DEA Method of Choosing Optimum Portfolio in Accordance with Stock Liquidity: The Case Study of Listed Companies of Tehran Stock Exchange

One of the main problems of choosing a portfolio which consists of stocks or assets is to consider their incongruous nature with a view to risk, return and liquidity. In other words, the inability to choose an optimum portfolio considering risk, return and liquidity at the same time is a problem. Hence, financial decision makers in order to have access to optimum portfolio have to trade off some of the mentioned criteria, inevitably. Various approaches have been utilized to resolve this problem. One of the models which is expressed recently and categorized as a nonparametric frontier model is data envelopment analysis. DEA can resolve the mentioned problem by measuring and assessing the efficiency of a portfolio. In this research liquidity is added to risk and return to identify its impact in choosing optimum portfolio. This means that if considering stock liquidity as a criterion in choosing optimum portfolio leads to a better result the investors must consider it. This study is accomplished by using DEA. Research Questions or hypotheses Based on the goals of this research which are 1) the study of stock liquidity influence in choosing portfolio and 2), DEA usefulness on choosing portfolio, hypotheses are expressed as follows. To have access to the first goal, the first hypothesis is as follows: H1: There are significant differences between two portfolio's return when one of them is chosen by DEA technique and considering risk, return and liquidity rank and the other one which does not consider these three variables. And to achieve second goal, the second hypothesis is expressed as follows: H2: There are significant differences between two portfolio's return when one of them consists of 30 companies are located at the first rank of efficiency point and the other one which consists of 30 companies are located at the last rank with view to efficiency point (The first portfolio is chosen by using DEA technique and the other one is not). At first in order to test the hypotheses, efficiency point is calculated by using DEA in two different situations. 1) Risk and liquidity rank are considered as input variables and return as output variable of DEA technique. 2) Risk is considered as an input variable and return as an output variable of DEA technique. Then significant differences of both hypotheses are tested by using t-test. It is important to notice that the number 30 is chosen to improve the results validity. DEA can be utilized by using BCC or CCR models. In this research the chosen model is BCC. As mentioned above and by using t-test, first hypothesis results show that there is not a significant difference between two portfolios’ return. Testing the second hypothesis suggests that there is a significant difference between the two portfolios’ return. This result reveals the usefulness of using DEA technique in choosing optimum portfolio. Discussion and This research is set up to study the influence of stock liquidity and DEA usefulness in choosing optimum portfolio. In comparison with Eslami Bidgoli and Saranj (1387) results show that stock liquidity could not be considered as influence criterion and decision makers do not consider it in the process of choosing optimum portfolio. Although, according to the results it is taken for granted that in Tehran Stock Exchange sufficient information about stock liquidity are not published. Moreover, the results essay that using DEA technique in choosing optimum portfolio is efficient.