||Efficient Group Stock Portfolio Optimization Algorithms with Natural Group Detection
||Master’s Program, Department of Computer Science and Information Engineering (English-taught program
Cluster validation indices
diverse group stock portfolio
grouping genetic algorithm
第一個方法主要用於解決前兩個問題。針對設定合適的群組數問題，所提的方法首先透過股東權益報酬率(ROE)與本益比(P/E)兩屬性將股票分群後，之後設計分群效度因子(cluster validation factor)並將之當成適合度函數的一部份，使演算法可以自動搜尋較佳之分群結果。為解決演化過程耗時問題，在方法一則設計暫存染色體(Temporary chromosome)透過降低需要評估的組合數使演化過程得以加速。
第二個方法則著手解決投資組合風險差異過高問題。首先，方法中設計風險比例因子(Risk ratio factor)計算多樣群組股票投資組合可產生之最大組合風險。接著，所提的演算法結合自我調適之交配(Adaptive crossover)、突變(Adaptive mutation)運算與排序為基礎之輪盤選擇法(Rank-based roulette wheel selection)以達更好的搜尋能力。
||Due to the variety of financial markets, stock portfolio optimization is an attractive research topic. In the past decades, many evolutionary-based algorithms have been proposed to optimize different types of stock portfolios, and one of them is named diverse group stock portfolio (DGSP). However, this study found that three problems remain to be solving in the existing DGSP approaches. They are how to set an appropriate group size, evolution process is time-consuming, and difference between risks of portfolios is too high. To solve these problems, two approaches by grouping genetic algorithms (GGA) are proposed for optimizing DGSPs in this thesis.
The first approach is used to deal with the first two problems. For setting an appropriate group size, the two attributes, Return on Equity (RoE) and Price Earnings Ratio (P/E), are utilized to group stocks. Then, cluster validation factor, which is used as a part of fitness function, is designed to derive better stock groups. To solve time-consuming problem, a temporary chromosome is designed to reduce number of stock portfolios should be evaluated to speed up the evolution process.
The second approach is then proposed to handle the third problem. It first designs risk ratio factor to calculate the maximum risk of a given DGSP. Then, by combining adaptive crossover, adaptive mutation, and rank-based roulette wheel selection, the second approach has higher searching ability to find better solution.
At last, experimental results on the two real datasets that contain 31 and 50 stocks were made to verify the two proposed approaches are effective and efficient. Comparing with the existing approach, the results show that the first approach can not only reach similar return but also reduce execution time up to 85%. The risk of optimized DGSP by second approach is significantly lower than that by the existing approaches.
CHAPTER 1 INTRODUCTION 1
1.1 Problem Definition and Motivation 1
1.2 Contributions 4
1.3 Reader’s Guide 6
CHAPTER 2 RELATED WORK 7
2.1 The M-V model 7
2.2 Metaheuristics for portfolio optimization 8
2.3 Metaheuristics for Clustering 10
2.4 Cluster Validation Indices 11
CHAPTER 3 DIVERSE GROUP STOCK PORTFOLIO OPTIMIZATION APPROACH WITHOUT SETTING A GROUP NUMBER 14
3.1 Motivation 14
3.2 Components of Proposed Approach 16
3.2.1 Clustering Attributes 16
3.2.2 Encoding Scheme 17
3.2.3 Temporary Chromosome 19
3.2.4 Initial Population 22
3.2.5 Fitness Evaluation 23
3.2.6 Genetic Operations 25
3.3 Algorithm for First Approach 27
3.4 An Example 30
CHAPTER 4 A ENHANCED ALGORITHM FOR OPTIMIZING DIVERSE GROUP STOCK PORTFOLIO 42
4.1 Motivation 42
4.2 Elements of the proposed algorithm 44
4.2.1 Encoding Scheme 45
4.2.2 Initial Population 47
4.2.3 Fitness Evaluation 47
4.2.4 Genetic Operations 53
4.3 Algorithm for Second Approach 59
4.4 An Example 62
CHAPTER 5 EXPERIMENTAL RESULTS 76
5.1 Experimental Results for Approach (I) 76
5.1.1 Experimental Datasets 76
5.1.2 Effectiveness of The Proposed Approach 79
184.108.40.206 Experimental Results for Different Desired Stock 80
220.127.116.11 Analysis of the Derived GSP 85
5.1.3 Efficiency of Proposed Approach 88
5.2 Experimental Results for Approach (II) 90
5.2.1 Experimental Datasets 91
5.2.2 Effectiveness Of The Proposed Approach 91
5.2.3 Efficiency of Proposed Approach 100
CHAPTER 6 CONCLUSION AND FUTURE WORKS 103
List of Figures
Figure 1. Encoding scheme of chromosome Cq 17
Figure 2. An example of the encoding scheme with three parts. 18
Figure 3. An example of a chromosome with four parts 19
Figure 4. An example of a chromosome from the previous approach 20
Figure 5. An example of a chromosome with relevant information 20
Figure 6. An example of a temporary chromosome 22
Figure 7. Encoding scheme of chromosome Cq. 45
Figure 8. An example of the encoding scheme. 46
Figure 9. The pie chart of the five chromosome in Table 10 58
Figure 10. The stock price series for 31 companies from the beginning of 2010 to the end of 2014 77
Figure 11. The stock price series for 50 companies from the beginning of 2012 to the end of 2014 78
Figure 12. The average fitness over 100 generations using elitist selection 80
Figure 13. The average fitness of the second approach with rank-based roulette wheel selection over 10 runs 92
Figure 14. The average risk of both approaches for 200 generations 96
List of Tables
Table 1. The relationship between group size and number of combinations. 21
Table 2. The 10 stocks used in the example 31
Table 3. The portfolio satisfaction for each chromosome 35
Table 4. The group balance for each chromosome 35
Table 5. The dissimilarity matrix for the proposed approach 35
Table 6. The diversity values for each chromosome 36
Table 7. The Davies-Bouldin Index for every chromosome 37
Table 8. The fitness for each chromosome 38
Table 9. Two generated DGSPs with similar ROI but different risk values 43
Table 10. Survival probabilities of five chromosomes 58
Table 11. The 10 stocks used in the example 62
Table 12. The portfolio satisfaction for each chromosome 66
Table 13. The group balance for each chromosome 66
Table 14. The dissimilarity matrix for the proposed approach 67
Table 15. The diversity values for each chromosome 67
Table 16. The values of Davies-Bouldin index for every chromosome 69
Table 17. The fitness for each chromosome 70
Table 18. The total fitness values for all the chromosomes 70
Table 19. The fitness f'(Cq) for all chromosomes after conversion for rank-based selection 71
Table 20. The probabilities of selection based on ranking 71
Table 21. The parameter settings for 31 and 50 company data sets 79
Table 22. The experimental results for the Davis-Bouldin Index approach on 31 stocks 80
Table 23. The experimental results for the C Index approach on 31 stocks 81
Table 24. The experimental results for the Dunn Index approach on 31 stocks 81
Table 25. The experimental results for the Silhouette approach on 31 stocks 82
Table 26. Approach using Davis-Bouldin Index with 50 stocks 84
Table 27. Approach using Silhouette index with 50 stocks 84
Table 28. Approach using Dunn index with 50 stocks 84
Table 29. Approach using C index with 50 stocks 85
Table 30. The initial and derived GSP for 31 stocks 86
Table 31. The initial and derived DGSP for 50 stocks 87
Table 32. The efficiency of previous and proposed approach 1 for 31 stocks 89
Table 33. The efficiency of Approach 1 using 50 stocks 90
Table 34. The experimental results for approach 2 using 31 stocks 93
Table 35. The experimental results for approach 2 using 50 companies 93
Table 36. The risk for 10 runs using the original approach 94
Table 37. The risk for approach 2 using 31 stocks 95
Table 38. The risk for the original approach using 50 stocks dataset 96
Table 39. The risk for proposed approach 2 using 50 stocks 97
Table 40. The initial and derived DGSP for 31 companies 98
Table 41. The initial and derived DGSP for approach 2 using 50 stocks 99
Table 42. The efficiency of approach 2 using 31 stocks 101
Table 43. The efficiency of approach 2 using 50 stocks 102
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