Question

Suppose our underlying is a stock XYZ. Today (t=0), XYZ is priced at $1,013. The storage and insurance cost is $19, paid in advance. The forward contract uses XYZ as the underlying, which will expire in one year from today. The interest rate is 0.042. The forward price at today (t=0) is $1,481.  
What is the arbitrage profit that you can make today based on cost-of-carry model, if you are only allowed to either long or short one forward contract (i.e. do not assume the arbitrage profit is unlimited in this particular case)?

Answer 1

Step 1: Calculation of intrinsic value of forward contract

Intrinsic value of forward contract = (Spot price + Storage and insurance cost) * (1 + Interest rate)

= ($1,013 + $19) * (1 + 0.042)

= $1,075.344

Actual forward price = $1,481

Actual forward price is more than its intrinsic value; therefore, it is an over-valued forward contract.

Step 2: Calculation of arbitrage profit

Arbitrage profit is the difference of acutal forward price and intrinsic value of forward price.

Arbitrage profit = $1,481 - $1,075.344 = $405.656