Why the Return Notion Matters

Abstract

Returns can be defined as log returns or as simple returns. Whereas on a numerical level the difference between these two terms is small as long as the return values are close to zero, there can be non-negligible differences if we look at expected values and (co)variances in a stochastic context. This paper examines the consequences of mixing up the two return terms when variances and convariances are considered. Three applications show that these consequences can be severe in the sense of suboptimal portfolio selection or invalid betas. The paper argues that more awareness of the suited return term is necessary.