From the June 2014 issue of Futures Magazine • Subscribe!

Capturing aluminum’s embedded call option

Famous last words and epitaphs are an endless source of amusement and the sort of inspirational quotes various newsletter writers think you need before you are jolted awake by your morning coffee. While futures traders as a whole have been deficient in this department, may we suggest inscribing, “If you can store it profitably, do so” across the gates to the Tomb of the Unknown Trader.

The reason is simple and goes right back to the very basis of cash-and-carry arbitrage. If you can take a physical commodity, place it in storage and hedge it with a short futures position at a price sufficient to cover all of the physical and financial costs of storage, the worst that can happen to you is you will make a profit equivalent to the amount at which you sold the futures contract over full carrying costs. 

You can determine this return in advance by calculating the convenience yield implied in the forward curve of a futures market. This payment often is referred to as the convenience yield of a market, described below in equation form where Month 1 and Month 2 are the first and second futures contracts. Storage is the physical cost of holding a commodity and “ert” is the capital cost of money tied up in inventory.

The “convenience” is the premium buyers in physical process industries are willing to pay to keep available inventories on-hand; alternatively, it is the discount at which risk-averse sellers are willing to accept when they sell futures to hedge their production.


A market in backwardation, also known as an inverse depending on the industry, always has a positive convenience yield; a market in a true contango has a negative convenience yield; and a market at full carry has a convenience yield of zero. We should expect inventories to decline in backwardated markets and to rise in contango markets because storage is unprofitable in the former and profitable in the latter.

If the worst that can happen to you in a storage situation is a return equivalent to the convenience yield, the best is an opportunity to deliver the commodity in storage to a buyer at a premium to the futures price prevailing at the time of sale. As the commodity was placed in storage at a discount to the futures contract, a sale at a price greater than the futures can represent a gain, one whose bounds are defined by an anxious buyer of the spot commodity who may need it to prevent a shutdown of a processing unit. This realization of the premium is the embedded call and will be illustrated here in the case of the aluminum market.

A snapshot of the London Metals Exchange’s aluminum futures market from March 24, 2014, indicates the upward-sloping forward curve was not in contango as convenience yields were not negative (“No free lunch,” below). This was to be expected as markets abhor free arbitrage opportunities. 

However, the spot price gains required for the trade to break even are quite low and might invite a speculative trader to take the gamble on a spot market premium for aluminum materializing.

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