Mean-Variance Approaches to Risk-Return Relationships in Strategy: Paradox Lost

A growing number of articles in the area of strategic management employ a mean-variance approach to risk-return relationships. Some researchers investigating risk-return relationships in this fashion claim to have found negative associations between the levels of return and risk. The analysis reported here demonstrates that the mean-variance approach to return and risk carries with it the consequence that statements about the relationship are inherently unverifiable in the context of the system being examined. This further implies that results obtained by using mean and variance of return are specific to the data and period examined and are not necessarily generalizable. Additionally, since mean and variance are arithmetically linked, augmenting the system with additional equations will not provide the information necessary to establish the validity or generalizability of statements involving the mean-variance relation. The analytic proofs are supplemented by examples drawn from an empirical study of the U.S. airline industry.