A convenience yield is an implied return on holding inventories.
It is an adjustment to the
cost of carry
The cost of carry or carrying charge is the cost of holding a security or a physical commodity over a period of time. The carrying charge includes insurance, storage and interest on the invested funds as well as other incidental costs. In intere ...
in the non-
arbitrage pricing formula for forward prices in markets with trading constraints.
Let
be the
forward price The forward price (or sometimes forward rate) is the agreed upon price of an asset in a forward contract. Using the rational pricing assumption, for a forward contract on an underlying asset that is tradeable, the forward price can be expressed in t ...
of an asset with initial price
and maturity
. Suppose that
is the continuously compounded interest rate for one year. Then, the non-arbitrage pricing formula should be
However, this relationship does not hold in most commodity markets, 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
. Hence
This makes it possible for
backwardation
Normal backwardation, also sometimes called backwardation, is the market condition where the price of a commodity's forward or futures contract is trading below the ''expected'' spot price at contract maturity. The resulting futures or forward ...
to be observable.
Example
A trader has observed that the price of six-month (
) gold futures price (F) is $1,300 per troy ounce, whereas the spot price (S) is $1,371 per troy ounce. The (not compounded) borrowing rate for a six-month loan (
) is 3.5% per annum, and storage cost for gold is negligible (0%). Since we know we have the relation: