The Square-Root Law of Precautionary Reserves

Abstract

This article presents a generalization of the square-root theorems formulated by various authors with regard to special kinds of safety reserves. Some of the results established in the paper are the following: (1) the validity of the square-root law does not require that the actual components of net demand be stochastically independent and identically distributed; (2) in particular, such a law is compatible with the existence of serial correlation among reserve changes; and (3) if expected net demand differs from zero, the elasticity of the total reserve with respect to expected demand is between 0.5 and 1.