Since the change of conditional value at risk (CVaR) in different confidence levels is very effective in portfolio optimization, the meta-Malmquist index (MMI) is utilized. For this purpose, mean-CVaR models by MMI in the presence of negative data are introduced. Like Markowitz theory in mean-variance framework, we use Conditional Value-at-risk as a risk measure and propose our models without considering the skewness and kurtosis of assets return. In our study there are some negative data, so our models is based on Range Directional Measure (RDM) model that can be taken positive and negative data. In this paper efficiencies are obtained in all confidence levels by mean-CVaR models and MMI is calculated on confidence levels as periods in the presence of negative data. This method could help the investors to construct their profitable portfolio by using MMI index. We, also carry out an empirical study within Iran stock exchange market . تفاصيل المقالة