Defining the Mean-Preserving Spread: 3-pt versus 4-pt

Eric Bennett Rasmusen, Kelley School of Business, Indiana University
Emmanuel Petrakis, University of Crete

Abstract

The standard way to define a mean-preserving spread is in terms of changes in the probability at four points of a distribution (Rothschild and Stiglitz [1970]). Our alternative definition is in terms of changes in the probability at just three points. Any 4-pt mean- preserving spread can be constructed from two 3-pt mean-preserving spreads, and any 3-pt mean-preserving spread can be constructed from two 4-pt mean- preserving spreads. The 3-pt definition is simpler and more often applicable. It also permits easy rectification of a mistake in the Rothschild-Stiglitz proof that adding a mean- preserving spread is equivalent to other measures of increasing risk.