Question

Suppose the spot price of a bushel of wheat is $2.00, the annual storage cost is $0.30 per/bushel, the risk‐free rate is 8%, and the costs of transporting wheat from the destination point specified on the futures contract to a local grain elevator, or vice versa, is $0.01/bu.

a. Use the cost‐of‐carry model to determine the equilibrium price of a September wheat futures contract (expiration of T = 0.25).

b. Explain the arbitrage strategy an arbitrageur would pursue if the September wheat contract is trading at $2.16/bu.

Answer 1

1.

Futures price refers to the price of financial or consumption asset which is computed as taking base of the spot price of such asset as well as taking into account of the other costs. Future price shall be computed by taking interest rate into account for the maturity period given in the case. If the computed future price is not equal to the actual price in the market then there is arbitrage opportunity available in the market.

Following is the formula for computation of futures price as follows:

Futures Price= (S₀+Storage Costs+Transportation Costs)*(1+r*0.25)

= ($2+($0.30*0.25)+$0.01)*(1+0.08*0.25)

= (2.085)*(1+0.02)

= $2.1267 per bushel

Thus the futures price has been computed above as $2.1267. But the actual price in the market is $2.16 per bushel which shows that there is arbitrage opportunity which needs to be exploited.

2. In the given case, actual price is $2.16 whereas computed price is $2.1267 which shows that future price of wheat is overvalued in the market. In order to exploit the opportunity, a strategy should be framed so that risk-less profit could be made out of it.

Following shall be the strategy to make the risk-less profit:

-Long the wheat in spot market at $2.00 per bushel

- Short futures contract of wheat at $2.16 per bushel

- At Maturity of contract, sell wheat in spot market

-Long wheat futures contract to cancel out the short futures position

Risk Less profit would be =$2.16-$2.1267

=$0.0333 per bushel

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