This paper deals with an exponential possibility distribution and its application to portfolio selection problems. The proposed method for possibility portfolio selection is based on a possibility distribution whereas conventional portfolio selection is based on a probability distribution. Since a possibility distribution depends on importance grades of data given by an expert, possibility portfolio selection can reflect the characteristics of expert judgement on importance grades. In order to compare a possibility portfolio model with a fuzzy one, a fuzzy portfolio model is formulated by the concept of the fuzzy probability, which is similar to Markowitz's model. >