Convenience yield

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A convenience yield is an implied return on holding inventories.[1] It is an adjustment to the cost of carry in the non-arbitrage pricing formula for forward prices in markets with trading constraints.

Let be the forward price 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 to be observable.


A trader has observed that the price of 6-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 6-month loan () is 3.5% per annum, and storage cost for gold is negligible (0%). Since we know we have the relation:

What is the convenience yield implied by the futures price?

From the formula above, we isolate the convenience yield (), and we obtain:

(per annum, not compounded)


And the convenience yield would therefore be:

(per annum, continuously compounded)

Why should a convenience yield exist?[edit]



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 of the asset should then be higher than the current spot price, . From the above formula, this only tells us that .


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


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