Question

Suppose our underlying is a stock XYZ. Today (t=0), XYZ is priced at $1,094. The storage and insurance cost is $10, paid in advance. The forward contract uses XYZ as the underlying, which will expire in one year from today. The interest rate is 0.04. The forward price at today (t=0) is $1,440.  
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

Forward Price = Spot Price*(1+Rate)^time + Cost of storage*(1+Rate)^time

Since the storage cost is paid in advance, therefore, the future value factor or rate and time wil be same for spot price and storage price calculation.

Forward Price = 1094*(1.04) + 10*(1.04) = 1,137.76 + 10.40 = $1,148.16

The forward price should be $1,148.16, However it is quoted as $1,440 at t0. It means the forward price is overvalued.

At time 0

You should sell in forward market and purhcase is stock market.

You should purchase the stock from market by borrowing amount equal to $1,094 + storage cost of $10 at an interest rate of 0.04. The total amount borrowed will be $1104.

Simultaneously, short a forward contract for $1,440.

At maturity

Pay the bank the amount borrowed including interest = 1104*1.04 = -1,148.16

Sell the stock in the market at contracted forward price(irrespective of market price) = $1,440

Arbitrage Profit = 1440 - 1148.16 = $291.84

If you have any doubt, ask me in the comment section please.