Yung Yan Keung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves 144-147). / Chapter Chapter 1: --- Introduction --- p.1 / Chapter 1.1 --- Review on Portfolio Theory --- p.3 / Chapter - 1.1.1 --- Expected Return and Risk of a Security --- p.3 / Chapter -1.1.2 --- Expected Return and Risk of a Portfolio --- p.4 / Chapter -1.1.3 --- The Feasible Set --- p.5 / Chapter - 1.1.4 --- Assumptions on the Investor --- p.6 / Chapter -1.1.5 --- Efficient Portfolios --- p.6 / Chapter -1.1.5.1 --- Bounds on the Return and Risk of a portfolio --- p.6 / Chapter -1.1.5.2 --- Concavity of the Efficient Set --- p.8 / Chapter -1.1.6 --- The Market Model --- p.9 / Chapter -1.1.7 --- Risk-free Asset --- p.11 / Chapter - 1.1.8 --- Portfolio involving Risk-free Asset --- p.12 / Chapter -1.1.9 --- The Sharpe Ratio --- p.14 / Chapter 1.2 --- Review on Some Trading Models --- p.19 / Chapter -1.2.1 --- Buy and Hold Model --- p.19 / Chapter -1.2.2 --- Trading Model with Prediction Criteria --- p.20 / Chapter -1.2.2.1 --- Two School of Theories --- p.20 / Chapter - 1.2.2.2 --- Prediction of the stock price movement --- p.20 / Chapter -1.2.2.3 --- The Use of Neural Network in Prediction --- p.21 / Chapter -1.2.2.4 --- Single Step and Multi-step Prediction --- p.23 / Chapter - 1.2.2.5 --- Trading Model based on Prediction Criteria --- p.25 / Chapter - 1.2.2.6 --- For More Accurate Prediction --- p.25 / Chapter -1.2.3 --- Weigend's Model --- p.26 / Chapter - 1.2.3.1 --- Introduction --- p.26 / Chapter -1.2.3.2 --- The Model Setup --- p.26 / Chapter -1.2.3.3 --- The Objective Functions --- p.27 / Chapter - 1.2.3.4 --- The Gradient Ascending Algorithm --- p.27 / Chapter -1.2.3.5 --- The Gradient of the Sharpe Ratio --- p.27 / Chapter - 1.2.3.6 --- The Training Procedure --- p.28 / Chapter - 1.2.3.7 --- Some Properties of the Sharpe Ratio Training --- p.28 / Chapter -1.2.4 --- Bengio's Model --- p.29 / Chapter -1.2.4.1. --- Overview --- p.29 / Chapter -1.2.4.2. --- The Trading System --- p.29 / Chapter - 1.2.4.3 --- The Objective Function: the Portfolio Return --- p.31 / Chapter - 1.2.4.4. --- The Training Process --- p.32 / Chapter - 1.2.4.5 --- Computer Simulation --- p.34 / Chapter - 1.2.4.6 --- Discussion --- p.36 / Chapter Chapter 2: --- The Naive Sharpe Ratio Model --- p.38 / Chapter - 2.1 --- Introduction --- p.39 / Chapter - 2.2 --- Definition of the Naive Sharpe Ratio --- p.39 / Chapter - 2.3 --- Gradient of Naive Sharpe Ratio with respect to the portfolio weighting: --- p.40 / Chapter - 2.4 --- The Training Process --- p.40 / Chapter - 2.5 --- Analysis of the Gradient --- p.41 / Chapter -2.6 --- Compare with Bengio's and Weigend's Model --- p.42 / Chapter -2.7. --- Computer Simulations --- p.43 / Chapter -2.7.1 --- Experiment 1: How the Sharpe Ratio is Maximized --- p.43 / Chapter -2.7.1.1 --- Experiment 11 --- p.44 / Chapter -2.7.1.2 --- Experiment 12 --- p.45 / Chapter -2.7.1.3 --- Experiment 13 --- p.46 / Chapter -2.7.2 --- Experiment 2: Reducing the Unique Risk --- p.49 / Chapter -2.7.3 --- Experiment 3: Apply to the Stock Market --- p.52 / Chapter -2.8 --- Redefining the Naive Sharpe ratio with down-side risk --- p.56 / Chapter -2.8.1 --- Definitions --- p.56 / Chapter -2.8.2 --- Gradient of the Downside Nai've Sharpe Ratio --- p.57 / Chapter -2.8.3 --- Analysis of the gradient of the new Sharpe ratio --- p.57 / Chapter -2.8.4 --- Experiment: Compared with Symmetric Risk --- p.59 / Chapter -2.8.4.1 --- Experimental Setup --- p.59 / Chapter -2.8.4.2 --- Experimental Result --- p.60 / Chapter -2.8.4.3 --- Discussion --- p.62 / Chapter - 2.9 --- Further Discussion --- p.63 / Chapter Chapter 3: --- The Total Sharpe Ratio Model --- p.64 / Chapter - 3.1 --- Introduction --- p.65 / Chapter -3.2 --- Defining risk of portfolio in terms of component securities' risk --- p.65 / Chapter -3.2.1. --- Return for Each Security and the Whole Portfolio at Each Time Step --- p.65 / Chapter -3.3.2. --- Covariance of the Individual Securities' Returns --- p.66 / Chapter -3.2.3. --- Define the Sharpe Ratio and the Objective Function --- p.66 / Chapter -3.2.3.1. --- The Excess Return --- p.66 / Chapter -3.2.3.2. --- The Risk --- p.67 / Chapter -3.2.3.3. --- The Sharpe Ratio at Time t --- p.67 / Chapter -3.2.3.4. --- The Objective Function: the total Sharpe ratio --- p.67 / Chapter -3.2.3.5. --- The Training Process --- p.68 / Chapter -3.3 --- Calculating the Gradient of the Total Sharpe Ratio --- p.69 / Chapter -3.4. --- Analysis of the Total Sharpe Ratio Gradient --- p.70 / Chapter -3.4.1 --- The Gradient Vector of the Sharpe Ratio at a Particular Time Step --- p.70 / Chapter -3.4.2 --- The Gradient Vector of the Risk --- p.70 / Chapter - 3.5 --- Computer Simulation: --- p.72 / Chapter -3.5.1 --- Apply to the Stock Market1 --- p.72 / Chapter -3.5.1.1 --- Objective --- p.72 / Chapter - 3.5.1.2 --- Experimental Setup --- p.72 / Chapter -3.5.1.3 --- The Experimental Result --- p.73 / Chapter -3.5.2 --- Apply to the Stock Market2 --- p.78 / Chapter -3.5.2.1 --- Objective --- p.78 / Chapter -3.5.2.2 --- Experimental Setup --- p.78 / Chapter -3.5.2.3 --- The Experimental Result --- p.79 / Chapter -3.6 --- Defining the Total Sharpe Ratio in terms of Downside Risk --- p.84 / Chapter - 3.6.1. --- Introduction --- p.84 / Chapter -3.6.2. --- Covariance of the individual securities' returns --- p.84 / Chapter -3.6.3. --- Define the Downside Risk Sharpe ratio and the objective function --- p.85 / Chapter -3.6.3.1. --- The Excess Return --- p.85 / Chapter -3.6.3.2. --- The Downside Risk --- p.85 / Chapter -3.6.3.3. --- The Sharpe ratio at time T --- p.85 / Chapter -3.6.3.4. --- The Objective function --- p.85 / Chapter -3.6.4. --- The Training Process --- p.85 / Chapter -3.7 --- Total Sharpe Ratio involving Transaction Cost --- p.86 / Chapter -3.7.1 --- Introduction --- p.86 / Chapter -3.7.2 --- Return for each stock and the whole portfolio at each time step --- p.86 / Chapter -3.7.3 --- Linear Approximation of the Portfolio's return --- p.88 / Chapter -3.7.4 --- Covariance of the individual securities' returns --- p.89 / Chapter -3.7.5 --- Define the Sharpe ratio and the objective function --- p.90 / Chapter -3.7.5.1 --- The Excess Return --- p.90 / Chapter -3.7.5.2 --- The Risk --- p.90 / Chapter -3.7.5.3 --- The Sharpe Ratio at time T --- p.90 / Chapter -3.7.5.4 --- The Objective Function --- p.90 / Chapter -3.7.6 --- Calculation of the gradient of the Total Sharpe ratio --- p.91 / Chapter -3.7.7. --- Analysis of the Total Sharpe Ratio Gradient --- p.94 / Chapter -3.7.7.1 --- The Gradient Vector of the Sharpe Ratio at a Particular Time Step --- p.94 / Chapter -3.7.7.2 --- The Gradient Vector of the Risk --- p.94 / Chapter -3.7.8 --- Experiment 1: Compare with Buy and Hold Method --- p.96 / Chapter -3.7.8.1 --- Experiment 11 --- p.96 / Chapter -3.7.8.2. --- Experiment 12 --- p.102 / Chapter -3.7.9 --- Experiment 2: Compared with Naive Sharpe Ratio --- p.108 / Chapter -3.7.9.1 --- Objective --- p.108 / Chapter -3.7.9.2. --- Experimental Setup --- p.108 / Chapter -3.7.9.3. --- The Experimental Result --- p.109 / Chapter - 3.7.10 --- Experiment 3: Compared with other models --- p.113 / Chapter - 3.7.10.1 --- Experiment 31 --- p.113 / Chapter - 3.7.10.2. --- Experiment 32 --- p.117 / Chapter -3.7.11 --- Experiment 4: Apply to the Stock Market --- p.121 / Chapter -3.7.11.1 --- Objective --- p.121 / Chapter - 3.7.11.2. --- Experimental Setup --- p.121 / Chapter -3.7.11.3. --- The Experimental Result --- p.121 / Chapter Chapter 4: --- Conclusion --- p.126 / Appendix A --- p.130 / Appendix B --- p.139 / Appendix C --- p.141 / Appendix D --- p.142 / Reference --- p.144
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_322742 |
| Date | January 1999 |
| Contributors | Yung, Yan Keung., Chinese University of Hong Kong Graduate School. Division of Computer Science and Engineering. |
| Source Sets | The Chinese University of Hong Kong |
| Language | English |
| Detected Language | English |
| Type | Text, bibliography |
| Format | print, iii, 147 leaves : ill. ; 30 cm. |
| Rights | Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
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