Performance comparison of software programs in solving the cardinality constrained portfolio optimization problem

Öz

Cardinality constrained portfolio optimization is one of the important problems in financial management, where the number of assets in the portfolio is limited. Unlike classical portfolio optimization, this problem is more complex in terms of computation since it also involves asset selection. In the literature, optimization software packages are widely used to solve this problem using exact solution methods. Commonly used software packages are Lingo, Gams/Dicopt, and Gurobi. In this study, the performances of the software programs in terms of solution quality, computational efficiency, and practicality in application were analyzed and compared by using these software programs in solving the cardinality-constrained portfolio optimization problem. The analyses were performed on data sets belonging to the Hang Seng, DAX 100, FTSE 100, S&P 100, and Nikkei 225 stock market indices, which are widely used in the literature. To make a correct and unbiased comparison, each software program was applied under the same conditions by maintaining consistency in parameters, restrictions, and calculation settings. Additionally, sensitivity analysis was conducted based on the number of assets. As a result of the comparison, it was seen that Gurobi is more successful than other solvers in terms of both computation time and better performance metric values. In addition, Gurobi's good performance and higher adaptability to large data sets are due to its advanced solver algorithms.

Anahtar Kelimeler

• Cardinality constrained
• portfolio optimization
• Lingo
• Gams
• Gurobi
• performance metrics

Varlık sayısı kısıtlı portföy optimizasyon probleminin çözümünde yazılım programlarının performans karşılaştırması

Öz

Varlık sayısı kısıtlı portföy optimizasyonu, portföydeki varlık sayısının sınırlı olduğu finansal yönetimde önemli problemlerden biridir. Klasik portföy optimizasyonu aksine, bu problemde ayrıca varlık seçimi söz konusu olması nedeniyle hesaplama açısından daha karmaşıktır. Literatürde bu problemi kesin çözüm yöntemleri kullanarak çözmek için yaygın olarak optimizasyon yazılım paket programları kullanılmaktadır. Genellikle kullanılan yazılım paket programları, Lingo, Gams/Dicopt ve Gurobi’dır. Bu çalışmada, varlık sayısı kısıtlı portföy optimizasyonu probleminin çözümünde bu yazılım programları kullanılarak çözüm kalitesi, hesaplama verimliliği ve uygulamada pratiklik açısından yazılım programlarının performansları analiz edilmiş ve karşılaştırılmıştır. Analizler, literatürde yaygın olarak kullanılan Hang Seng, DAX 100, FTSE 100, S&P 100 ve Nikkei 225 borsa endekslerine ait veri setleri üzerine gerçekleştirilmiştir. Doğru ve tarafsız bir karşılaştırma yapabilmek için her bir yazılım programı, parametreler, kısıtlamalar ve hesaplama ayarlarındaki tutarlılığı koruyarak aynı koşullar altında uygulanmıştır. Ayrıca varlık sayısına göre duyarlılık analizi yapılmıştır. Karşılaştırma sonucunda Gurobi'nin hem hesaplama süresi hem de daha iyi performans metriği değerlerine sahip olması açısından diğer çözücülerden daha başarılı olduğu görülmüştür. Buna ek olarak, Gurobi’nin iyi bir performans sergilemesi ve büyük veri setlerine karşı daha yüksek uyum yeteneğine sahip olması, gelişmiş çözücü algoritmalarına sahip olmasından kaynaklanmaktadır.

Anahtar Kelimeler

• Varlık sayısı
• portföy optimizasyonu
• Lingo
• Gams
• Gurobi
• performans metrikleri

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