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

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

Öz

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.

Anahtar Kelimeler

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

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