Risk-Based DEA Efficiency and SSD Efficiency of OECD Members Stock Indices

Year 2018, Volume 6, Issue 1, 2018, 25 - 36, 25.03.2018

Neslihan Fidan Keçeci , Yonca Erdem Demirtaş

https://doi.org/10.17093/alphanumeric.345483

Cited By: 1

Abstract

A stock market index gives some illustrative information regarding the financial market. In this study, we are interested in stock indices efficiency of OECD member countries. We use Data Envelopment Analysis (DEA) methodology and Second Order Stochastic Dominance (SSD) Criteria as an efficiency metrics. DEA is a linear programming based technique for measuring the relative efficiency of homogenous decision making units by their input-output rates. In the Risk-Based DEA, traditional and modern risk measures are used as inputs of the model and the mean return as an output. We consider Conditional Value at Risk (CVaR) as a modern risk measure of financial asset returns. Another approach for the efficiency is Stochastic Dominance (SD) rule that takes into account the entire distribution of return, rather than the return distribution characteristics. There are several papers show that SSD constraints related to the CVaR constraints in an optimization model. Therefore, we compare Risk-Based DEA results with optimization problem with SSD constraints in the empirical study. We also test SSD efficiency of stock index pairs. The results are valuable for the asset managers who need to evaluate the performance of a stock index among others.

Keywords

Data Envelopment Analysis, Stochastic Dominance, Conditional Value at Risk, Index Efficiency

Risk-Tabanlı VZA ve Stokastik Baskınlık Kriteri ile OECD Üyelerinin Hisse Senedi Endekslerinin Etkinliği

Abstract

Bir hisse senedi endeksi finansal piyasalara ilişkin bazı tanımlayıcı bilgiler vermektedir. Bu çalışmada, biz OECD ülkelerinin hisse senetleri etkinliğiyle ilgilenmekteyiz. Etkinlik ölçüsü olarak Veri Zarflama Analizi (VZA) ve İkinci Dereceden Stokastik Baskınlık (İDSB) Kriterini kullanmaktayız. VZA benzer karar verme birimlerinin göreli etkinliğinin ölçümü için bir doğrusal programlama tekniğidir. Risk Tabanlı VZA’da geleneksel ve modern risk ölçüleri modelin girdileri olarak ve ortalama getiri ise çıktı olarak kullanılır. Finansal yatırım getirilerinin modern bir risk ölçüsü olarak Koşullu Riske Maruz Değeri (RMD) dikkate almaktadyız. Etkinlik için bir başka yaklaşım ise getiri dağılımının spesifik karakteristiklerindense dağılımın tamamını dikkate alan Stokastik Baskınlık kuralıdır. Bir optimizasyon modelinde Koşullu RMD kısıtları ile İDSB kısıtlarının ilişkili olduğunu gösteren pek çok çalışma bulunmaktadır. Bu bağlamda, biz Risk Tabanlı VZA ile İDSB kısıtlı optimizasyon problemlerinin çözümlerini uygulamalı olarak bu çalışmada karşılaştırmaktayız. Ayrıca endeks çiftlerinin İDSB etkinliklerini de test etmekteyiz. Sonuçlar bir endeksin diğer endekler arasında getiri-riskleri açısından nasıl bir perfomansa sahip olduğunu göstermesi açısından yatırım yöneticileri için değerlidir.

Keywords

Veri Zarflama Analizi, Stokastik Baskınlık, Koşullu Riske Maruz Değer, Endeks Etkinliği

References

• Basso, A. & Funari, S. (2001). A data envelopment analysis approach to measure the mutual fund performance. European Journal of Operations Research, 135(3):477–492.
• Branda, M. & Kopa, M. (2012). DEA-risk efficiency and stochastic dominance efficiency of stock indices. Finance a Uver, 62.2: 106.
• Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European journal of operational research, 2(6), 429-444.
• Daraio C. & Simar L. (2006). A robust nonparametric approach to evaluate and explain the performance of mutual funds. European Journal of Operational Research, 175(1):516–542.
• Dentcheva, D., & Ruszczyński, A. (2006). Portfolio optimization with stochastic dominance constraints. Journal of Banking & Finance, 30(2), 433-451.
• Edirisinghe, N. C. P. & Zhang, X. (2008). Portfolio selection under DEA-based relative financial strength indicators: case of US industries. Journal of the Operational Research Society, 842-856
• Fabian, C.I., Mitra, G., Roman, D. & V. Zverovich (2011a): An enhanced model for portfolio choice with SSD criteria: a constructive approach. Quantitative Finance, 11(10), pp.1525-1534.
• Fabian, C.I., Mitra, G., & Roman, D. (2011b). Processing second-order stochastic dominance models using cutting-plane representations. Mathematical Programming, 130(1), 33-57.
• Fidan Keçeci, N., Kuzmenko, V., & Uryasev, S. (2016). Portfolios Dominating Indices: Optimization with Second-Order Stochastic Dominance Constraints vs. Minimum and Mean Variance Portfolios. Journal of Risk and Financial Management, 9(4), 11.
• Hadar, J., & Russell, W. R. (1971). Rules for ordering uncertain prospects. The American economic review, 59(1), 25-34.
• Kopa, M. & Chovanec, P. (2008) A second-order stochastic dominance portfolio efficiency measure. Kybernetika, 44, 243–258.
• Kuosmanen, T. (2004) Efficient Diversification According to Stochastic Dominance Criteria. Manag. Sci., 50, 1390–1406.
• Lamb, J. D., & Tee, K. H. (2012). Data envelopment analysis models of investment funds. European Journal of Operational Research, 216(3), 687-696.
• Levy, H. (2006). Stochastic dominance: Investment decision making under uncertainty (Vol. 12). Springer Science & Business Media.
• Lozano, S., & Gutiérrez, E. (2008). Data envelopment analysis of mutual funds based on second-order stochastic dominance. European Journal of Operational Research, 189(1), 230-244.
• Markowitz, Harry. (1952). Portfolio selection. The journal of finance 7, no. 1: 77-91.
• MATLAB R2012b, The MathWorks, Inc.: Natick, Massachusetts, United States, 2012.
• Murthi, B. P. S., Choi, Y. K., & Desai, P. (1997). Efficiency of mutual funds and portfolio performance measurement: A non-parametric approach. European Journal of Operational Research, 98(2), 408-418.
• Ogryczak, W., & Ruszczyński, A. (1999). From stochastic dominance to mean-risk models: Semideviations as risk measures. European Journal of Operational Research, 116(1), 33-50.
• Pflug, G. C. (2000). Some remarks on the value-at-risk and the conditional value-at-risk. In Probabilistic constrained optimization (pp. 272-281). Springer US.
• Roman, D., Darby-Dowman, K., & G. Mitra (2006): Portfolio construction based on stochastic dominance and target return distributions, Mathematical Programming, Series B, 108, pp. 541-569.
• Rudolf, G. & A. Ruszczynski (2008): Optimization problems with second order stochastic dominance constraints: duality, compact formulations, and cut generation methods, SIAM J. OPTIM, Vol. 19, No. 3, pp. 1326–1343.
• Whitmore, G. A. & Findlay, M. C. (Eds.). (1978). Stochastic dominance: an approach to decision-making under risk. Lexington Books.