Describe an arbitrage strategy to take advantage of this mispricing. When storin

Question

Describe an arbitrage strategy to take advantage of this mispricing.

When storing corn there is spoilage, i.e. the amount of usable corn shrinks over time. Assume that corn spoils continuously at rate of 2% per month. Also, assume that corn storage carries fixed (upfront) costs of $0.20 per bushel per month. You're given that today's price of corn is $10 per bushel, interest rate is 6% annualized, continuously compounded, and the corn forward price for delivery in 2 months is F = 10.25. Describe an arbitrage strategy to take advantage of this mispricing.

Explanation / Answer

Spot Price per Bushel = $10

2 month forward rate per bushel = $10.25

Annual interest rate = 6%

If someone can take loan of $10 from bank and buy 1 bushel of corn

Then total payment he has to make after 2 month at continuous compounding is calculated below:

Corn Spoil per month = 2%

So total corn Spoil = $10 × 2%

                                  = $0.20

Storage carry cost = $0.20

So total payment for 2 month of corn = $10.10 + $0.20 +$0.20

                                                                    = $10.50

Forward rate = $10.25

Arbitrage profit = $10.50 - $10.25

                             = $0.25

So one can get arbitrage profit of $0.25 if he buy forward contract instead of Buy corn as physical.

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