2.4 The No-Arbitrage Pricing 160
8.3 Intertemporal Asset Accumulation with Inflation Risk 163
8.3.1 The Intertemporal Asset Allocation Model 163
8.3.2 The Systematic Factors 164
8.3.3 The Investment Opportunity Set 164
8.3.4 Agents' Action 165
8.3.5 Dynamic Programming Approach 166
8.3.6 Solving for the Intertemporal Portfolio 170
8.4 Model Estimation 172
8.4.1 The Term Structure of Real Yields 172
8.4.2 The Term Structure of Nominal Yields 175
8.4.3 Estimation of Realized Inflation Dynamics 179
8.4.4 Estimation of Stock Return Dynamics 181
8.5 Application of Intertemporal Optimal Portfolios 182
8.5.1 Example 1: Expected Optimal Final Utility and the Factors 182
8.5.2 Example 2: Asset Allocation and Risk Aversion Parameter ? 184
8.5.3 Example 3: Asset Allocation and Investment Horizon 186
8.6 Conclusions 187
Appendix 188
9 Concluding Remarks 193
Appendix A: Dynamic Programming as Solution Method 195
Bibliography 197