روشي جديد براي ارزيابي عملكرد سبد سهام در مدل ميانگين، واريانس و چولگي با استفاده از تكنيك تحليل پوششي داده‌ها (مطالعه‌ي موردي: بازار بورس ايران)

A New Approach for Portfolio Performance Evaluation in MVS Modeling via Data Envelopment Analysis: (Case Study: Iran Stock Market)

تصميمگيري براي سرمايه‌گذاري يك‌پارچه و كارا يكي از پيچيدهترين و پرچالشترين موضوعات مديريت و تحليل سرمايه‌گذاري است. از نظر ماركويتز، يك پورتفوليوي كارا سبد سهامي است كه در سطح مشخصي از بازده، كم‌ترين ريسك را دارد. در اين نوشتار كاربرد مدل ميانگين ـ واريانس ـ چولگي (MVS)، به‌جاي مدل ميانگين ـ واريانس (MV) ماركويتز، به‌منظور سنجش كارايي پيشنهاد مي‏شود. البته اين‌گونه مدلها در عين برخورداري از كارايي بالاتر، پيچيدگيهاي محاسباتي خاص خود را نيز دارند كه براي غلبه بر آن، روشي ساده و كاربردي برمبناي روش تحليل پوششي داده‌ها (DEA) پيشنهاد شده است. ايده‌ي اصلي اين روش، تركيب سه معيار ميانگين، واريانس و چولگي بازده و نيز ارايه‌ي معياري واحد براي ارزيابي كارايي سهام است. اين معيار، امكان رتبه‌بندي واحد سرمايه‌گذاران را فراهم ميكند. نكته‌ي جالب ديگر درمورد اين پژوهش آن است كه با استفاده از DEA، ارزيابي كارايي بدون رسم مرز كارا و تنها با تصوير‌كردن سهام‏ بر آن صورت ميگيرد. به‌عنوان يك مطالعه‌ي موردي، اين مدل براي شركت‌هاي برتر بورس ايران اجرا و مجموعه سهامهاي كارا مشخص شده است.

People, during their lifetime, make investment decisions in various areas including real estate, gold, stocks, and bonds, and these decisions have an internal relationship between them that is unbreakable. The link between these decisions lies in the risks taken and the return on investments for the selected market. Decision making, with regard to investments, is one of the most difficult and complicated subjects in management and investment analysis. Generally speaking, an efficient portfolio is a portfolio with a specified return amount and the lowest possible risk level. The content of this article suggests that to find an efficient frontier, instead of using the Markowitz mean-variance (MV) model, we can use the Mean-Variance-Skewness model (MVS). This paper introduces a practical model for evaluation of an efficient portfolio based upon the MVS model using a Data Envelopment Analysis approach. The main idea of this approach is to evaluate the performance of a set of funds by taking into account expected returns, variance and skewness, and synthesizing them in a numerical value via an input oriented data envelopment analysis model. The DEA technique is a multi criterion decision making tool for making appropriate and sound decisions. In this technique, we can, at the same time as using some input and output variables, calculate and separate the efficiency of a set of efficient company stocks from inefficient ones. In addition, the optimal portfolio among the efficient companies can be determined using the information obtained The high point of this research is efficient frontier generation through projecting the stocks on the frontier without actually generating the frontier at all, and then determining the efficiency of the stocks. As a case study, this model was implemented for the top 37 companies in Iranʹs stock markets. The results obtained from the model execution indicate that the stocks of three companies; Saipa, Alborz Daru and Tehran Cement, are the most appropriate for portfolio selection, due to their appropriateness of returns and variance of stocks, as well as their skewness positivity.