Introduction (Władysław Milo, Piotr Wdowiński and Grzegorz
Szafrański) ..................................................... 7
Part One: Modelling Stock Markets
1 Testing the Arbitrage Pricing Model with a Factor GARCH
Model for the Polish Stock Market (Piotr Fiszeder) .......... 11
1.1 Introduction ........................................... 11
1.2 Specification of the APT Model with the Factor GARCH
Covariance Structure ................................... 12
1.3 Test of the APT Model with the Factor GARCH Model for
the Polish Stock Market ................................ 15
1.4 Economic Interpretation of Factors ..................... 20
1.5 Conclusions ............................................ 22
References .................................................. 23
2 The Profitability of Simple Trading Strategies Exploiting
the Forward Premium Bias in Foreign Exchange Markets and
the Time Premium in Yield Curves (Andres Vesilind) .......... 25
2.1 Introduction ........................................... 25
2.2 Theoretical Overview of the Structural Risk Premiums
in the Foreign Exchange and Fixed Income Markets ....... 27
2.2.1 Forward Premium Bias in the Foreign Exchange
Markets ......................................... 27
2.2.2 Structural Time Premium in Interest Rate
Markets ......................................... 29
2.3 Empirical Estimation of Active Investment Models ....... 30
2.3.1 Overview of Data, Methodology and Investment
Framework ....................................... 30
2.3.2 Models Exploiting the Forward Premium Bias in
Foreign Exchange Markets ........................ 32
2.3.2.1 Simple Carry-Based Model of 10 Major
Currencies ............................. 32
2.3.2.2 Adding Risk Factors to Simple Carry-
Based FX Model ......................... 34
2.3.3 Models Exploiting the Time Premium in Interest
Rate Markets .................................... 35
2.3.3.1 Long-Only Positions in Interest Rate
Markets Using Government Bond and
Money Market Futures ................... 35
2.3.3.2 Adding Filters to Long-Only Strategy ... 38
2.3.4 Combining Estimated Models into One Portfolio ... 40
2.4 Conclusions ............................................ 42
References .................................................. 44
3 The Market Ratios on Polish Capital Market - Application
to Portfolio Analysis (Waldemar Tarczyński and Małgorzata
Łuniewska) .................................................. 45
3.1 Introduction ........................................... 45
3.2 Statistical Analysis of Selected Market Ratios ......... 48
3.3 Application of Market Ratios in Portfolio Analysis ..... 52
3.4 Conclusions ............................................ 54
References .................................................. 54
Part Two: Bonds and Term Structure oflnterest Rates
4 Examination of the Term Structure oflnterest Rates in
Poland - Linear and Non-Linear Cointegration Analysis
(Joanna Bruzda, Dorota Górecka and Tomasz Koźliński) ........ 59
4.1 Introduction ........................................... 59
4.2 Methodology ............................................ 62
4.3 Empirical Results ...................................... 67
4.4 Final Conclusion ....................................... 76
References .................................................. 77
5 Utility Function Approach in the Context of Immunization
(Alina Kondratiuk-Janyska and Marek Kaluszka) ............... 79
5.1 Introduction ........................................... 79
5.2 Preliminary Notations and Results ...................... 88
5.3 Main Result ............................................ 81
5.4 Examples ............................................... 85
Appendix .................................................... 89
References .................................................. 90
6 Properties of the Duration Vector in the Polish and German
Bonds' Markets (Agata Kliber) ............................... 93
6.1 Introduction ........................................... 93
6.2 Bond Risk Measures - the Classical Point of View ....... 93
6.2.1 Bond Price and Interest Rate .................... 94
6.2.2 Duration ........................................ 94
6.2.3 Convexity ....................................... 95
6.3 Bond Risk Measures - the Modern Approach ............... 96
6.3.1 Term Structure .................................. 96
6.3.2 Duration Vector ................................. 96
6.4 Empirical Study ........................................ 98
6.4.1 The Data ........................................ 98
6.4.2 Computation of Dependencies Between Duration,
Convexity and Interest Rate Changes ............. 99
6.4.3 Comparison with Mature (German) Market ......... 101
6.4.4 Taking into Account the Inflation Factor ....... 103
6.5 Conclusions ........................................... 105
References ................................................. 106
7 Bond's Duration in Single-Factor Models for Short Rate
(Paweł Kliber) ............................................. 107
7.1 Introduction .......................................... 107
7.2 The Classical Approach ................................ 108
7.3 Short Rate Models ..................................... 109
7.3.1 Vasicek Model .................................. 110
7.3.2 Cox-Ingersoll-Ross (CIR) Model ................. 111
7.3.3 Longstaff Model ................................ 111
7.4 Duration in Short Rate mModels ........................ 112
7.4.1 Affine Term Structure .......................... 112
7.4.2 Term Structure of Longstaff's Type ............. 113
7.5 An Empirical Example .................................. 114
7.6 Conclusions ........................................... 117
References ................................................. 118
8 The Polish Term Structure Versus Its Core Market
Counterparts - A Comparative Analysis (Marcin
Stamirowski) ............................................... 119
8.1 Introduction .......................................... 119
8.2 The Data .............................................. 120
8.3 The Model ............................................. 121
8.4 Empirical Application ................................. 123
8.4.1 Estimation ..................................... 123
8.4.2 Results ........................................ 124
8.4.2.1 Goodness of Fit ....................... 124
8.4.2.2 Risk Factor Estimates ................. 125
8.4.2.3 Statistical Significance of the
Differences in Factor Distributions ... 128
8.5 Conclusions ........................................... 131
References ................................................. 131
Part Three: Investment Funds and Portfolio Selection
9 Pension Funds as a Factor Stimulating Development of the
Capital Market in Poland (Wiesław Dębski) .................. 135
9.1 Introductory Remarks .................................. 135
9.2 General Principles Followed in Operation of the
Pension Funds ......................................... 137
9.2.1 The Open Pension Funds ......................... 138
9.2.2 Employee Pension Programmes .................... 139
9.3 The Investment Policy of the Pension Funds ............ 141
9.4 Influence Exerted by the Pension Funds on
Development of the Capital Market ..................... 144
References ................................................. 147
10 Decomposing Value-at-Risk: The Case of Fund of Funds
Portfolio (Joanna Olbryś) .................................. 149
10.1 Introduction .......................................... 149
10.2 Funds of Funds ........................................ 150
10.3 Value-at-Risk: Some Definitions ....................... 151
10.4 Decomposition of Return-VaR ........................... 152
10.5 Practical Estimation of the Marginal Return - VaR
and the Component Return - VaR ........................ 154
10.6 Empirical Examples .................................... 155
References ................................................. 161
11 An Analysis of Distributions of Rates of Return for
Investment Funds Game (Anna Zamojska) ...................... 163
11.1 Introduction .......................................... 163
11.2 Theoretical Background ................................ 163
11.3 Data and Methodology .................................. 164
11.4 Empirical Results ..................................... 167
11.5 Conclusions ........................................... 173
References ................................................. 173
12 Automatic Trading Agent. RMT Based Portfolio Selection -
Theoretical Aspects (Małgorzata Snarska) ................... 175
12.1 Portfolio Theory - Elementary Definitions and the
Markowitz Model ....................................... 175
12.1.2 Construction of an Efficient Portfolio of
Multiple Assets ................................ 175
12.1.2 Optimization of a Portfolio .................... 177
12.2 Covariance Matrix and Portfolio Construction .......... 177
12.2.1 Gaussian Correlated Variables .................. 178
12.2.2 Covariance Estimator ........................... 178
12.2.3 RMT Based Data Filtering and Denoising
Procedure - the Shrinkage Method ............... 179
12.2.3.1 RMT Predictions for Behaviour of
Eigenvalues ........................... 179
12.2.3.2 Standard Denoising Procedure and the
Shrinkage Method ...................... 180
12.2.3.3 'Signal and Noise' Procedure .......... 181
12.2.4 Covariance Matrix Reconstruction ............... 182
12.3 An Overview of the System ............................. 183
12.4 Warsaw Stock Exchange Simulator and ATA
Implementation Results ................................ 184
12.4.1 Rules of the Game .............................. 184
12.4.2 Data Selection and Analysis .................... 185
12.4.3 Simulation on the Historical Data and Its
Results ........................................ 187
12.5 Conclusions and Future Work ........................... 188
References ................................................. 189
13 Improving Portfolio Efficiency by Including Index
Options. Empirical Examples Using WIG20 Index Options
(Mateusz Knop and Nina Łapińska-Sobczak) ................... 191
13.1 Introduction .......................................... 191
13.2 Construction of an Option-Based Hedge ................. 192
13.3 Empirical Results from Warsaw Stock Exchange .......... 195
References ................................................. 200
Part Four: Applied Financial Modelling
14 Investigation of the Wave Nature of the Ukrainian Stock
Market (Olena Rayevnyeva and Kostyantyn Stryzhychenko) ..... 205
14.1 Introduction .......................................... 205
14.2 Tasks ................................................. 206
14.3 Methodology of the Investigation ...................... 207
14.4 Results ............................................... 212
14.4.1 The Investigation of the PFTS Index Time
Series for the Determination of the
Supporting Tendency ............................ 212
14.4.2 Investigation of the Wave Nature of the Time
Series ......................................... 214
14.4.3 Separation of the Short-term and Long-term
Cycles in the Time Series and Determination
of the Stock Market Stability .................. 217
14.5 Conclusions ........................................... 219
Appendix ................................................... 220
References ................................................. 225
15 One Factor Risk Model and Capital Requirements for Credit
Risk in the New Capital Accord (Adam Frok) ................. 227
15.1 Introduction .......................................... 227
15.2 Asymptotic Single Risk Factor Model ................... 229
15.3 Calibration of the Correlation Parameter .............. 233
15.4 Maturity Adjustment ................................... 235
15.5 Capital Requirements in IRB Approach .................. 236
15.6 Conclusions ........................................... 239
References ................................................. 240
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