Convenience yield

A convenience yield is an implied return on holding inventories. It is an adjustment to the cost of carry in the non-arbitrage pricing formula for forward prices in markets with trading constraints.

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

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

However, this relationship does not hold in most commodity markets, partly because of the inability of investors and speculators to short the underlying asset, ${\displaystyle S_{t}}$. Instead, there is a correction to the forward pricing formula given by the convenience yield ${\displaystyle c}$. Hence

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

This makes it possible for backwardation to be observable.