Time-limited Metaheuristics for Cardinality-constrained Portfolio Optimisation

A financial portfolio contains assets that offer a return with a certain level of risk. To maximise returns or minimise risk, the portfolio must be optimised - the ideal combination of optimal quantities of assets must be found. The number of possible combinations is vast. Furthermore, to make the problem realistic, constraints can be imposed on the number of assets held in the portfolio and the maximum proportion of the portfolio that can be allocated to an asset. This problem is unsolvable using quadratic programming, which means that the optimal solution cannot be calculated. A group of algorithms, called metaheuristics, can find near-optimal solutions in a practical computing time. These algorithms have been successfully used in constrained portfolio optimisation. However, in past studies the computation time of metaheuristics is not limited, which means that the results differ in both quality and computation time, and cannot be easily compared. This study proposes a different way of testing metaheuristics, limiting their computation time to a certain duration, yielding results that differ only in quality. Given that in some use cases the priority is the quality of the solution and in others the speed, time limits of 1, 5 and 25 seconds were tested. Three metaheuristics - simulated annealing, tabu search, and genetic algorithm - were evaluated on five sets of historical market data with different numbers of assets. Although the metaheuristics could not find a competitive solution in 1 second, simulated annealing found a near-optimal solution in 5 seconds in all but one dataset. The lowest quality solutions were obtained by genetic algorithm.Comment: 51 pages, 8 tables, 3 figure

بناء المحفظة الاستثمارية المثلى وفق اسلوب التدريج البسيط بظل السماح وعدم السماح بالبيع القصير: دراسة تطبيقية في سوق العراق للأوراق المالية

يهدف البحث إلى بناء المحفظة الاستثمارية المثلى باستخدام انموذج Simple Ranking الذي يستند الى انموذج مؤشر السوق بظل السماح وعدم السماح بالبيع القصير. وإن مجتمع البحث يشمل جميع الشركات المدرجة في سوق العراق للأوراق المالية للقطاعات الثمان وهي (المصارف، التأمين، الاستثمار، الخدمات، الصناعة، الفنادق والسياحة، الزراعة، الاتصالات، التحويل المالي) والتي بلغت 133 شركة، تم اختيار عينة البحث والتي تتألف من 41 شركة تنتمي لمختلف القطاعات الاقتصادية ومدرجة في سوق العراق للأوراق المالية[1] ولمدة (87 شهر)، أي المدة الممتدة 17/3/2015-17/5/2022. ونستنتج من خلال البحث أنه بالإمكان بناء محفظة مثلى بإنموذج Simple Ranking المستند لنموذج السوق ذو المؤشر الواحد في ظل السماح وعدم السماح بالبيع القصير ومقارنتها بمحفظة السوق. ويوصي ضرورة توعية المستثمرين والمتعاملين في سوق العراق للأوراق المالية لغرض الاعتماد على نموذج Simple Ranking بظل السماح وعدم السماح بالبيع القصير لبناء محفظة المثلى لما يقدمه من تبسيط للمدخلات ونتائج دقيقة يمكن الاعتماد عليها لاختيار الأسهم التي تحقق أفضل مبادلة بين العائد والمخاطرة

Roboadvisors

Treballs Finals del Doble Grau d'Administració i Direcció d'Empreses i de Matemàtiques, Facultat d'Economia i Empresa i Facultat de Matemàtiques i Informàtica, Universitat de Barcelona, Curs: 2022-2023, Tutor: Josep Vives i Santa Eulàlia i Yulia Kasperskaya[en] One of the main objectives of this study is to describe and understand how roboadvisors work. Roboadvisors emerged with the fintech disruption. Providing user-friendly and automated process for creating and managing portfolios. We are going to examine all the steps required to create these portfolios, from investor profile creation to portfolio creation using algorithms like Modern Portfolio Theory.We are also going to go though rebalancing process to maintain the portfolio in time. Additionally, we will replicate some of these methods using real data from Yahoo Finance combined with tools like R, Excel and Portfolio Visualizer

Long-Wave Infrared Digital Holography

peer reviewe

[[alternative]]具群組偵測之有效率的群組股票組合最佳化演算法

碩士[[abstract]]由於金融市場的多變性，投資組合最佳化至今仍是相當吸引人的研究主題。過去幾十年間，許多不同的演化式演算法針對不同的投資組合亦不斷的被提出，其中一種就是多樣群組投資組合。然而，本研究發現現存的多樣群組投資組合最佳化技術仍有三個問題待解決，分別是：如何設定合適的群組數、演化過程耗時、投資組合風險差異過高。故為解決這些問題，本論文使用群組遺傳演算法提出兩個多樣群組股票投資組合最佳化方法。 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。 最後，實驗透過31與50家公司之真實股市資料驗證所提方法的效率與效能確實優於現存的最佳化技術。與現存方法比較顯示，方法一不但在獲利上可達到相似結果，在執行時間上亦可減少約原來的百分之八十五。而方法二所找出之多樣群組投資組合其風險上也有明顯降低。[[abstract]]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.[[tableofcontents]]Contents 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 5.1.2.1 Experimental Results for Different Desired Stock 80 5.1.2.2 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 REFERENCES 106 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[[note]]學號: 603780106, 學年度: 10