The return rate in imprecision risk may be described as a fuzzy probabilistic set (Piasecki, 2011a). Properties of this return are considered in (Piasecki, 2011b) for any probability distribution of future value. On the other side, in (Piasecki, Tomasik, 2013) is shown that the Normal Inverse Gaussian distribution (NIG distribution) is the best matching probability distribution of logarithmic returns on Warsaw Stock Exchange. There will be presented the basic properties if imprecise return with NIG distribution of future value logarithm. The existence of expected return rate and basis risk characteristic will be discussed.