Convenience Yield Revisited: Using Profit Maximization Discrete-Time Model

Abstract

This study analyzes the relationships of commodity spot and futures prices with convenience yield. Convenience yield is received by the owner of a spot commodity but not by the owner of the right to the commodity (e.g., futures). This is the first study to explicitly model commodity spot and futures prices using firms and speculators (i.e., supply and demand of a commodity). We found that spot and futures prices are related to convenience yield. Based on this we were able identify the structure of convenience yield, which can be decomposed into two components: yield and cost. Furthermore, these relations offer a basis for at least three ways of interpreting convenience yield. We obtained similar results using models that consider cash settlement and hedging with output commodity futures. We found that, when speculators are introduced, the differences in valuation of the futures price between risk-neutral and risk-averse entities consisted of future marginal storage costs plus convenience yield on futures. Thus, convenience yield arises from heterogeneous agents. Our model can be generalized to include multiple firms that take multiple input and output commodities and multiple speculators. We also derived the optimal production and trading strategy for spot commodities and futures, and we define and prove the existence of the equilibrium for this economy using additional assumptions.