Convenience yield

A convenience yield is an implied return on holding inventories. It is the difference between the theoretically implied non-arbitrage forward price based on the current spot price and the cost of carry, and the actually observed forward price which is usually lower.

Let $F_{t,T}$ be the forward price of an asset with initial price $S_{t}$ and maturity $T$. Suppose that $r$ is the continuously compounded interest rate for one year. Then, the non-arbitrage pricing formula should be

$F_{t,T}=S_{t}\cdot e^{r(T-t)}$

If the forward price exceeded this amount, arbitrageurs would buy the commodity, store it, and deliver it in the future to fulfil the forward contract, thus making a riskless profit.

However, in most commodity markets, the forward price is lower than this implied price, partly because of the inability of investors and speculators to short the underlying asset. Instead, there is a correction to the forward pricing formula given by the convenience yield $c$. Hence

$F_{t,T}=S_{t}\cdot e^{(r-c)(T-t)}$