The functional specification of mean-standard deviation approach is examined under location and scale parameter condition. Firstly, the full set of restrictions imposed on the mean-standard deviation function under the location and scale parameter condition are made clear. Secondly, the examination based on the restrictions mentioned in the previous sentence derives the new properties of the mean-standard deviation function on the applicability of additive separability and the curvature of expansion path which links the points that give the same slope of indifference curve. It reveals that attention has not been sufficiently paid to the restrictions in interpreting the linear mean-standard deviation model and the nonlinear mean-standard deviation model that have been used in previous research. Thirdly, the interpretation of the nonlinear mean-standard deviation model is reconsidered in detail and then an alternative nonlinear mean-standard deviation model is proposed. The implication of the two nonlinear mean-standard deviation models to the empirical approach called "joint analysis of risk preference structure and technology" is discussed.