The Simple Meaning of Complex Rates of Return

Abstract

This note proposes a coherent system enabling interpretation and manipulation of rates of interest (or rates of return) including an imaginary component. This may help to shed new light on equations involving complex solutions, especially when valuing investment projects. In addition, a series of real rates can be associated with any complex rate. Each real rate can then be interpreted as a portfolio's expected return. As an example of application, when a project involves the joint production of two outputs whose markets have not the same risk, our approach allows the project's cash flow to be discounted at a single (but complex) rate.

Notes

According to the Capital Asset Pricing Model (CAPM), only the exposure of an asset's return to the systematic risk involves a risk premium in the asset's expected return.