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Futures on Consumption Assets

  • F0 ≤ S0 e(r+u)T
    • Where u is the storage cost per unit time as a percent of the asset value
  • Alternatively,  F0 ≤ (S0 + U )erT
    • Where U is the present value of the storage costs

Example

The current spot price for cotton is $0.325 per pound. The annual risk-free rate is 3.0%, and the cost to store and insure cotton is $0.002 per pound per month. A 3 month futures contract for cotton is trading at $0.3368 per pound. Is there an arbitrage opportunity available, and if so, how should an investor take advantage of it?
 

Solution

The Forward price = 0.325e0.03*0.25 + (0.002+ 0.002*1.0025+ 0.002*1.0025^2) = 0.3335; Yes; the investor should sell the futures contract, borrow at the risk-free rate, and buy the spot asset.
 



 

Example

The spot rate for a commodity is $19. The annual lease rate for the commodity is 5%. The appropriate continuously compounding annual risk-free rate is 6.5%. What is the 3-month commodity forward price?
 

Solution

 





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