Why should a convenience yield exist?

Users of a consumption asset may obtain a benefit from physically holding the asset (as inventory ) prior to T (maturity) which is not obtained from the futures contract. These benefits include the ability to profit from temporary shortages, and the ability to keep a production process running.

One of the main reasons that it appears is due to availability of stocks and inventories of the commodity in question. Everyone who owns inventory has the choice between consumption today versus investment for the future. A rational investor will choose the outcome that is best.

When inventories are high, this suggests an expected relatively low scarcity of the commodity today versus some time in the future. Otherwise, the investor would not perceive that there is any benefit of holding onto inventory and therefore sell his stocks. Hence, expected future prices should be higher than they currently are. Futures or forward prices Ft,T of the asset should then be higher than the current spot price, St. From the above formula, this only tells us that r − c > 0.

The interesting line of reasoning comes when inventories are low. When inventories are low, we expect that scarcity now is greater than in the future. Unlike the previous case, the investor can not buy inventory to make up for demand today. In a sense, the investor wants to borrow inventory from the future but is unable. Therefore, we expect future prices to be lower than today and hence that Ft,T < St. This implies that r − c < 0.

Consequently, the convenience yield is inversely related to inventory levels.