Do Inventories Really Yield a Convenience? An Empirical Analysis of the Risk-Adjusted Spread

This paper considers four competing propositions to explain the convex relationship between inventories and the risk-adjusted spread called the 'Working curve': the convenience yield, the risk premium, data aggregation and the imbedded options value inherent to a futures contract. We use 70 years of weekly data from two different periods, 1/1885 to 12/1935 and 1/1985 to 12/2005, and we study contracts for storable agricultural commodities, namely wheat, corn and oats. The historical data are particularly interesting in this respect because they allow us to test quality aggregation issues, the role of location, and the potential impact of the imbedded options. The convenience yield hypothesis emerges as having the best explanatory power for the 'Working curve'. Although some of the other hypotheses predict a relationship between inventories and the risk-adjusted spread to some degree, the explanatory power is weak at best. For instance, the risk premium is often related to initial inventory levels but the result is not consistent across commodities and maturity months, the relationship is weak, and it does not subsume the strong negative-sloping/convex link with inventories that is present in the risk-adjusted spread. Similarly, we confirm empirically that data aggregation can indeed lead to a 'Working curve' even if the underlying disaggregated qualities show no such curve. Still, we also find a direct yield/inventory relation for the majority of disaggregated qualities, thus undermining the data aggregation hypothesis as the sole or major explanation. Finally, we show that also the imbedded option value is unlikely to explain the relationship between the risk-adjusted spread and inventories.