مسيله انتخاب سبد سهام با رويكرد بنيادين و حذف همبستگي بين شاخص‌هاي ارزيابي

Portfolio Selection Problem with Eliminated Correlation between Indices Based on Fundamental Approach

هدف از اين مقاله ارايه رويكردي مناسب در مواجهه با مسيله انتخاب سبد سهام با استفاده از رويكرد بنيادين با در نظر گرفتن همبستگي بين معيارهاي ارزيابي است. در اين پژوهش با استفاده از مقايسات زوجي، شركت‌هاي مغلوب حذف و همبستگي بين نسبت‌هاي مالي به عنوان شاخص‌هاي ارزيابي با استفاده از فرآيند گرام-اشميت در جبر خطي، حذف يا كاهش داده مي‌شود و در نهايت از رويكرد DEA با استفاده از مدل MSBM سهام برتر معرفي مي‌شود. براي بيان كارآيي رويكرد توسعه داده شده، از داده‌هاي 202 شركت فعال در 22 گروه‌ صنعت موجود در بورس اوراق بهادار تهران در فاصله زماني سال‌هاي 88-89 استفاده شده و در دو حالت وجود و نبود همپوشاني بين مدل‌ها، سبد سهامي معرفي مي‌شود. نتايج نشان مي‌دهد كه سبد حاصل از اجراي اين رويكرد، نسبت به بازده دو مدل CCR, BCC و بازار بهتر عمل مي‌كند.

Correlation among financial ratios motivated us to find a method to eliminate these correlations and multi-correlation among indices which may distort the results. In this paper we propose a method to make better decision which stock is best and proper to be selected for investment. We used Gram-Schmidt process to eliminate correlations, peer comparisons matrix to reduce calculations and cumulative round off error and Data Envelopment Analysis to evaluate simultaneously the quality of financial leverages and reversed liquidity ratios as inputs and profit making factors such as EPS, Net profit margin, Operational income margin, Book value divided by share’s price and EPS divided by share’s price as Outputs in Tehran Security Exchange (TSE). For selecting order of Gram-Schmidt basic vectors we used minimum sum of absolute correlation between indices separately for inputs and outputs data that will be used in DEA. Results show that when multi-collinearity exists among indices some correlation will remain after orthogonalization. Our approach offers more alternative stocks which will reduce drastically portfolio’s risk while the same or better return than use of ordinary (CCR) or( BCC) models in envelopment form, furthermore the proposed approach model that used to evaluate stocks give a better return than the market’s return during summer 2010. 202 companies in deferent industries investigated in this paper. Insurance, Investment, Banking, Leasing, financial, Housing and construction sectors cause of being different to ordinary companies has been neglected. The aforementioned procedure in this paper offers two portfolio sets which lead to better return than ordinary DEA models.