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Pricing of commodity futures contracts

Commodity investments often involve the use of futures contracts in which the long position (buyer) receives the commodity or its cash equivalent based on the expiration spot price, from the short position (seller) and pays the settlement price. The value of a contract to the long position increases with an increase in the price of the underlying.

Futures contracts are often closed by entering into an offsetting contract i.e. long takes a short position and vice versa. If a contract is outstanding at expiration, it is settled through cash. Futures contracts are marked to market daily and any gains and losses are credited/debited to margin accounts maintained by each party with the clearinghouse.

Futures price can be given by the following equation:

\[ Futures\ Price = Spot\ Price × (1 + r) + Storage – Convenience\ Yield \]

Where r is the short-term risk-free interest rate. Futures price increases due to storage costs because a long position in a futures contract can avoid these costs, hence it must pay a higher price, otherwise, an arbitrage opportunity would exist. Similarly, convenience yield is the value that a commodity-holder obtains from its possession, but a future-holder does not. Hence, it causes a decrease in the futures price.

Contango vs backwardation

When futures prices are higher than spot prices mostly when convenience yield is zero or very low, the commodity forward curve is upward sloping and the situation is called contango.

When futures prices are lower than spot prices, which is the case when convenience yield is high, it is called backwardation.

Sources of return on commodities futures contracts

Return on a futures contract has three sources of return: roll yield, collateral yield and changes in spot prices.

Roll yield

Roll yield is the return that corresponds to the difference between the spot price at which a futures contract converges and the futures price dictated by the futures contract. It is positive when the market is in backwardation i.e. when forward prices are lower than spot prices. This movement is referred to as the theory of storage.

Collateral yield

Collateral yield is the return earned on any collateral put up by the investor to cover his futures position. Changes in spot prices refer to changes in current prices.

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