GRAFİKSEL LASSO İLE PORTFÖY OPTİMİZASYONU VE BORSA İSTANBUL’DA BİR UYGULAMA

Year 2022, , 760 - 765, 26.07.2022

Erhan Ustaoğlu

https://doi.org/10.14783/maruoneri.1073352

Cited By: 1

Abstract

Grafiksel Lasso (least absolute shrinkage and selection operator) algoritması son yıllarda makine öğrenmesi alanında popüler bir araç oldu. Genel olarak sınıflandırma problemlerinin özellik seçimi için kullanılıyor olsa da aynı zamanda kovaryans matris tahmininde de başvurulur hale geldi. Ortalama-varyans portföy optimizasyonu, portföy riskinin hesaplanmasında tarihi verilerden yararlanılarak oluşturulan kovaryans matrisini kullanmaktadır. Bu aynı zamanda ortalama-varyans portföy optimizasyonu metodunun en çok eleştiri aldığı konudur. Bu çalışmanın amacı farklı L1 ceza faktörleri kullanarak grafiksel Lasso algoritmasının kovaryans matris tahminine ve bunun portföy optimizasyon performansına olan etkilerini göstermektir. Çalışmada ortalama-varyans portföy optimizasyonu amprik ve tahmini kovaryans matrisleri kullanılarak BIST 30 endeksine uygulanmakta ve sonuçlar karşılaştırılmaktadır.

Keywords

Grafiksel Lasso, Portföy Optimizasyonu, Kovaryans Matrisi

PORTFOLIO OPTIMIZATION WITH GRAPHICAL LASSO AND AN APPLICATION IN BORSA ISTANBUL

Abstract

Graphical Lasso (Least absolute shrinkage and selection operator) has become a popular tool in the field of machine learning in recent years. Although it has been deployed mainly for feature selection in classification problems, it is also used for covariance matrix estimation. Mean-variance portfolio optimization relies on sample covariance matrix for the calculation of the portfolio’s risk, whereas it has been most hardly criticized. The aim of this study is to demonstrate the effect of the covariance matrix estimation by Graphical Lasso algorithm with varying L1 penalty factors. Mean-variance portfolio optimization using empirical and estimated covariance matrices are applied to BIST 30 index and the results are compared.

Keywords

Graphical Lasso, Portfolio Optimization, Covariance Matrix

References

• Avagyan, V., Alonso A. M., & Nogales F. J. (2017). Improving the graphical lasso estimation for the precision matrix through roots of the sample covariance matrix. Journal of Computational and Graphical Statistics, 26(4), 865–72. Bai, Z., Liu H., & Wong, W. K. (2009). Enhancement of the applicability of Markowitz’s portfolio optimization by utilizing random matrix theory, Mathematical Finance, 19(4), 639–667.
• Bodnar, T., Gupta, & A.K., Parolya, N. (2014). On the strong convergence of the optimal linear shrinkage estimator for large dimensional covariance matrix, Journal of Multivariate Analysis, 132, 215-228.
• DeMiguel, V., Garlappi, L., & Uppal, R. (2009). Optimal versus naive diversification: How inefficient is the 1/N portfolio strategy? Review of Financial Studies, 22, 1915–1953.
• Friedman, J., Hastie, T., & Tibshirani, R. (2008). Sparse inverse covariance estimation with the graphical lasso, Biostatistics, 9(3), 432–441.
• Jalal, K., Camp, C., & Pezeshk, S. (2019). On the application of machine learning techniques to derive seismic fragility curves. Computers & Structures. 218.
• Kolm, N., Tütüncü, R., & Fabozzi, F. (2014). 60 years of portfolio optimization: Practical challenges and current trends. European Journal of Operational Research, 234 (2), 356–371. Ledoit, O., & Wolf, M. (2003). Improved estimation of the covariance matrix of stock returns with an application to portfolio selection. Journal of Empirical Finance, 10, 603–621.
• Ledoit, O., Wolf, M. (2004). A well-conditioned estimator for large-dimensional covariance matrices. J. Multivariate Analysis, 88, 365-411.
• Liu, Y., Chan, N.H., Ng, C.T. & Wong, S.P.S. (2016). Shrinkage Estimation of Mean-Variance Portfolio, International Journal of Theoretical and Applied Finance, 19(1), 1-25.
• Loukina, A., Zechner, K., Lei, C., & Heilman, M. (2015). Feature selection for automated speech scoring. Proceedings of the Tenth Workshop on Innovative Use of NLP for Building Educational Applications,12–19, Denver, Colorado.
• Markowitz, H. (1952). Portfolio selection. The journal of finance, 7(1), 77–91.
• Michaud, Richard. (1989). The Markowitz Optimization Enigma: Is ‘Optimized’ Optimal?. Financial Analysts Journal, 45, 31-42.
• Muthukrishnan, R., & Rohini, R. (2016). LASSO: A feature selection technique in predictive modeling for machine learning. 2016 IEEE International Conference on Advances in Computer Applications (ICACA), 18-20.
• Perrin, S., & Roncalli, T. (2019). Machine Learning Optimization Algorithms & Portfolio Allocation, https://ssrn.com/abstract=3425827. Sharpe, W. (1966). Mutual Fund Performance. The Journal of Business, 39(1), 119-138.
• Tibshirani, R. (1996). Regression Shrinkage and Selection via the Lasso, Journal of the Royal Statistical Society B, 58(1), 267-288.
• Yuan, X., Yu, W., Yin Z., & Wang, G. (2020). Improved Large Dynamic Covariance Matrix Estimation with Graphical Lasso and Its Application in Portfolio Selection. IEEE Access, 8, 189179-189188.