For physical commodities the fair value is not always linked to the expected market prices, as the concept of fair value is based on arbitrage alone. Arbitrage may be impossible in some cases.
If the futures price trades above fair value
-> sell a futures contract
-> borrow money and purchase the equivalent basket of stocks
-> receive the dividend payments until the expiry of the futures contract
-> receive the fees for renting out the stock to short sellers
-> deliver the stocks at expiry of the futures contract
and you would keep a small profit. In case that the futures price trades below fair value, you would purchase a futures contracts and sell the underlying stock basket short, which is more difficult.
This shows that arbitrage is not that easy, as you would need to sell short the 500 underlying stocks of the S&P500 to benefit from a situation where the futures contract ES is undervalued.
Physical Commodities (Crude Oil):
The concept of fair value cannot easily be applied to physical commodities. Arbitrage is comparatively easy, if crude oil futures trade above fair value. In that case you could
- sell a futures contract
- borrow money and purchase the physical oil
- store that physical oil in Cushing Oklahoma
- deliver that oil in fulfillment of the futures contract at expiry
Although this looks easy, it is not. You would need to know the spot price for oil at Cushing, have an idea about the fees to rent storage space. At least it would come close a risk free arbitrage
The reverse operation however is more difficult. Consider that the oil futures trade below fair value. In that case you would
- buy a futures contract
- sell physical oil and put the proceeds into bank account
- await delivery at expiry of the futures contract
Unlike stocks, you cannot easily sell physical oil short on the spot market. To do so you would need to borrow oil from somebody else. This basically limits the reverse arbitrage to market participants who hold physical stocks for their operational requirements, or who hold reserve stocks in different places such that they can be swapped.
In case of a physical shortage, there is no spare oil that can be sold. Unlike for financial futures, the reverse arbitrage becomes impossible, when the physical oil is exhausted. Futures can trade far below a calculated fair value. The market is then said to be in backwardation.
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