When storing corn there is spoilage, i.e. the amount of usable corn shrinks over
ID: 3225432 • Letter: W
Question
When storing corn there is spoilage, i.e. the amount of usable corn shrinks over time. Assume that corn spoils at an annualized, continuously compounded rate of 4%. Also, assume that corn storage carries fixed (upfront) costs of $0.50 per bushel per month. You are given that today's price of corn is $10 per bushel, interest rate is 2% annualized, continuously compounded, and the corn forward price for delivery in 2 months is F = 12. Describe an arbitrage strategy to take advantage of this mispricing.Explanation / Answer
Recall that 1 forward entitles the owner to exchange 1 bushel of corn atTforFdollars. In order to have 1 bushel atT, one needs to buy more than 1 bushel today, to accountfor intermediate spoilage.
given risk free rate = 2%
spoilage rate =4%
upfront cost =0.50
forward price = spot price * e^ (risk free rate + spoilage rate )*(2/12) +upfrontstorage cost
=10 *e^(2%/12)+4%)*(2/12)+0.50
= 10.26175
since forward is over priced sell forward @10.26
borrow 10 @ 2%
buy corn @ 10per bushel
at settlement after 2 months
deliver corn @ 10.26 under forward contract
loan repay amount =10*(1+2%)^(2/12)
=10.1157
profit =10.2675-10.1157=0.1518
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