Convenience yield
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A convenience yield is an adjustment to the cost of carry in the non-arbitrage pricing formula for forward prices in markets with trading constraints.
Let Ft,T be the forward price of an asset with initial price St and maturity T. Suppose that r is the continuously compounded interest rate for one year. Then, the non-arbitrage pricing formula should be
Ft,T = Ster(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, St. Instead, there is a correction to the forward pricing formula given by the convenience yield c. Hence
Ft,T = Ste(r − c)(T − t).
This makes it possible for backwardation to be observable.
[edit] The theory of storage
Why should a convenience yield exist? One of the main reasons appears to be due to availability of stocks and inventories of the commodity in question. Everyone who owns inventory has the choice between consumption today versus investment in 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.
